Once a potential energy surface (PES) has been generated by the XSURF program, it can be transformed to different representations. The first possibility (analytical representations (POLY)) is a representation by basis functions, i.e. the POLY program. The PESTRANS program (transformation of the coordinate system (PESTRANS)) offers a transformation of the PES for vibrational structure calculations of isotopologues or Franck-Condon factors.
POLY,options [poly]
The POLY program allows for the transformation of the potential energy surface and property surfaces from a grid representation to an analytical representation by polynomials, Gaussians or B-splines.
B. Ziegler, G. Rauhut, Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions., J. Chem. Phys. 144, 114114 (2016)
The following options are available:
CHI_AV_xD=value (x=1..3 default=1.d-10; x=4 default=1.d-5) Threshold for the average least squares criterion to be met for the individual orders of the potential.CHI_MAX_xD=value (x=1 default=1.d-10; x=2 default=1.d-8, x=3 default=1.d-6, x=4 default=1.d-5) Threshold for the maximum least squares criterion to be met for the individual orders of the potential.DELAUTO=value In order to delete troublesome 2D, 3D or 4D surfaces from the multi-mode expansion of the potential, the DELAUTO keyword sets all coefficients of the polynomial expansion of these surfaces to zero. The threshold passed to the DELAUTO keyword corresponds to the $\chi^2$ value of the least squares fitting procedure. It acts on both, the energy and the dipole surfaces. The default is set to 9.d99, i.e. all surfaces with $\chi^2$ values below this threshold will not be affected.INFO=n INFO=1 provides a list of the values of all relevant program parameters (options).MAXBF=n This keyword controls the maximum number of basis functions to be used. This keyword may be used to restrict the basis for certain purposes.MINBF=n (=7 Default) This keyword controls the minimum number of basis functions to be used.NDIM=n The keyword NDIM=n terminates the transformation after the $n$D terms within the $n$-mode expansion of the surfaces. The default is set to 3. The transformation of the 4D terms can be very time consuming.NDIMDIP=n Term after which the $n$-body expansions of the dipole surfaces are truncated. The default is set to 3. Note that NDIMDIP has to be lower or equal than NDIM.NDIMPOL=n Term after which the $n$-body expansions of the polarizability tensor surfaces are truncated. The default is 0. NDIMPOL has to be lower or equal than NDIM and must be smaller than 4.NDIMQUAD=n Term after which the $n$-body expansions of the quadrupole tensor surfaces are truncated. The default is 0. NDIMQUAD has to be lower or equal than NDIM and must be smaller than 4.NDIMMU=n An n-mode expansion of the $\mu$-tensor will be generated and transformed to polynomials up to 3rd order (default). The order can be changed by the integer passed to the NDIMMU keyword.PSUM=n Maximum number of basis functions to be used within the fits of the surfaces (sum of exponents).
SHOW=n The coefficients of the polynomial representation can be printed. In order to identify quartic potentials, it is recommended to use SHOW=1. Higher values will lead to very long output files.TYPE=variable Once polynomials have been generated, the expansion of the potential can be restricted to the harmonic approximation or a semi-quartic force field, i.e. TYPE=HARM or TYPE=QFF.VAM=n The Watson correction term, i.e. VAM=1, is absorbed in the potential by default. Once the polynomials to be generated should exclude this correction, this needs to be specified by VAM=0. Any other values, i.e. 2 or 3, will be ignored.
DISK,options
The DISK directive allows to specify explicitly, from where the grid information shall be taken and where it shall be stored to disk. This can also be accomplished in an automated manner, which is recommended. These features are only relevant for the simulation of vibronic spectra as one has to deal with several PESs in the same input. For simple VCI calculations, no information is needed here.
AUTO=n Rather than using the options START and SAVE one may simply assign a label n to a a certain PES and all the records will be set automatically. The grid information is read from the last PES specified in the call of the XSURF program.
FIT,options
A fit function has to be defined for each coordinate. These fit functions are used to transform an grid representation of a surface generated by the XSURF program to an analytical representation. If no fit functions are given, the fit functions used in the XSURF program for the intermediate fitting are used.
This directive also exists in the XSURF program. If no fit functions are defined within the XSURF program, but in the POLY program, the fit functions of the POLY program are also used in the XSURF program.
COORD(x)=variable Defines the fit function for coordinate $x$. The possible fit functions are B-splines (bspline), Gaussian functions (gauss), Morse functions (morse), polynomials (poly) and trigonometric functions (trigo).
ONLY=variable Sets one fit function for all coordinates. The possible fit functions are the same as for the option COORD.
PSCAL,options
The 1D potential functions can be scaled by user-defined factors. This allows to fit potentials to experimentally determined frequencies.
MODE=n This is a mandatory information, which determines the mode to be scaled.SFAC=value Scaling factor to be used for the respective mode.The following example shows the scaling of the three modes of water.
{poly
pscal,mode=1,sfac=0.99924787
pscal,mode=2,sfac=0.99850975
pscal,mode=3,sfac=0.99900217}
PESTRANS,options [pestrans]
The PESTRANS program allows to change the coordinate system being used within the representation of the potential by a Duschinsky-like transformation. This allows for the transformation of PESs as needed for the calculation of the vibrational spectra of isotopologues or Franck-Condon factors including Duschinsky rotations. This requires a representation of the potential energy surface by polynomials. Different versions of the PESTRANS program will be used in combination with the XSURF program. For further details see:
P. Meier, D. Oschetzki, R. Berger, G. Rauhut, Transformation of potential energy surfaces for estimating isotopic shifts in anharmonic vibrational frequency calculations, J. Chem. Phys. 140, 184111 (2014).
DVEC=n (=0 Default) This keyword controls the shift vector within the transformation. DVEC=0 sets this vector to zero. ECKART=n By default the Eckart transformation matrix needed within the PESTRANS program will be computed explicitly. ECKART=0 replaces the Eckart transformation matrix by a unit matrix.NDIM=n Order of the $n$-mode potential for the transformed potential. The information of the original potential will be taken from the the POLY calculation. Note, the NDIMDIP keyword requests the intensity directive. THRSMAT=value Threshold controlling the analysis of the S-matrix indicating the accuracy of the transformation (default: THRSMAT=0.3).THRQ=value Elements in the displacement vectors below this threshold (default THRQ=10^{-8}) will be neglected within the transformation.TRANSTYPE=variable specifies the transformation to be performed by PESTRANS. The default is generated automatically based on the given directives in the input stream.TRANSTYPE=QFF transforms an n-mode expansion of the PES into a quartic force field (QFF).TRANSTYPE=ISO indicates a transformation of the spanning axes of the PES for the calculation of isotopologues.TRANSTYPE=FCF performs a Duschinsky transformation as needed for the calculation of Franck-Condon factors.
UMAT=n As needed for Franck-Condon calculations, UMAT=1 defines the linear combinations of the displacement vectors due to Duschinsky rotations, which influences the selection of states in subsequent VCI calculations. The default, UMAT=0, switches off this feature.
Most options and directives of the XSURF program can also be used in the PESTRANS program (i.e. INFO, INTENSITY, SCALNM, DISK, LINCOMB, VTAYLOR), while specific ones had to be excluded (i.e. NGRID, etc. ).
MASS,options
Once the PESTRANS program will be used for the calculation of isotopologues, the atomic masses of the individual atoms can be specified by this directive. Note, the use of the MASS directive here differs from that in the electronic structure code as it requests the running number of the atoms in the geometry definition.
MASS,n,value The $n$th atom is supposed to have the mass value.
DISK,options
The DISK directive essentially is the same as in the XSURF program, i.e. a transformed surface can be dumped or a restart can be performed from an external file.
AUTO=n For Franck-Condon calculations this allows to specify the number of the two potential energy surfaces.DUMP=file name Specifies the name of the ASCII restart file (see the XSURF program) of the transformed potential to be dumped.EXTERN=file name Specifies the name of an external ASCII restart file to be used. This may be used to continue the transformation of partly transformed potentials or for reading the header of a restart file in Franck-Condon calculations.WHERE=variable In combination with the keywords DUMP and EXTERN for an external restart file, the keyword WHERE specifies the path for the external ASCII file. Two options are available, WHERE=home and WHERE=scr. As the external files can be huge for XSURF calculations, they will be stored on the scratch disk given by the Molpro variable $TMPDIR by default.
The following example shows a standard calculation for water, the VSCF and VCI calculations after the call of the PESTRANS program refer a to doubly deuterated water.
memory,100,m
gthresh,optgrad=1.d-7,twoint=1.d-14,prefac=1.d-16
geometry={
O ,, 0.0000000000 , 0.0000000000 , 0.1241819425
H ,, 0.0000000000 , -1.4320403835 , -0.9855926792
H ,, 0.0000000000 , 1.4320403835 , -0.9855926792
}
basis=vtz-f12
hf
optg
ccsd(t)-f12
freq,symm=auto
label1
int
{hf
start,atden}
ccsd(t)-f12
{xsurf,sym=auto
disk,where=home,dump='h2o.pot'}
poly
vscf,pot=poly
vci,pot=poly
poly,vam=0
{pestrans
mass,2,2.0141017778d0
mass,3,2.0141017778d0
disk,where=home,dump='d2o.pot'}
poly
vscf,pot=poly
vci,pot=poly