As an example, take a look at the input files allene_e.inp and allene_b.inp with common settings
in the include files allene_common1.inc and
allene_common2.inc.
These examples are also listed in the examples section below.
The order and placement of the keywords within a section is usually arbitrary. Exceptions are described below.
rd sin 36 3.800 5.60This input format is used in the PRIMITIVEBASISSECTION and, similarly, in the INIT_WFSECTION. In the operatorfile (*.op) (see Hamiltonians) there may appear functions with arguments. Such a construct, as e.g.
CAP_rd = CAP [ 5.0 0.357 3 ]may appear in the OPERATORSECTION of the inputfile when 'alterlabels/endalterlabels' is used. Note that these latter inputs are not freeformat, the order of the arguments matters! Moreover, the fixedformat inputs must have a line for their own; they must not be followed by another keyword.
Keyword  Description  Conversion factor 

au  atomic units  1 (may be omitted) 
mH  milli Hartree  1000 
ev  electron volts  27.21138386 
mev  milli electron volts  27211.38386 
cm1  wave number cm^1  2.1947463137d+5 
kcal/mol  kcal/mol  627.503 
kJ/mol  kJoule/mol  2.6255d+3 
Kelvin  Kelvin  3.15777d+5 
nmwl  wavelength in nanometer  10^{7}/cm1 
aJ  atto Joule (10^{18}J)  1.602177d1*ev 
invev  (electron volts)^1  0.036749325398 
debye  unit of electrical dipole moment  1 / 0.39343 
AMU  atomic mass unit  1 / 1822.88848325 
pmass  mass of proton  1 / 1836.15267247 
Hmass  mass of Hydrogen atom  1 / 1837.15264409 
Dmass  mass of Deuterium atom  1 / 3671.482934845 
Angst  Angstroem  0.52917720859 
pm  picometer  52.917720859 
nm  nanometer  0.052917720859 
deg  degree  180.0/pi 
Angst1  Angstroem^1  1/Angst 
pm1  picometer^1  1/pm 
nm1  nanometer^1  1/nm 
eV*AMU  sqrt(2mE)  
fs  femtosecond  1/41.34137333656 = 0.02418884326505 
ps  picosecond  1/41341.37333656 = 2.418884326505d5 
invfs  femtosecond^1  41.34137333656 
The input sections reflect the structure of the program. The
RUNSECTION defines what sort of calculation is desired.
Depending on what is requested here the remaining sections
provide the required information. The various sections are listed
below. There is no predefined order for the sections.
XXX  Description 

RUN  Whether propagation, relaxation, or diagonalisation, whether to generate or read DVR information, propagation and outputtimes, etc. 
PRIMITIVEBASIS  Definition of primitive basis, e.g. DVR / FFT. Note: PBASIS is a short form for PRIMITIVEBASIS . 
SPFBASIS  Definition of the singleparticle function basis, e.g. whether to combine any degrees of freedom, how to treat an electronic degree of freedom, how many functions etc. Note: SBASIS is a short form for SPFBASIS . 
SPDOBASIS  This is a special feature of density operators of type I. The section corresponds to the SPFBASIS section. It accounts for the special structure of this type of density operators. 
OPERATOR  Which operator to be used, any parameter changes to be made etc. 
INIT_WF  How to generate the initial wavefunction. 
INTEGRATOR  Which integrator to be used, and with what parameters. 
Below are tables of keywords for each input section. The
number and type of arguments is specified. The type is S for
character string, R for real number, and I for integer. e.g.
keyword = S, R
indicates that the keyword takes two arguments, the first is a
string, the second a real number. Default values for keywords and
arguments are also listed.
Keywords defining how output files will be treated  

name = S  The name of the calculation. A directory with name S is required in which files related to the calculation, unless otherwise explicitely stated, will be written.  
overwrite  Any files already in namedirectory will be
overwritten. If this keyword is not given, and files already exist in namedirectory, calculation will stop without these files being overwritten. It is recommended not to set overwrite but rather to use the option w . 

title  If the keyword title appears in one line of the runsection, then the next line is supposed to contain a headline title of the run. This line will be written to output, timing and log files. Note the title line will be read regardless of special characters like '#' or '!' . Alternatively, when an equal sign, = , follows the keyword title, then everything that follows, from the equal sign till the end of the line, is regarded as title. 
The following keywords define the method used to describe the system  

Keyword  Description 
wavefunction  The system will be described by a wavefunction (default) 
density1  The system will be described by a density operator, using the type I formalism 
density2  The system will be described by a density operator, using the type II formalism 
The following keywords define the calculation to be made  

Keyword  Level  Description 
gendvr  1  A DVR file will be generated. 
genoper  2  An operator file will be generated. 
genpes  2  A special operator file, called pes, will be generated, to be used by showsys to plot the PES. (See below). 
gengmat = I1,I2  2  A special operator file, called pes, will be generated, to be used by showsys to plot the (I1,I2) element of the Gmatrix of the kinetic energy. (See below). 
geninwf  3  An initial wavefunction will be generated. 
propagation  4  Propagation in real time. 
relaxation  4  The propagation will be in imaginary time i.e. the wavepacket will be relaxed to the ground state. 
relaxation = I(,S1(,S2(,S3))) relaxation = S(,S1(,S2(,S3))) 
4  Improved relaxation. Requires CMF integration scheme. If an integer I is specified, the Ith eigenstate will be computed (I < 900). If I is replaced by the string follow then the eigenstate closest to the previous WF is computed. The strings full and ortho may be given as second or third arguments. If the Davidson integrator, DAV, is used, the inputs relaxation= I, relaxation=follow or relaxation=lock may be used. The strings full , quad , olsen , backrotate , quadphi , and cn (where n is an integer), may be given as additional arguments. See remarks below. 
continuation  4  A continuation of the run in the namedirectory will be performed. 
diagonalisation = I  4  The Hamiltonian will be diagonalised using a Lanczos algorithm with I iterations. The SPFBASISSECTION and the INTEGRATORSECTION are ignored for a (Lanczos) diagonalisation run. The WF is expanded in exact format. 
There are 4 levels of calculation types, reflecting the four
stages of a calculation. Only one runtype keyword of a
particular level is allowed. All lower level keywords are
automatically included. Thus
propagation
or
gendvr genoper geninwf propagation
are equivalent.
When relaxation=I is given, the Ith eigenstate
(counting from 0) is computed by taking the Ith eigenstate
(Avector) of a Lanczos matrix, rather than propagating the
Avector in imaginary time. (The singleparticle functions are
still propagated in imaginary time.) This requires, that one uses
the CMF integrator in the fix or varphi mode and
employs the SIL integrator for the Avector. (NB: The keyword
CMF is interpreted as CMF/varphi when the runtype
is improved relaxation. Otherwise CMF is always
interpreted as CMF/var, see INTEGRATORSECTION). It also requires, that the
Hamiltonian is hermitian such that the SILintegrator and not the
ArnoldiLanczos (CSIL) integrator is taken. If I is replaced by
the string follow then the eigenvector with the largest
overlap with the restart vector is computed. (The restart WF may
be generated by build or taken from a file. See INIT_WFSECTION).
The size of the Lanczos matrix used depends on the SIL order and
accuracy parameters. The Lanczos iteration is stopped when the
SIL order is reached or when the estimated error of the Lanczos
eigenvalue (in milli Hartree) is smaller than the SIL accuracy
parameter. When the keyword full is given, the very first
Lanczos space is build up to maximal order, irrespectively of the
accuracy. This feature is useful to ensure, that one starts with
an appropriate approximation of a desired excited state. When the
keyword ortho is given, a full reorthonormalisation of
the Lanczos vectors (or Krylov vectors) is performed. In general
it is recommended to use ortho.
The keyword ortho must not be given when the Davidson
integrator DAV is used.
When the chosen integrator mode is CMF/varphi (or just
CMF ), then the output starts at t=tinittpsi. The initial
wavefunction is reported at this time. At t=tinit (i.e. usually
at t=0) we report the wavefunction obtained after diagonalising
the Hamiltonian in the basis of the singleparticle functions
(without having relaxed these functions). The next steps include
first a relaxation of the singleparticle functions followed by a
(Lanczos) diagonalisation of the Hamiltonian.
The calculation stops, when the final relaxation time is reached
or when the Avector changes less than the SILaccuracy. The
program then stops with the message stop by internal
check. Note, that "relaxation" to exited states may require
a rather large Lanczos order. See the steps file and in
particular the rlx_info file for details on the
computation.
When the calculation starts converging to the desired state but
after a few iterations jumps to another state, then the numbers
of singleparticle functions are too small or the chosen
accuracies are to low. Increase the accuracy of CMF/varphi
(or decrease the step size of CMF/fix). It may also be
necessary to increase the Lanczos accuracy and/or order. Inspect
the rlx_info file to see what Lanczos orders are actually
taken. Also inspect the update file. If a "*" appears at
the beginning of a line, then the corresponding update time was
too large.
The inputs relaxation and relaxation=0 both
generate the groundstate wavefunction. However, different
algorithms are used and the latter calculation will in general be
considerably faster. NB: Only the simple relaxation works for
density operators, relaxation=I will not work for density
operators.
For an example see the input files co2_gs.inp and co2_asym.inp which generate the
ground state and the asymmetric stretch excited state,
respectively. See also the User's Guide, section 3.4 .
The recently introduced Davidson "integrator" DAV is much more powerful for improved relaxation than the SIL. For DAV one of the three inputs: relaxation= I or relaxation=follow or relaxation=lock may be used. For the first input, the program seeks the groundstate (I=0) or for the Ith excited state. However, the program takes the Ith state of the first diagonalisation, which may not be the Ith state of the Hamiltonian. With the option full the program tries to converge as many states as it can within the limited space supplied by the "integrator". full thus makes the counting safer, but the computation more costly. With follow the Davidson diagonalisation takes that eigenvector which is closest to the one of the previous diagonalisation. With lock the Davidson diagonalisation takes that eigenvector which is closest to the initial WF as defined in the Init_WFSection. lock is hence the safer choice for finding excited states, but it is numerically more demanding than follow. lock requires that the keyword cross is given in the RunSection.
There are three Davidsonroutines implemented: DAV, RDAV, and
CDAV. (See INTEGRATORSECTION). The RDAV
routine allows to additionally use the keywords quad,
olsen, backrotate, quadphi, and cn,
(where n denotes an integer, e.g. c6) as arguments to
relaxation .
The keyword quad lets the program switch to use a
quadratic variational principle (i.e. (HE)**2 is diagonalised
within the space of Davidsonvectors rather than H).
With the keyword olsen the program applies the Olsen
correction to the residual Davidson vector. This is only useful
when a preconditioner is used. (Keyword precon).
The keyword backrotate lets the program rotate the SPFs
after relaxation, such that they have maximal overlap with the
orbitals prior to the orbital relaxation step. This sometimes
improves the overlap with the previous Avector.
The keyword quadphi lets the program use a different
propagation algorithm for orbital relaxation (experimental).
The keyword cn lets the program perform n orbital
relaxation steps, before a new diagonalisation step is
done.
The file rlx_info contains a lot of information on the relaxation process. If DAV / RDAV / CDAV is employed, use the script rdrlx to read it. With the aid of the keyword rlxunit one may set the energyunit for the output to the rlx_info file. One also may apply an energyshift (e.g. subtract the groundstate energy). See the table Keywords associated with a propagation or relaxation calculation below.
Keywords augmenting the calculation type  

exact  A numerically exact wavepacket calculation will be made. 
The exact keyword can be added to any runtype
keyword. For example,
propagation exact
will result in a numerically exact wavepacket propagation (i.e.
the wavefunction will be represented in the full product
primitive basis). Similarly,
geninwf exact
will set up a wavepacket for a numerically exact calculation.
The following keywords define calculations that generate files to help the analysis of calculations.  

Keyword  Level  Description 
genoper=S  2  An operator file with the name S will be generated from the .op. This can be used together with the EXPECT program to calculate the time dependence of the expectation value of an operator. 
genpes  2  A pes file will be generated from the .op file. This file can be used together with the SHOWSYS program to plot the potential energy surface, or together with VMINMAX program to determine minima and maxima of the potential energy surface. 
gengmat = I1,I2  2  A pes file will be generated from the .op file, containing the (I1,I2) element of the Gmatrix defined by the kinetic energy part of the Hamiltonian. This file can be used together with the SHOWSYS program to plot a energy surface. This keyword, gengmat, is introduced for testing the kinetic energy operator for correctness. 
These keywords are equivalent to a runtype keyword of the level given.
Keywords defining how the readwrite files will be handled.  

readdvr = S  The DVR information will be taken from the DVR file in directory S.  
readoper = S  The operator information will be taken from the OPER file
in directory S. 

readinwf = S  The initial wavefunction will be taken from the RESTART file in directory S.  
deldvr  The DVR file will be deleted at the end of the calculation.  
deloper  The OPER file will be deleted at the end of the calculation. 
The tfinal keyword must be given. All other keywords are optional. The following default values are used.
Keyword  Default 

tinit  0.0 
tout  tfinaltinit 
tpsi  tout 
The following keywords define the data calculated and saved. If keywords are omitted, data will not be calculated.
Keywords defining outputdata files to be opened.  

Keyword  Description 
all  All the (optional) files discussed below will be opened. More precisely, a propagation/relatation run will open the files: auto, autoe, gridpop, output, pdensity, psi, speed, steps, stop, timing, and update. In a diagonalisation run, only the files output, timing, lanczvec, and eigvec are opened. 
auto = S (,S1) (,S2)  The autocorrelation function will be written to the file
auto. If S = twice, autocorrelation function is written twice in interval tout (only for CMF) . If S = once, autocorrelation function is written only once in interval tout. If S = no, no autofile will be opened. This only makes sense, if the keyword all was given previously. If S, S1, or S2 = error, the autoe file will be opened, which contains the autocorrelation function computed with the least important natural orbital omitted. This information is useful for estimating the error. If S, S1 or S2 = order1, the file auto1 will be opened. If S, S1, or S2 = order2, the files auto1 and auto2 will be opened. These files contain the first and second order autocorrelation function, respectively, needed in the filterdiagonalisation method. Note that in a multipacket run, i.e. when packets > 1, the files auto, auto1, and auto2 contain cross rather than autocorrelation functions. 
auto  Synonymous for auto = once. 
cross (= S (,I))  A crosscorrelation
function will be calculated and written to the file "cross".
The reference wavefunction will be taken from the "restart"
file residing in the directory named S. If S=name, the restart file will be taken from the current name directory, which means that the autocorrelation function will be calculated (but without the t/2trick). This is also the default (i.e. if no argument is given). If an integer I is given after the path S, then the crosscorrelation will be evaluated for the electronic state I only. 
ctrace = D  The trace tr(D rho) is written to the file ctrace in a density operator propagation. If no operator is given, D = s><t, where s=left_state and t=right_state (see Init_wfSection). 
eigvec  In a diagonalisation run, the eigenvectors of the tridiagonal Lanczos matrix are written to the eigvec file. 
expect = S (,S1, S2, ...)  The expectation value of the operator S,
<psi(t)Spsi(t)> / <psi(t)psi(t)>, is
evaluated and written to the file expectation. Up to maxham
operators may be specified. (If S=system then the expectation
value of the whole SystemHamiltonian is derived, i.e. the
total systemenergy.) The norm (not norm**2) of Psi is
additionally written to the expectation file. For density operators the expectation value is tr(H rho)/tr(rho). There may be more than one expect line. I.e expect = S, S1, S2 is equivalent to expect = S expect = S1 expect = S2 When the first argument to expect, S, is realonly , then only the real parts of the expectation values will be output to file expectation. 
expect1 = S (,S1, S2, ...)  Same as expect, except that the data is written to
the file expect1. This second expectation file is useful for
a better organisation of the data if several expectation
values are computed. One file may store real, the other
complex expectation values. Important Note: The expect1 keyword(s) must appear in the input file after the expect keyword(s). There must not be an expect1 keyword without a previous expect keyword. 
gridpop  The grid populations will be written to the file gridpop. Note: The grid populations of the different states will be summed. 
gridpop=el  The grid populations will be written to the file gridpop. The grid populations of the different states of a multiset run will be stored separately. 
lanczvec  In a diagonalisation run, the Lanczos vectors are written to the lanczvec file. 
orben  The orbital energies, i.e. the eigenvalues of the trace of the meanfield operators, are calculated and written to the orben file. Note: orben must be set, when the propagation is in energy orbitals (keyword energyorb, IntegratorSection) 
output  The output will be written to the file output rather than to the screen. (default). 
screen  The output will be written to the screen rather than to the file output. Alternatively to screen one may give the keyword nooutput. 
pdensity (=I1,I2,I3,I4)  The oneparticle density will be written to the file pdensity. If the pdensity keyword is followed by an equal sign and up to four integers, the oneparticle density will be output only for the specified (contracted) modes. 
psi = S (, S1 or R)  The wavefunction will be written to a file every tpsi fs.
If no arguments are given, it is written single precision to
the file psi. If S or S1 = single, the wavefunction will be written single precision. If S or S1 = double, the wavefunction will be written double precision. If S or S1 = natur, the wavefunction will be written as natural orbitals. This option is automatically taken if natural orbitals are propagated. If S = compact, the wavefunction is written in natural orbital representation and compact form using the cutoff R. If S or S1 = no, no psifile will be opened. This only makes sense, if the keyword all was given previously. 
psi  Synonymous for psi = single. 
speed  The CPUtime used within an output interval will be written to the file speed. (default). 
nospeed  The speed file is not opened. 
steps  Information on the integrator step sizes will be written to the file steps. 
stop  The file stop is created. It allows to stop the run in a controlled way by writing 'stop' or the desired stop time (realtime and/or CPUtime) to the stop file. (default). 
nostop  The stop file is not opened. 
timing  Program timing information will be written to the file timing. (default). 
notiming  The timing file is not opened. 
update  If the constantmeanfield integrator with adaptive step size is used, the update time for the meanfields is written to the file update. (default). 
noupdate  The update file is not opened. 
veigen  The eigenvectors and eigenvalues of a 1D operator, set up in the the INIT_WF section with the spf type eigenf, are written to the veigen file. 
quadpop  If set, the grid populations and state populations are calculated using rho^2 rather than rho. This keyword is needed, if a traceless density operator is propagated. Otherwise, all populations are zero. Only for Density Operators of Typ I. 
Keyword  Default 

auto  S = once 
cross  S = name 
psi  S = single 
psi = compact  R = 1.0d6 
Keyword  Description 

opname = S  The operator with name S.op will be used. 
oppath = S  The path S will be used to find the operator file. If oppath is not given, the program will first look in the startup directory and then the default operator path. 
closed  Density operators are propagated in a closed system, i.e. possible dissipative operators are ignored and the Hamiltonian is used only. This is the default. 
open  Density operators are propagated in an open system. 
projection  Modified equations of motion for the coefficients are
used if density operators of type II are propagated in an
open system. This ensures that the trace is conserved. To
switch off this feature use the key word
no_projection. Note: projection is the default. 
alterparameters ..... endalterparameters 
The lines between the keywords define parameters to be used in building the Hamiltonian, using the same format as in the PARAMETERSECTION of the .op file. 
parfile = S  The parameters to be used in building the Hamiltonian are
listed in the file S. The parameters are defined using the
same format as in the PARAMETERSECTION of the .op file.
The file must end with the line endparameterfile 
alterlabels ..... endalterlabels 
The lines between the keywords redefine labels specified in the LABELSSECTION of the operator file opname.op 
v < R  Energy cutoff used for potential energy surface in exact calculations. All potential energy values greater than R are set to R. 
v > R  Energy cutoff used for potential energy surface in exact calculations. All potential energy values less than R are set to R. 
analytic_pes  If the operator contains a nonseparable potential this will not be stored explicitely on the primitive grid points, but in an analytic form which can be used to generate the potential onthefly at any point. This should be set if the CDVR method is to be used. 
cutoff = R, unit  All real diagonal Hamiltonian terms (except natpots) which are smaller than cutoff are removed. (Note, all nondiagonal Hamiltonian terms which are on all gridpoints smaller than 1.d12 au are removed as well). The default is cutoff=tiny (i.e. 1.d9 au). For an improved relaxation run it may be useful to set cutoff to a lower value. The value of cutoff and the number of Hamiltonian terms removed are protocoled in the op.log file. NB cutoff is not applied to natural potentials. Use natpotcut for those. 
natpotcut {V1,V2,...} = R, unit  The real constant R sets the threshold for removing
natpot terms. This feature may reduce the number of natpot
terms while only marginally reducing the quality of the
potfit potential. The labels V1, V2, ... are the
labels assigned to a natpot in a LabelsSection of the
operator file. The keyword natpotcut may appear
multiple times in the input file, if different thresholds for
different natural potentials are used. If no potential label
is given, i.e. natpotcut = R, unit (the equivalent
form: natpotcut {all} = R, unit is also possible),
the program will use the same threshold for all natural
potentials. The keyword unit denotes the MCTDH
units. If unit is not given, au is
assumed. Information on the removed natpot terms is given in
the op.log file. The default value for the threshold R is R = tiny (i.e, 1.0d9 au). I.e., even when the natpotcut keyword is not given, all terms which are smaller then 1.0d9 au will be removed. In fact, this holds for all operators, not only for natural potentials. Using an increased value for the natpotcut threshold (e.g. R=1.d6) may speed up the calculation, because several natpot terms have been removed. The accuracy of the potentials may decrease, but this effect is negligible, as long as R is sufficiently small. 
fast = V1,V2{n},...  An more efficient algorithm for H(natpot)*A operation is used. The Avector is premultiplied with several natpot terms and the results are stored for further use. (Hence fast requires slightly more memory). The labels V1, V2, ... are the labels assigned to a natpot in a LabelsSection of the operator file. The (optional) specification of an order n is possible by attaching this number in curly brackets ({}) to the label. n denotes the number of modes used for premultiplication. The larger n is, the larger will be the speedup. However, n is limited to min(4,nmode2), where nmode denotes the number of (combined) modes (or MCTDH particles). The n orders are optional, i.e. if no order for the current label is given, n=min(4,nmode2) will be used. If no potential label is given, i.e. only fast (or fast = all), the maximum order for all natpots will be set. Some information about using the "Fast" is written to op.log file. "Fast" works also for a multipackage but not for a multiset propagation and not for SMCTDH. 
If no OPERATORSECTION is included, the program looks for the operator information in the input file. This can be useful if a small model operator is studied. A full log of the operator is then automatically output.
The following lines define the singleparticle function basis to be used in a wave function calculation or a calculation employing density operators of type II. The input defines firstly how many degrees of freedom are contained within a mode. Secondly, the number of spfs are given; a list being needed for a multiset basis. The format is:
mode_label1 , mode_label2 , ... = nspf1 , nspf2 , ...where the degrees of freedom labelled mode_label1, mode_label2 etc. are contracted together in a single mode, and the number of singleparticle functions for this mode are nspf1 in the first set, nspf2 in the second set etc. More than one mode definition can be written on a line.
For example for a 3mode system, with labels X, Y and Z,
to define an spf basis of 3 functions per mode,
spfbasissection X = 3 Y = 3 Z = 3 endspfbasissectionor
spfbasissection X = 3 Y = 3 Z = 3 endspfbasisTo contract the degrees of freedom X and Y into a single mode,
spfbasis X, Y = 3 Z = 3 endspfbasissectionIf a multiset basis is used, then to have 3 functions in the first set and 2 in the second,
spfbasissection multiset X , Y = 3 , 2 Z = 3,2 endspfbasissection
Note: The electronic SPFBasis is not to be specified in the spfbasissection, as it is always complete. The electronic mode will always be the last mode in a singleset run.
If many electronic states are present, the definition of singleparticle functions for a mode can be continued on a second line by using a continuation mark %, e.g.
spfbasissection X = 5 , 5 , 5 , 5 , 6 , 10 , 5 , 2 , 2 , % 5 , 5 endspfbasissection
If for symmetry reasons one set of SPFs is always identical to another one, the latter set need not to be propagated numerically. In such a situation, e.g. H_{2}O in valence coordinates and for a symmetric initial state, one may tell the program not to propagate the second identical set of SPFs. This is done by specifying with the id keyword the mode to which the present mode is identical. E.g.:
spfbasissection R1 = 8 R2 = id,1 Theta = 9 endspfbasissectionMode 2 is now identified with mode 1 and the calculation is faster, because the propagation of mode 2 is skipped.
The following keywords, if given, define multistate or mutipacket runs. Note: A SPFBASISSECTION does not need to exist for an exact calculation, except if packets is specified.
Keyword  Description  Default 

multiset  If an electronic basis is defined it is treated using the multiset formalism, i.e. a set of singleparticle functions per state. If this keyword is not present, the singleset formalism is used.  not set 
packets = I  I independent wavepackets will be simultaneously propagated.  I = 1 
id,I  I denotes the modenumber (particlenumber) with which the present mode is to be identified. See the note above for the correct use of the id keyword.  not set 
The SPDOBASISSECTION is a special feature of a calculation using density operators of type I. It is organised almost as the SPFBASISSECTION. For a singleset calculation these sections are in fact identical. In a multiset calculation differences occur due to the special structure of density operators of type I.
The number of sets in a multiset calculation using a density operator of type I is the squared number of sets used in the corresponding calculation emplyoing a wave function or a density operator of type II. This can be seen in the following example:
If the SPFBASISSECTION reads (two sets for each DOF)
spfbasissection multiset X , Y = 3, 2 Z = 4, 2 endspfbasissection
the SPDOBASISSECTION may be chosen as (four sets for each DOF)
spdobasissection multiset X , Y = 2, 2, 2, 2 Z = 2, 2, 2, 2 endspdobasissection
The ordering is here as
n(1,1), n(1,2), n(1,3), ..., n(2,1), n(2,2), n(3,2),
...
where n(s,t) is the number of SPDOs for the pair of
states (s,t).
mode_label basis_type basis_size parameters
mode_label is an alphanumeric string (case sensitive)
labelling the degree of freedom.
basis_type must be one of the following:
Parameter  Description 

el  Electronic basis. 
elcont  Electronic basis including continuum states. 
HO  Harmonic oscillator (Hermite) DVR. 
rHO  Radial Harmonic oscillator (oddHermite) DVR. 
Leg  Rotator (Legendre) DVR. 
Leg/R  Rotator (Legendre) DVR for a restricted range on angles. 
Lagu1  Laguerre DVR for boundary condition x^{1/2}. 
Lagu2  Laguerre DVR for boundary condition x^{1}. 
Lagu3  Laguerre DVR for boundary condition x^{3/2}. 
Lagu4  Laguerre DVR for boundary condition x^{2}. 
sin  Sine (Chebyshev) DVR. 
FFT  Fast Fourier transform collocation. 
exp  Exponential DVR. Periodic boundary condition. 
cos  Cos DVR. "gerage" solutions with periodic boundary condition. 
sphFBR  Spherical harmonics FBR. 
KLeg  Extended Legendre DVR. 
K  Kquantum number appearing with KLegDVR. 
PLeg  TwoDimensional Legendre DVR. 
Extern  External DVR. 
basis_size is an integer specifying the primitive basis
size, e.g. grid points or vector elements etc. Note that for an
FFTrepresentation basis_size (i.e. gdim in the
program) must have a prime factor decomposition with only 2's,
3's and 5's but should have a decomposition with only 2's and 3's
for optimal performance, i. e. basis_size = 2^m * 3^n
where m and n are positive integers. Note also
that basis_size must be odd for the expDVR.
For a sphFBRrepresentation, basis_size is not required in
input. The number of basis functions is calculated by the program
itself, according to the type of basis (see parameter
description).
For a KDVR basis_size is not required in input. It will
be calculated from the kmin,kmax parameters given in this
section. NB: The basis_size is called gdim.
The parameters to be input depend on the basis type as follows:
Basis  Parameters  Parameter description 

Elcont  Nstates:  Total no. of electronic states. 
Elbnd:  No. of bound electronic states.  
HO  hoxeq:  Equilibrium position of harmonic oscillator basis functions. 
hofreq:  Frequency of harmonic oscillator basis functions.  
homass:  Mass of harmonic oscillator basis functions. If no mass is given, then the mass is set to 1.  
HO  S:  String S = xixf. This string serves as a switch between the two possible input formats. 
xi:  First grid point.  
xf:  Last grid point.  
rHO  hoxeq:  Equilibrium position of harmonic oscillator basis functions, which  because only the positive halfaxis is used  is the lefthand boundary of the wavefunction. 
hofreq:  Frequency of harmonic oscillator basis functions.  
homass:  Mass of harmonic oscillator basis functions. If no mass is given, then the mass is set to 1.  
rHO  S:  String S = xixf or S = x0xf. This string serves as a switch between the possible input formats. 
xi or x0:  First grid point, or left boundary (i.e. hoxeq).  
xf:  Last grid point.  
Leg  blz:  Magnetic rotational quantum number. Alternatively to a number one may input the string jbfXXX. blz will then be set to the value of the parameter jbfXXX. Here XXX stand for any characters. I.e. one may use jbf or jbf_1 etc. Note: jbfXXX must be defined in the parameter section of the inputfile or via an option on the command line. (alterparameter and operator file definitions come too late). 
string:  Controls whether symmetry to be used. all: no symmetry (use all l values, l=m, m+1,...,m+N1 ). odd: odd symmetry (i.e. l=odd ). even: even symmetry (i.e. l=even ). 

Leg/R  blz:  see Leg 
string:  see Leg  
theta1  Lowest value of theta (in rad) to be included in the restricted grid.  
theta2  Largest value of theta (in rad) to be included in the restricted grid.  
Lagu1  x0:  Sarting point of the radial interval (usually zero). 
b:  Length parameter. Chi_{n}(x) = 1/b * Sqrt((xx_{0})/n) * exp((xx_{0})/(2*b)) * L^{1}_{n1} ((xx_{0})/b)  
icut:  Cut parameter to avoid excessively large kinetic energy contributions. icut=0 leaves the second derivative matrix unmodified. See remarks below  
Lagu1  S:  String S = xixf. This string serves as a switch between the three possible input formats. 
xi:  First grid point.  
xf:  Last grid point.  
icut:  See icut above. See remarks below.  
Lagu1  S:  String S = x0xf. This string serves as a switch between the three possible input formats. 
x0:  Sarting point of the radial interval (usually zero).  
xf:  Last grid point.  
icut:  See icut above. See remarks below.  
Lagu2    Input identical to Lagu1 
Lagu3    Input identical to Lagu1 
Lagu4    Input identical to Lagu1 
sin  xi:  First grid point. 
xf:  Last grid point.  
string:  short , long (short is the default), and/or sdq , or spin . See note below.  
sin  string:  2pi or 2pi/m , where m is a positive
integer (its default is 1) denoting the multiplicity (e.g. of
the rotational axis). The wavefunction is assumed to be
periodic on the interval 2pi/m to 2pi/m. Because only ungerade (asymmetric) wavefunctions are computed, the grid is halved and only grid points for positive x appear. 
string:  sdq . If sdq is set, the symmetrized first derivative, (sin*d/dx+d/dx*sin)/2 is used rather than the simple first derivative.  
fft or exp  xi:  First grid point. 
xf:  Last grid point.  
string:  linear, periodic or speriodic (linear is the default).  
fft or exp  string:  2pi , s2pi , c2pi or
2pi/m , s2pi/m , c2pi/m , where
m is a positive integer (its default is 1) denoting the
multiplicity (e.g. of the rotational axis). The grid is
assumed to be periodic, ranging from 0 to 2pi/m. (See note
below). For an expDVR which follows PLeg, the input k= kmin,kmax may follow. The default is kmax=kmin=(N1)/2. (See note below,PLeg). 
exp (If combined with PLeg) 
k=kmin,kmax (optional) 
The range of magnetic rotational quantum number of the PLeg. If kmax is omited (k=kmin), the range [kmin,kmin] is chosen. Default is the full range [(gdim1)/2, (gdim1)/2] (or [jtot,jtot] if jtot is set). 
cos  xi:  First grid point. 
xf:  Last grid point.  
string:  short or long (short is default). See note below.  
cos  string:  2pi or 2pi/m , where m is a positive
integer (its default is 1) denoting the multiplicity (e.g. of
the rotational axis). The wavefunction is assumed to be
periodic on the interval 2pi/m to 2pi/m. Because only gerade (symmetric) wavefunctions are computed, the grid is halved and only grid points for positive x appear. 
sphFBR  jmax:  Maximum value of quantum number j of the spherical harmonics basis functions. Note: jmax replaces N, the number of basisfunctions/gridpoints. N is computed from the input. See log file. 
string:  nosym: no symmetry (uses all values of j below
jmax, j=0,1,...jmax). sym : symmetry (uses values of j of the same parity as jmax, i.e. jmaxj = even). 

thrshld:  Threshold for convergence when the FBR integrals are performed. This input is optional, default: thrshld=1.d10.  
j_off:  Offset value used when the FBR integrals are performed. The first iteration uses j_max + j_off quadrature points. This input is optional, default: j_off=6.  
phiFBR (Must follow sphFBR) 
mmax: (optional) 
Maximum value of quantum number m of the spherical harmonics basis functions. Uses only values of m, such as m < = mmax and m <= j. Default is mmax=jmax. 
mincr: (optional) 
Increment of m's, starting from mmax (must be given:
mmax mincr). Default is 1. 

KLeg  string:  Controls whether symmetry to be used. all: no symmetry (use all lvalues). odd: odd symmetry (i.e. l = odd). even: even symmetry (i.e. l = even). 
K (Must follow KLeg) 
kmin:  Minimum value of body fixed magnetic quantum number of basis functions. 
kmax:  Maximum value of body fixed magnetic quantum number of basis functions.  
dk: (optional)  Delta K. Increment in Kvalue. Default dk=1.  
PLeg  string:  Controls whether symmetry to be used. all: no symmetry (use all lvalues). odd: odd symmetry (i.e. l = odd). even: even symmetry (i.e. l = even). 
Extern  string:  Name of file containing grid points and DVR derivative matrices. The file may contain only grid points. Then the derivative matrices will be zeroed. (See remark below). 
string:  ascii: the file is read in ascii format
(default). binary: the file is read in binary format. 

unit:  The (optional) string unit is a length unit (e.g. angst, nm, pm, or deg) with which the input data is multiplied. 
Remarks on continuum electronic basis:
To define continuum electronic states two consecutive lines are required in the section. The first uses the elcont basis type to define the number of electronic states in the problem, while the second line defines the DVR used to discretise the continuum. Thus the linesel elcont 4 2 Elcont sin 101 0.0, ev 3.75, evdefine an electronic basis with 4 states, the first 2 of which are bound states while states 3 and 4 are coupled to a continuum. The continuum is then discretised using a sin DVR which sets 101 points between 0 and 3.75 eV. The singleparticle functions for the continuum are then set up as for a normal mode using, e.g. a set of gaussian functions for the el mode in the SBASISSECTION, e.g.
el gauss 1.0, ev 0.0 0.3, ev
Remarks on harmonic oscillator DVR:
The HODVR depends only on the product
hofreq*homass. If the homass entry is missing,
the program sets homass to 1. Alternatively, one may specify the
first and last gridpoint. The program then computes the
corresponding product hofreq*homass.
Example: The following lines are equivalent.
Y HO 32 0.00 0.10 1822.89 Y HO 32 0.00 2.721,eV 1822.89,au Y HO 32 0.00 0.1,au 1.0,AMU Y HO 32 0.00 21947.46,cm1 1.0,AMU Y HO 32 xixf 0.528 0.528
Remarks on Laguerre DVR:
The LaguaDVR is build from the basis functions:
phi(n,x) = Sqrt((n1)!/(n+a1)!) * x^(a/2) *
exp(x/2) * L(n1,a,x) ,
where a = 1,2,3 or 4 (Lagu1  Lagu4). Hence, the boundary
condition for x > 0 is phi(x) ~ x^(a/2). (With the aid of the
parameters x0 and b the coordinates may be shifted and scaled,
i.e. phi(x) < phi((xx0)/b)) ). The distribution of the grid
points is very uneven, being very dense for small x and widely
spaced for large x. The matrix of second derivatives may have
very large negative eigenvalues. These will slow down the
integrator. The integer parameter icut helps to fix this
problem. The matrix of second derivatives is diagonalized and the
first icut eigenvalues (these are the largest negative
eigenvalues) are replaced by the icut+1st one. The thus modified
eigenvalues and the eigenvectors are then used to build the
working matrix of second derivatives. Note that the FBR matrix
representation of { d^2/dx^2  c/x^2) } is analytically evaluated
( c = 1/4, 0, 3/4, 2 for a = 1, 2, 3, 4). After this matrix is
transformed to the DVR representation, the centrifugal term c/x^2
is removed by substraction. The width parameter b has to
be chosen carefully. Its optimal numerical value will depend on
N, the number of grid points. Alternatively, one may use
the input formats xixf (not recommended in general) or
x0xf. These formats compute b.
Remarks on sine DVR:
short: xi and xf denote, as
usual, the first and last grid point. short is default and need not to be given.
long : xi and xf denote the
boundaries of the sine basis functions (i.e. boundaries of the
'box') and not the first and last grid point.
Example: The following lines are equivalent.
x sin 19 1.00 19.0 short x sin 19 0.00 20.0 longFor the 2pi and sdq keywords see remarks on cosine DVR. (Note that cosDVR always uses sdq, whereas for sinDVR one must explicitly give the sdq keyword. Otherwise dq will be assumed.)
Remarks on cosine DVR:
The basis functions underlying the DVR are 1/sqrt(L),
(2/sqrt(L))*cos[(j*pi/L)*(xx_{0})]. The symmetrized
derivative, sdq = 0.5*( sin[(pi/L)*(xx_{0})] * d/dx +
d/dx * sin[(pi/L)*(xx_{0})] ) is used as first
derivative. Because only gerade (symmetric) wavefunctions are
computed, we consider only the interval
[x_{0},x_{0}+L], although the wavefunction is
periodic on the interval [x_{0}L,x_{0}+L]. xi
and xf are the first and last gridpoint, but when long is
given, the input is interpreted as x_{0} and
x_{0}+L.
Example: The following lines are equivalent.
x cos 36 2pi/2 x cos 36 0.00 3.1415926535897 long x sin 36 0.0436332313 3.097959422 short x sin 36 0.0436332313 3.097959422
Remarks on FFT and exponential DVR:
FFT and expDVR have an identical set of input
parameters (if expDVR is not combined with
PLegDVR). These two methods are in fact largely
equivalent and produce identical results (for same parameters).
The numeric, however, is different and the expDVR will be
faster for small grids whereas FFT is faster for long
grids. Around 30 grid points both methods are of similar speed.
The use of the interactionpicture is possible for
expDVR.
FFT and expDVR enforce periodic boundary
conditions, but they are often used for ordinary coordinates. A
set of keywords adapts the input to the various situations:
linear: xi and xf are the coordinates of first and the last point of the grid. The gridspacing is dx = (xfxi)/(N1). Due to the periodic boundary conditions the first grid point and the one following the last grid point are to be identified.
periodic: xi and xf are considered as identical due to the periodic boundary conditions. The gridspacing is dx = (xfxi)/N. The routine eingabe.f rescales xf > xfdx.
speriodic: xi and xf are considered as identical due to the periodic boundary conditions. The gridspacing is dx = (xfxi)/N. The grid points, however, are now placed symmetrically on the interval (xi,xf) and eingabe.f rescales xi > xi+dx/2, xf > xfdx/2.
2pi/mult or s2pi/mult or
c2pi/mult: The routine eingabe.f sets xi=0 and
xf=2*pi/mult and then performs according to the periodic
or speriodic keyword. For c2pi/mult the grid
is shifted such that xi=xf.
Example: The following sets of lines are equivalent.
x fft 32 0.00 3.0434179 linear x fft 32 0.00 3.1415927 periodic x fft 32 2pi/2 or x fft 32 0.0981748 6.1850105 linear x fft 32 0.00 6.2831853 speriodic x fft 32 s2pi or x fft 32 3.0434179 3.0434179 linear x fft 32 3.1415927 3.1415927 speriodic x fft 32 c2pi
Example:
For a system with two degrees of freedom, labeled X and Y, the following would define for X an FFT grid of 32 points from 2 to 2, and for Y a DVR basis of 32 harmonic oscillator functions generated with the given parameters. To show the use of the elkeyword we assume that there are three electronic states.
primitivebasissection el el 3 X FFT 32 2.00 2.00 linear Y HO 32 0.00 5.2,eV 1.00 endprimitivebasissection
Remarks on External DVR:
ExternDVR is an external DVR, where grid points and
DVR derivative matrices are read from a file. The file can be
read in ascii or binary format:
in ascii format (default):
do i=1,gdim read(unit,*) ort(g) enddo do i=1,gdim read(unit,*) (dif2mat(j,i),j=1,gdim) enddo do i=1,gdim read(unit,*) (dif1mat(j,i),j=1,gdim) enddo
do i=1,gdim read(unit) ort(g) enddo do i=1,gdim read(unit) (dif2mat(j,i),j=1,gdim) enddo do i=1,gdim read(unit) (dif1mat(j,i),j=1,gdim) enddo
where gdim is the basis_size. The file can have absolute or relative path. If file containes only grid points (for example in POTFIT program, when only grid points are used), the DVR matrices will be zeroed. If only second derivative matrix dif2mat is given, dif1mat will be zeroed.
Example:
x extern 30 x_data y extern 50 y_data binary z extern 42 z_data binary angst theta extern 23 theta_data deg
Remarks on KLeg, PLeg and sphFBR:
KLeg, PLeg and sphFBR all define 2D singleparticle functions, although the basis definition is for each degree of freedom individually. KLeg must hence be followed by K and PLeg by exp and sphFBR by phiFBR.
Example:
PRIMITIVEBASISSECTION alpha sphFBR 30 sym beta phiFBR 5 theta1 PLeg 31 even phi exp 15 2pi k=6,6 theta2 KLeg 31 even K_th K 5 5 endprimitivebasissectionThe exp line end with the keywords k=6,6. These are optional. Without this statement, K would span the full range from 7 to 7 (yielding 15 points). The restriction of the Krange is mainly for tests.
The KLeg/K, PLeg/exp and sphFBR/phiFB combinations generate modeoperators. Hence the DOFs (theta2, K_th), (theta1,phi), and (alpha,beta) must be combined with each other and must not be combined with any other mode. This excludes the use of these DVR's when the WF is expanded in exact format, because the exact format combines all modes into one particle. Note that the exact format is used by a diagonalisation run.
The above restriction has been relaxed somewhat in recent versions of MCTDH. Since version 8.3.13, you can combine several KLeg/K into one mode, even along with other DOFs. This makes it also possible to use KLegs in exact calculations. However, since this feature is rather new, you are advised to check your results carefully if you use it.
Keyword  Description 

file = S1 (,S2,S3)  The initial wavefunction will be read from the restart
file in directory S1. If S1 is not specified, the restart
file will be taken from the namedirectory. For a density
operator II propagation, the restart file may contain a
wavefunction. It will then automatically be transformed to a
purestate density operator of type II. S2 = orthopsi : The singleparticle functions of the initial wavefunction are transformed to natural orbitals, Schmidtorthogonalised and transformed back after being read from file (this is the default). S2 = noorthopsi : The initial wavefunction is not Schmidtorthogonalised after being read. S2 = realpsi : The real part of the wavefunction will be Schmidtorthogonalised as in the orthopsicase and used for the initial wavefunction. S3 = ignore : Ignore that primitive bases are different. This is a very dangerous option, because when the grids do not match, your results will be wrong. However, it allows you to use a restart file which is, say, generated with sinDVR, whereas you want to use FFT during the propagation. 
build ..... endbuild 
The initial wavefunction will be build using the data specified between these keywords. See Building the initial wavepacket. 
readinwf ..... endreadinwf 
The initial wavefunction will be read from one or several restart files. The SPFs (and/or the coefficients) for different electronic states can be read from different restart files. See: Reading the initial wavepacket. 
After some initial WF is generated, either by file,or
build, or readinwf, this WF may be modified by one
or several of the following procedures. The program will take
actions in the order:
Acoeff, meigenf,
operate, orthogonalisation,
correction,
irrespectively of the order in the input file.
The INIT_WFSECTION is used also for generating an initial density operator (of type I and II). For the generation of a pure state the initial wave function ket is multiplied with the corresponding bra, i.e.
rho =  Psi > < Psi 
Hence, in this case it is necessary only to specify an initial wave function. To obtain a thermalised initial state the temperature key word (see below) has to be used. The initial wave function is then assumed to represent the ground state, and the parameter values are taken to generate the appropriate thermalised state.
The selection of configurations is controlled by the cutoff parameter which is given as an argument to the keyword smctdh. The method is described in G. A. Worth, J. Chem. Phys. 112, 8322 (2000). The default value for the selection parameter is 2.0. Smaller values may lead to rather inaccurate results and larger values may not lead to a speedup. In general, SMCTDH will only be useful, if there are several particles (5 or more) and if the propagation of the Avector is much more costly than the propagation of the SPFs. SMCTDH is incompatible with operate and cross, requires that the wavefunction is build and not read in from a file, and requires CMF propagation with natorb. Finally, several of the analyse routines are not able to handle SMCTDH wavefunctions.
The information needed to generate the initial wavefunction is written one line per degree of freedom between the keywords build and endbuild. The input is free format, with blanks dividing the various parameters. The format for each line is
modelabel type parameters
The modelabel is an alphanumeric string attached to the degree of freedom. This must match a label specified in the primitivebasis section.
If one uses an electronic basis (i.e. one degree of freedom has the primitive basis type el), then the electronic initial state can be specified by the init_state keyword,
init_state = s
where the integer s specifies the initial state. This statement must be the only one on a line. If the lowest electronic state is selected, this keyword is not required.
If one uses electronic states in a density operator propagation the keywords corresponding to init_state are left_state and right_state (for both types). The usage is
left_state = s
right_state = t
where the integers s,t specify the initial states of the density operator. In a ketbra notation this means s><<I>t. Each statement must be the only one on a line. If s or t denotes the lowest electronic state, the corresponding keyword is not required.
To obtain a thermalised initial state for a densityoperator propagation the keyword
temperature = T
has to be used where T is the temperature. For density operators of type I an analytical formula is applied to generate the thermalised initial state. Here the size of the primitive grid has to be chosen large enough to obtain an accurate representation. For density operators of type II the number of SPFs is crucial for an accurate representation.
To summarize:
Keyword  Description 

Acoeff ..... endAcoeff 
The lines between the keywords contain in free format one
integer (Aindex) and one complex number (Avalue) per line,
thus defining the initial Avector. The default is A(1) =
(1.0,0.0) and zero for all other coefficients. For a multiset run, the input line must contain two integers. The first is the Aindex and the second the electronic state. A multiset densityoperator run requires three integers before the complex number (Avalue), the Aindex and the two electronic state indices s and t. E.g.: 518 (0.717,0.0) (singleset, wavefunction and densities) 518 1 (0.717,0.0) (multiset, wavefunction) 518 1 1 (0.717,0.0) (multiset, densities) There is also a long form of the Acoeff input, which however is only allowed for nmode < 33 (nmode < 17 for density type II). Here the number of the particle for each mode (and the electronic state(s) in case of a multiset run) is input followed by the value of the Acoefficient. E.g.: 1 4 1 3 1 2 (0.5,0.0) would be a correct input for either a 6mode singleset, or a 5mode multiset WFcalculation. In the latter case the 2 would specify the electronic state. For densities type I this would be a correct input for either a 6mode singleset, or a or a 4mode multiset calculation. In the latter case the last two indices 1 2 would specify the electronic states. For densities type II this would be a correct input for either a 3mode singleset (j_{1}, j_{2},j_{3},k_{1},k_{2},k _{3}), or a or a 2mode multiset calculation (j_{1}, j_{2},k_{1},k_{2},s,t). This redefinition of the Avector is also possible, when the initial wavefunction is read in (file keyword, restart run). The Avector is renormalised before being used. The nonzero entries of the Avector are protocolled in the logfile. 
meigenf = I,S, I1S1(,S2,S3,S4,I2)  Generate the modeeigenfunctions using operator S, where
S = XX is the name of an operator, defined in the
HAMILTONIANSECTION_XX. Only that uncorrelated part of the
operator S, which acts on the mode I, will be used. The
operator must be generated with the usediag keyword.
I1 denotes the number of the eigenstate (counting from zero),
which is taken as the first SPF. The ordering and the
eigenenergies are protocoled in the log file. The number I1
may be replaced by the string S1 = follow. In this
case the eigenstate with the largest overlap with the
starting vector (usually defined in a build block) is taken
as first SPF. If the optional number I2 is given, the maximal
Lanczos space is restricted to I2. Otherwise the maximal
Lanczos space size is equal to the length of the mode vector
(i.e. subdim). If the optional string S2=full is
given, the number of Lanczos iterations is limited by I2 (or
subdim) only. Otherwise the Lanczos iteration is stopped,
when the chosen vector (i.e. I1) is converged. If the
optional string S3=select or S3=noselect is
given, states with zero overlap (<10^{13}) will
be ignored/not ignored when mapping the eigenvectors to the
psi function. When S3 is not given, then noselect is
chosen by default when full is given and I2=subdim
(e.g. I2 not given). Otherwise the default is select.
If the optional string S4=write is given, the
eigenvectors will be written to the (ASCII) file
meigen_mode_ state. Examples: meigenf = 3,oper,0 meigenf = 3,oper,follow,full,125 meigenf = 3,oper,follow,full,select,write,125 
operate = S(,S1(,S2,...))  Operate on the initial wavefunction using operator S,
where S = XX is the name of an operator, defined in the
HAMILTONIANSECTION_XX. One may apply up to 15 operators to
the WF. operate = O1, O2, O3 will produce
O3*O2*O1*psi>. The wavefunction is renormalised after
each application of an operator. The normalisation factors
are protocoled in the logfile. For density operators it calculates the commutator i [O1,rho_{0}] . operate = O1,O2, ... ,On will produce (i)^{n} [On,...[O2,[O1,rho_{0}]]...] . 
operate_iter = I  Maximum no. of iterations to be used in applying an operator to an MCTDH wavefunction. Default = 10. Only the Avector but not the SPFs will be modified, if operate_iter=0 is given. This can be useful when generating an initial WF for improved relaxation. 
operate_tol = R  Convergence tolerance to be used in applying an operator to an MCTDH wavefunction. Default = 1.0d8 
operate_nonorm  The normalisation factor is removed from operator*psi, i.e. the initial wavefunction is no longer normalised. 
operate_nodirect  A noniterative algorithm may be applied first before the iterative improvement the wavefunction. With the keyword operate_nodirect, the noniterative part is skipped. (operate_nodirect is default.) 
operate_direct  With the keyword operate_direct, first the noniterative algorithm is applied before the iterative procedure starts (only for nstate=1). 
orthogonalisation = S (,S1 (,S2 ..))  S = path_to_foreign_restart_file_or_directory The initial WF is orthogonalised against the WF on the specified file. One may give several files in one orthogonalisation statement, or one may give more than one of such a statement, in order to orthogonalise against several wavefunctions. This feature is useful in particular for improved relaxation. If the path points to a directory, /psi is automatically appended. 
symorb = I1,I2  I1 = Number of first set of SPFs (mode number),
I2 = Number of second set of SPFs. With this keyword one mixes two sets of SPFs. The new order (in both sets) is now: 1st SPF of 1st set, 1st SPF of 2nd set, 2nd SPF of 1st set, 2nd SPF of 2nd set, etc. The SPFs were orthonormalized and those which tend to be linearly dependent are removed. As the two sets of SPFs are now identical, one may define symmetric and antisymmetric linear combinations with the aid of Acoeff. 
sym1d = I ((,S),I1(,S),..) asym1d = I ((,S),I1(,S),..) 
I = Number of DOF which is to be (a)symmetrized. S
= persist phi(i) = phi(gdim+1i), i=1,...,gdim, for symmetrization and phi(i) = phi(gdim+1i) for asymmetrization. In order not to annihilate a function by (a)symmetrization one should use in the build block the types: HO odd, HO even, gauss odd, gauss even, or sym as argument to pop when the type eigenf is used. The (a)symmetrization is applied to the initial wavefunction only. However, if the keyword persist is given and when an improved relaxation run is performed, then the (a)symmetrization is done additionally after each orbital relaxation. 
parity = I ((,S),I1(,S),..)  I = Number DOF which is to be (a)symmetrized.
S = persist Similar to sym1d and asym1d. Functions which are predominantly symmetric are symmetrized, and those predominantly antisymmetric are antisymmetrized. The (a)symmetrization is applied to the initial wavefunction only. However, if the keyword persist is given and when an improved relaxation run is performed, then the (a)symmetrization is done additionally after each orbital relaxation. 
sym2d = I ((,S),I1(,S),..) asym2d = I ((,S),I1(,S),..) 
I = Number 2Dmode which is to be (a)symmetrized.
S = persist phi(x,y) = phi(y,x), for symmetrization and phi(x,y) = phi(y,x) for asymmetrization. The mode(s) specified must be 2D combined modes and the primitive grids within these modes must be identical. The (a)symmetrization is applied to the initial wavefunction only. However, if the keyword persist is given and when an improved relaxation run is performed, then the (a)symmetrization is done additionally after each orbital relaxation. 
nsym2d = I ((,S),I1(,S),..)  I = Number of the 2Dmode for which the symmetric and
antisymmetric combinations of the spfs have to be made.
S = persist The mode(s) specified must be 2D combined modes and the primitive grids within these modes must be identical. NOTE: This also changes the Avector! (see the example input "H2H2_nsym.inp" in the "Further Example input" section) 
sym2kleg = I (,I1,...) asym2kleg = I (,I1,...) 
I = Number of 4Dmode (2x KLeg/K) which is to be
(a)symmetrized. phi(θ_{1},k_{1},θ_{2},k_{2}) = phi(θ_{2},k_{2},θ_{1},k_{1}) for symmetrization and phi(θ_{1},k_{1},θ_{2},k_{2}) = −phi(θ_{2},k_{2},θ_{1},k_{1}) for asymmetrization. The mode(s) specified must be 4D combined modes of the form KLeg/K/KLeg/K, and the primitive grids for the two KLeg and K DOFs must be identical. 
sym3d = I ((,S),I1(,S),..)  I = Number 3Dmode which is to be symmetrized. S =
persist phi(x,y,z) = phi(y,z,x) = phi(z,x,y) = phi(y,x,z) = phi(x,z,y) = phi(z,y,x). The mode(s) specified must be 3D combined modes and the primitive grids within these modes must be identical. The symmetrization is applied to the initial wavefunction only. However, if the argument persist is given and when an improved relaxation run is performed, then the symmetrization is done additionally after each orbital relaxation. 
symcoeff ( = S)  S = persist The Avector is symmetrised by summing all permutations of its indices. This makes only sense, if all modes are identical, i.e. if the id keyword (SPFBasisSection) is used. The symmetrization is applied to the initial wavefunction only. However, if the argument persist is given and when an improved relaxation run is performed, then the symmetrization is done additionally after each orbital relaxation. 
asymcoeff ( = S)  S = persist The Avector is asymmetrised by summing sig(P)*A(P(j1,..,jp)), where P denotes a permutation. This makes only sense, if all modes are identical, i.e. if the id keyword (SPFBasisSection) is used. The symmetrization is applied to the initial wavefunction only. However, if the argument persist is given and when an improved relaxation run is performed, then the symmetrization is done additionally after each orbital relaxation. 
correction = S1,S2  S1,S2 = edstr, dia, ad, hh2. edstr: compute the (uncorrected) energy distribution for the flux analysis. dia: compute the diabatically corrected energy distribution. ad: adiabatic correction. hh2: use the routines specially written for H+H_{2} reactive scattering using LSTH PES. hh2bkmp2: use the routines specially written for H+H_{2} reactive scattering using BKMP2 PES. Note that the translational degree of freedom has to be specified by the trans keyword if it is not the first DOF. 
trans = I1(,I2)  I1,I2 = dof and state of the translational
mode. (Needed for correction). If the keyword trans is not given, dof=1, state=1 is assumed when computing the correction. 
tfac = R  R = partition factor for Jacobian coordinates. R = m1/(m1+m2) where m1 and m2 are the masses of the two atoms of the diatomic molecule. If not given, tfac=0.5 is assumed. 
smctdh = R  An SMCTDH wavefunction will be generated with a cutoff for selecting the configurations of R. (see Eq.(21) of JCP 112, 8322 (2000)). See note below. 
Special keywords for build subsection  
Keyword  Description 
init_state = I  Initial electronic state of a wavefunction propagation. 
left_state = I  Initial electronic state for the ket part of a density operator. 
right_state = I  Initial electronic state for the bra part of a density operator. 
temperature=R  Initial temperature for a density operator propagation. 
Print some information to the log file on how multidimensional modefunctions are build from 1Dfunctions. NB Not for KLeg. 
When building the initial wavefunction, the type of the 1D functions can be chosen from one of the following:
Building the initial wavefunction  

Type  Description 
HO  Harmonic oscillator eigenfunction. 
HO odd  Odd harmonic oscillator eigenfunctions (n=1, 3, 5 ...). 
HO even  Even harmonic oscillator eigenfunctions (n=0, 2, 4, ....). 
gauss  Gaussian wavepacket. 
gauss odd  Gaussian wavepacket. Odd functions only 
gauss even  Gaussian wavepacket. Even functions only. 
Leg  Legendre polynomial. 
sphFBR  Spherical harmonics. 
phiFBR  Indicates second coordinate of sphFBR. 
eigenf  Specified potential eigenfunction. 
KLeg  Associated Legendre polynomial. Requires KLeg or Pleg in PrimitiveBasisSection. 
K  Body fixed magnetic quantum number for KLeg (or PLeg). 
map  Use the initial (1D) singleparticle functions of another DOF. 
The parameters needed for each type of function are as follows:
Type  Parameters  Parameter Description 

HO HO odd HO even 
centre  Centre of oscillator potential. 
momentum  Initial momentum of wavepacket.  
frequency  Frequency of harmonic oscillator. The frequency may be complex.  
mass  Mass of harmonic oscillator.  
pop = p  The pth singleparticle function will be populated initially. This parameter is optional, the default is p = 1.  
pack = p  The Buildline is for the pth packet in a multipacket run. This parameter is optional, the default is p = 1.  
periodic  The grid is assumed to be periodic. This keyword is meaningful only if the primitive representation is FFT or expDVR and if the primitive grid is periodic (one of the keywords: periodic, speriodic, 2pi or s2pi must be given in the primitive basis section). If one places a gaussian at the origin of a 2pi grid, then only half of the gaussian is taken as singleparticle function. With the aid of the keyword periodic also the region near 2pi gains intensity.  
gauss gauss odd gauss even 
center  Center of initial Gaussian wavepacket. 
momentum  Initial momentum of wavepacket.  
width  Denotes width of initial Gaussian wavepacket. The width here is defined as the standard deviation of the initial Gaussian, i.e. Sqrt(<x^{2}><x>^{2}). The width parameter may be complex.  
pop = p  The pth singleparticle function will be populated initially. This parameter is optional, the default is p = 1.  
pack = p  The Buildline is for the pth packet in a multipacket run. This parameter is optional, the default is p = 1.  
periodic  Same as for HO.  
Leg  m  Magnetic rotational quantum number. Alternatively to a number one may input the string jbfXXX or slzXXX or blz. m will then be set to the value of the parameter jbfXXX or slzXXX, or to the value of the magnetic rotational quantum number, blz, as defined in the primitive basis set. Here XXX stand for any characters. I.e. one may use slz or slz_1 etc. Note: if jbfXXX or slzXXX is used, they must be defined in the parameter section of the inputfile or via an option on the command line. (operator file definitions come too late). 
l  The lquantum number of the first singleparticle function. Alternatively to a number one may input the string sl0XXX. l will then be set to the value of the parameter sl0XXX. Here XXX stand for any characters. I.e. one may use sl0 or sl0_1 etc. Note: if sl0XXX is used, it must be defined in the parameter section of the inputfile or via an option on the command line. (operator file definitions come too late). Note: l >= m.  
symmetry  Indicates symmetry. nosym: no symmetry (all l values are used). sym: symmetry used (gerade if l is gerade and vice versa). 

sphFBR  j  Quantum number j of the initial spherical harmonic. 
phiFBR  m  Quantum number m of the initial spherical harmonic. 
eigenf  potential  Name of onedimensional potential curve, XX, defined in
the HAMILTONIANSECTION_XX. (See note below). 
pop = p (,S(,S1))  The pth eigenfunction will be populated initially.
This parameter is optional, the default is the lowest,
p = 1. Note : p=1 > ground state, p=2 > first
excited state, etc. If additionally S=sym is given,
only every second eigenstate is taken. I.e. for a symmetric
potential pop=1,sym selects even, and pop=2,sym
odd states as initial single particle functions. If
additionally S1=check is given, the program tests for
the correct symmetry. This is useful if the symmetric
potential is a double well, such that the odd/even character
of the eigenfunctions do not follow a simple alternating
pattern. The selection of the eigenstates is protocoled in
the logfile. If you want the eigenvectors printed, specify "veigen" in the RUNSECTION. 

KLeg  l  Initial rotational quantum number. Alternatively to a number one may input the string sl0XXX. l will then be set to the value of the parameter sl0XXX. Here XXX stand for any characters. I.e. one may use sl0 or sl0_1 etc. Note: if sl0XXX is used, it must be defined in the parameter section of the inputfile or via an option on the command line. (operator file definitions come too late). 
symmetry  Indicates symmetry. nosym: no symmetry (all l values are used.) sym: symmetry used (gerade if l is gerade and vice versa). 

excite=s  Excitation algorithm for the generation of (unoccupied)
spf's. s=j: Excitation of jstates is preferred (default). s=m: Excitation of mstates is preferred (j goes down). s=mold: Excitation of mstates is preferred (j goes up; old behaviour, deprecated). 

Optional. Prints (j,m) quantum numbers of the generated
spf's to the 'log'file. (This option may tell you the
difference between the excite=s options.) 

nspf=I  Optional. Only used for multiKLeg modes (i.e. modes with more than one KLeg). This sets the number of 1D SPFs which are initially generated; the real (multiD) mode SPFs are later built from these 1D SPFs. If omitted, or set to zero, an automatic value is chosen. Use the print option to see how many (and which) 1D SPFs are generated.  
K  k  Body fixed magnetic quantum number of initial wavefunction (note: k <= l). Alternatively to a number one may input the string slz or jbf. k will then be set to the value of the parameter slz or jbf, respectively. Note: if slz or jbf is used, it must be defined in the parameter section of the inputfile or via an option on the command line. (operator file definitions come too late). 
kmin  Minimum value of the body fixed magnetic quantum number
for the initial wavefunction. Default is the corresponding value given in the primitivebasissection. 

kmax  Maximum value of the body fixed magnetic quantum number
for the initial wavefunction. Default is the corresponding value given in the primitivebasissection. 

dk  Step of the body fixed magnetic quantum number
k. Default is 1. 

map  label  Modelabel of the DOF from where to take the initial orbitals. (See note below). 
The initial singleparticle functions are formed as follows:
y eigenf Hspf pop=2Then each of the following three Hamiltonians can be used equally well to generate the desired initial singleparticle functions.
HAMILTONIANSECTION_Hspf modes  y 1.0  KE omy  q^2 endhamiltoniansection
HAMILTONIANSECTION_Hspf  modes  x  y  z  el  1.0  1  KE  1  1 omy  1  q^2  1  1  endhamiltoniansection
HAMILTONIANSECTION_Hspf  modes  x  y  z  1.0  KE  1  1 omx  q^2  1  1 1.0  1  KE  1 omy  1  q^2  1 1.0  1  1  KE omz  1  1  q^2 const  q^3  sin  q  endhamiltoniansectionThe lines 1,2 and 5,6 of the tableau of the third Hamiltonian are ignored, as they refer to other degrees of freedom than the y one. The last line is ignored, as it represents a correlated Hamiltonian term.
PRIMITIVEBASISSECTION  # Mode DVR N xi xf  z fft 96 0.75 4.5000 linear x fft 24 0.00 5.3669 periodic y fft 24 0.00 5.3669 periodic theta PLeg 36 even phi exp 9 2pi  ENDPRIMITIVEBASISSECTION INIT_WFSECTION build  # mode type center moment. freq. mass  z HO 1.80 24.d0 694.1683673,eV 1.d0 x HO 0.00 0.0 0.0 1.d0 # flat function y HO 0.00 0.0 0.0 1.d0 # flat function theta KLeg 2 sym # j of initial spherical harmonic phi K 1 # m of initial spherical harmonic  endbuild endinit_wfsection
PRIMITIVEBASISSECTION . . R FFT 192 0.6 3.0 R_dum sin 60 0.5057591623 0.6062827225 endprimitivebasissection INIT_WFSECTION build . . R map R_dum R_dum eigenf operator pop=1 endbuild endinit_wfsectionSince the DOF R_dum (in our example) is not defined in the SPFBASISSECTION it will be ignored, when the operator is build. To avoid this, one has to use the addmode keyword.
HAMILTONIANSECTION_operator addmode = R_dum  modes ......  R_dum  ....  . .
For multiset calculations, the initial functions can be defined differently for each state by using the state keyword:
modelabel type parameters state = sThe same function type must be used for each state, but the parameters can be different. It is however possible to choose between the different harmonic oscillator function sets HO, HO odd and Ho even. Thus even functions can be used on one state and odd functions on the other. If the state keyword is not used, the same function parameters are used to generate the spfs for each state.
For multipacket calculations, i.e. when packets > 1, the initial function definition must be given for each packet as
modelabel type parameters pack = pwhere the integer number p defines to which initial packet the corresponding input line belongs. It is possible to specify more initial packets in this section than given by the packets argument. All data with p > packets is then ignored.
By default the 1st single particle function of each degree of freedom is used to form the initial Hartree product wavefunction. The initially populated singleparticle function can be selected using the pop keyword:
modelabel type parameters pop = iwhich populates the i th function.
Reading the initial wavefunction  

Keyword  Description  
file = S  The string S is a path of a diretory which contains a restart file. Up to 8 restart files may be read. Each file statement must be followed by SPF and/or A line(s).  
SPF  SPF i > k : Write
the SPFs of electronic state i of the restart file
just read to the electronic state k of the system. SPF i > k1,k2,k3,... : Write the SPFs to states k1,k2,k3,..., i.e. those states will have identical sets of SPFs. 

A  A i > k : Write the Avector block of electronic state i of the restart file just being read to the electronic state k of the system.  
init_state = I  If an Avector is not specified, a Hartree product is assumed and placed on the electronic state of number I. If init_state is not given, init_state=1 is assumed.  
orthopsi  The SPFs are transformed to natural orbitals and then orthonormalized. orthopsi is the default.  
noorthopsi  The SPFs remain untouched, they are not reorthonormalized  
realpsi  Only the real part of the wavefunction is used and Schmidtorthonormalised as in the orthopsicase.  
ignore  The different primitive bases error will be ignored. 
Examples:
For a two state WF the following input is equivalent to a simple
file = <restartdirectory> statement.
ReadInwf orthopsi # This is default, opposite: noorthopsi file = <restartdirectory> SPF 1 > 1 SPF 2 > 2 A 1 > 1 A 2 > 2 endreadinwfThe following two inputs are equivalent. In both cases the SPFs of the first state of the gscalculation (which may have only one state) is put on state 1, 2 and 3 of the initial WF. The Avector of the first state of the gscalculation is put on the second state of the initial WF. The Avector for states 1 and 3 is zero.
ReadInwf file = gs SPF 1 > 1 SPF 1 > 2 SPF 1 > 3 A 1 > 2 endreadinwf ReadInwf file = gs SPF 1 > 1,2,3 A 1 > 2 endreadinwfOne may use more than one (up to eight) restart files to build the initial wavefunction.
ReadInwf file = run1 SPF 1 > 1 file = run2 SPF 1 > 2 A 1 > 1 file = run3 A 2 > 2 endreadinwfIn a multipacket run the different packets are treated as different electronic states. The ReadInwf statement does not know packets and one has to do the assignment by "hand" using the formula s1 = (p1)*nstate + s, where p and s denote the actual packet and state and s1 is the effective state number, which one must enter in the ReadInwf block.
ReadInwf file = run1 SPF 1 > 2 endreadinwf
To control how often the mean field matrices are updated, one of the following keywords may be chosen. Default is VMF.  

Keyword  Description 
VMF  Variable mean fields: The mean fields are calculated at each integration step. 
CMF = R, R1  Constant mean fields: The mean fields are kept constant
over a variable time interval. Equivalent to CMF/var for propagation and relaxation but equivalent to CMF/varphi for improved relaxation. R is the initial time interval (in fs). R1 is an accuracy parameter for the timestep control. 
CMF/fix = R  The mean fields are kept constant over a fixed time interval, specified by R (in fs). 
CMF/var = R, R1  The mean fields are kept constant over a variable time
interval, determined by the errors of both the MCTDH
coefficients and the singleparticle functions. var is default; CMF/var is equivalent to CMF, except for improved relaxation. R is the initial time interval (in fs). R1 is an accuracy parameter for the timestep control. 
CMF/varphi = R, R1  The mean fields are kept constant over a variable time
interval, determined by the error of the singleparticle
functions only. In case of improved relaxation varphi is default making CMF/varphi equivalent to CMF in this case. R is the initial time interval (in fs). R1 is an accuracy parameter for the timestep control. 
CMF/vara = R, R1  The mean fields are kept constant over a variable time
interval, determined by the error of the MCTDH coefficients
(Avector) only. R is the initial time interval (in fs). R1 is an accuracy parameter for the timestep control. 
The following keywords define the integrator to be used.  

Keyword  Description 
ABM/S = I, R, R1  AdamsBashforthMoulton predictorcorrector integrator
used for S = all, spf, A. I = order R = accuracy R1 = initial stepsize 
BS/S = I, R, R1  BulirschStoer extrapolation integrator used for S = all,
spf, A. I = maximal order R = accuracy R1 = initial stepsize 
RK5/S = R, R1 (,S)  RungeKutta integrator of order 5, used for S = all, spf,
A. R = accuracy R1 = initial stepsize (can be omitted or set to zero, then the integrator guesses a suitable value) S=importho (improved orthogonality of SPFs, see below) 
RK8/S = R, R1 (,S)  RungeKutta integrator of order 8, used for S = all, spf,
A. R = accuracy R1 = initial stepsize (can be omitted or set to zero, then the integrator guesses a suitable value) S=importho (improved orthogonality of SPFs, see below) 
SIL/S = I, R, S1  SIL integrator used for S = all, spf, A. I = maximal order R = accuracy S1 = standard: The standard error estimate is used (default). S1 = novel: The improved error criterion is taken. See note below! 
CSIL/S = I, R, S1  complexSIL integrator used for S = all, spf, A. Same as SIL/S (see above), but the use of the (complex) LanczosArnoldi integrator is enforced. (SIL tries to make the choice Lanczos/LanczosArnoldi automatically). 
DAV = I, R rDAV = I, R rrDAV = I, R cDAV = I, R 
Davidson "integrator" allowed for improved relaxation
only. The keywords DAV and DAV/A are equivalent. See note below. I = maximal order, R = accuracy There are three routines: DAV is for hermitian Hamiltonians, rDAV and rrDav are for real Hamiltonians and real wavefunctions. Memory is saved as only real data is stored. rrDAV uses more real arithmetic and is hence faster, but not general.(See note below). cDAV is for nonhermitian Hamiltonians (resonances). 
The string S=all after the integrator name may be omitted, i.e. ABM is equivalent to ABM/ALL. For VMF calculations, only the BS, ABM or RK5/8 integrator may be used for the differential equations. Default is ABM. For VMF calculations the integrator must carry the extension S=all (or no extension at all), i.e. there is only one integrator within the VMF scheme. For CMF calculations, the following combinations of integrators are possible: ABM/spf + SIL/A, BS/spf + SIL/A, RKx/spf + SIL/A, BS/all, ABM/all, RKx/all. Default is BS/spf + SIL/A. For numerically exact calculations (i.e. the keyword exact has been specified in the RUNSECTION), any of the integrators may be chosen, with S = all, or S = spf. Default is ABM, but more efficient is usually SIL (or CSIL).
The Davidson "integrator", DAV, (actually a diagonaliser, of course) is the optimal choice for the "Apropagation" of improved relaxation. The accuracy parameter is an upper limit (in au) for the error of the eigenvalue. Improved relaxation requires CMF/varphi or CMF/fix. (Simply use CMF). The routine DAV is for hermitian Hamiltonians and general wavefunctions. rDAV is for real Hamiltonians (i.e. H*psi = real for all real psi) and real (initial) WF. Memory is saved as the Davidson vectors are stored as real. Most of the arithmetic (in particular H*psi), however, is still complex. This problem is partly solved by rrDAV. rrDAV uses the same Davidson routine, but a simplified routine is employed to perform the matrix product H*A. This routine is faster, because it uses more real arithmetic, but works only for simple Hamiltonians (no electronic states, only real operators, e.g. no p. NB: The propagation of the SPFs is always done in complex arithmetic. cDAV is for nonhermitian Hamiltonians. This allows to compute resonances of CAP augmented Hamiltonians. The convergence, however, is slower. cDAV is chosen automatically, if CAPs are present.
NOTE: There are two Lanczos integrators, a real version for hermitian Hamiltonians and a complex version (LanczosArnoldi) for nonhermitian ones. If one gives the keyword SIL, then the program tries to detect whether the Hamiltonian is hermitian or not and it makes the appropriate choice. This, however, works safely only for CAPs. When one knows that the Hamiltonian is nonhermitian, one should use CSIL. The use of SIL in case of a nonhermitian Hamiltonian may lead to wrong results.
The following keywords may be used to further define the method of propagation.  

Keyword  Description 
eps_inv = R  R is the value used to regularise the inverse of the reduced density matrices. (Default: 10^{8}. See eq.(82) review.) 
eps_no = R  R is the value used to regularise the "natural orbital Hamiltonians". (Default: 10^{8}) 
projh  One dimensional Hamiltonians are not extracted to be in front of the projector. (See eq.(45) review) 
hproj  One dimensional Hamiltonians are extracted to be in front of the projector. (See eq.(44) review) 
natorb  Natural orbitals are propagated in place of spfs. When the CMFintegrator is employed, the spfs are propagated normally, but the whole wavefunction is transformed to natural orbital picture after each CMF step. In case of a relaxation run the orbitals are reorthonormalised after each CMF step. 
energyorb  Energy orbitals are propagated in place of spfs. Only for CMF. The spfs are propagated normally, but the whole wavefunction is transformed to energy orbital picture after each output (out1). energyorb is default when the Davidson "integrator" is employed (improved relaxation). energyorb requires that the orben file is set (RunSection). 
stdorb  Standard orbitals are propagated. This is default, except for improved relaxation using DAV. 
interpic  Spfs are propagated using the interaction picture. interpic is not allowed for CMFintegration. 
simpleproj  The simple projector is used rather than the improved one. The inversion of the spfoverlapmatrix is thus avoided. 
nohsym  The symmetry of the operators determined by the program is not used to calculate the operator matirx elements. 
CDVR  Multidimensional potential terms are evaluated using CDVR . The analytic_pes keyword needs to be set in the OPERATORSECTION 
TDDVR  Multidimensional potential terms are evaluated using TDDVR. The analytic_pes keyword needs to be set in the OPERATORSECTION 
directmultid  Multidimensional potential terms are evaluated using a direct algorithm, i.e. the potential is not stored on the full grid but recalculated each time it is needed. This is much slower, but needs minimal memory. The analytic_pes keyword needs to be set in the OPERATORSECTION 
update = R  For numerically exact calculations, if the SIL integrator has been chosen the update time (i.e. step size) is set to R. The default is R = tout. 
lmf  The equations of motion of the Linear meanfield approach are used to propagate density operators of type II (no effect for type I or wave functions). 
df  The equations of motion derived from the DiracFrenkel/McLachlan variational principle are used to propagate density operators of type II (no effect for type I or wave functions). This is the default. 
importho  Improve the orthonormality of the SPFs after each
integration step. The long form
improvedorthonormality is also possible. The keyword
may also be given as a third argument to the RK5/8
integrators. Note: currently works only with the RK5/8 integrators. 
Omitted integrator parameters default to:
Keyword  Default  

CMF/fix  R = min(1.0,tout)  
CMF/var  R = min(1.0,tout)  R1 = 1.0e6  
CMF/varphi  R = min(1.0,tout)  R1 = 1.0e6  
ABM  I = 6  R = 1.0e5  R1 = 1.0e4 
BS  I = 8  R = 1.0e6  R1 = updatetime/2 for CMF or R1 = 0.2 for VMF 
SIL  I = 30  R = 1.0e6  S1 = standard 
RK5  R = 1.0e6  R1 = 0 (i.e. autoguess)  
RK8  R = 1.0e6  R1 = 0 (i.e. autoguess)  
projh / hproj  in VMF mode: hproj in CMF mode: projh 

eps_inv  R = 1.0e8  
eps_no  R = 1.0e8 