54.1 The VSCF program (VSCF)


The VSCF program is exclusively based on the Watson Hamiltonian

\hat{H} = \frac{1}{2} \sum_{\alpha\beta} ( \hat{J}_\alpha - ...
...um_i \frac{\partial^2}{\partial q_i^2} + V(q_1,\dots,q_{3N-6})
\end{displaymath} (63)

in which the potential energy surfaces, $V(q_1,\dots,q_{3N-6})$, are provided by the SURF module. The Watson correction term and the 0D term of the vibrational angular momentum terms are by default (VAM=2) included. Within the grid-based version of the program the one-dimensional Schrödinger equation is solved by the DVR procedure of Hamilton and Light. Note that, the number of basis functions (distributed Gaussians) is determined by the grid points of the potential and cannot be increased without changing the PES grid representation. In contrast to that the number of basis functions can be modified without restrictions in the polynomial based version. In all cases the basis is fixed to distributed Gaussians (DG). As VSCF calculations are extremely fast, these calculations cannot be restarted. For details see:

G. Rauhut, T. Hrenar, A Combined Variational and Perturbational Study on the Vibrational Spectrum of P$_2$F$_4$, Chem. Phys. 346, 160 (2008).

The anharmonic frequencies and intensities calculated by the VSCF program can be used to plot an IR spectrum, using the PUT command (see subsection 10.3) with the style IRSPEC.

The following options are available:

VSCF solutions can be obtained using a potential in grid representation, i.e. TYPE=GRID, or in a polynomial representation, TYPE=POLY. In the latter case the POLY program needs to be called prior to the VSCF program in order to transform the potential.
By default, i.e. SADDLE=0, the VSCF program assumes, that the reference point of the potential belongs to a local minimum. Once the PES calculation has been started from a transition state, this information must be provided to VSCF program by using SADDLE=1. Currently, the VSCF program can only handle symmetrical double-minimum potentials.
The 0D terms of the vibrational angular momentum terms,
i.e. $\frac{1}{2} \sum_{\alpha\beta} \hat{\pi}_\alpha\mu_{\alpha\beta} \hat{\pi}_\beta$, and the Watson correction term are by default (VAM=2) included.
VAM=1 adds the Watson correction term (see eq. 65) as a pseudo-potential like contribution to the fine grid of the potential.
VAM=2 allows for the calculation of the integrals of the VAM operator using the approximation that the $\mu$ tensor is given as the inverse of the moment of inertia tensor at equilibrium geometry.i
When using VAM=4 the expansion of the effective moment of inertia tensor will be truncated after the 1D terms (rather than the 0D term in case of VAM=2). Note that values higher than 2 are only active for non-linear molecules. VAM=5 truncates the series after the 2D term. In almost all cases VAM=2 is fully sufficient. Vibrational angular momentum terms are accounted for in a perturbational manner and do not affect the wavefunction.
Plots all $\mu$-tensor surfaces up to nD and a corresponding GNUPLOT script in a separate subdirectory (plots). This option works only in combination with TYPE=POLY. The VAM option has to be set accordingly.
By default the VSCF program calculates the fundamental modes of the molecule only. However, choosing COMBI=$n$ allows for the calculation of the vibrational overtones and combination bands. The value of $n$ controls the excitation level, i.e. the number of states to be computed increases very rapidly for large values of $n$. Therefore, by default the upper limit is set to 5000 cm$^{-1}$, but this cutoff can be changed by the option UBOUND. See also the VIBSTATE program (section 54.3) for even more possibilities of defining vibrational states.
Once vibrational states have been defined with the VIBSTATE program (section 54.3), the VSCF program can be forced to compute just these states by the option USERMODE=1. Note that the vibrational ground state will always be computed and needs not to be specified explicitly.
Once overtones and combination bands shall be computed, the upper energy limit is controlled by the keyword UBOND, i.e. states, for which the harmonic estimate is larger than $n$, will not be computed. the default is set to $n$=5000 cm$^{-1}$.
For solving the one-dimensional Schrödinger equation within a grid representation two different algorithms can be used. The default, i.e. SOLVER=1, calls the discrete variable representation (DVR) as proposed by Hamilton and Light. Alternatively, the collocation algorithm of Young and Peet can be used (SOLVER=2).
The initial guess for the VSCF programs is by default generated from the uncoupled one-dimensional potentials, i.e. GUESS=1. Alternatively, one may start within the calculation of excited vibrational states from the solution of the vibrational ground state, GUESS=2.
BASIS=1 (default) defines a mode-specific basis of distributed Gaussians, which is the recommended choice. However, for certain applications a mode-independent basis (BASIS=2) can be used as well. Very often this leads to worse results for torsional modes. BASIS=3 distributes the Gaussians in a way, that the overlap integral between two functions is always the same (controlled by THRBASOVLP. This guarantees that an increasing number of basis functions will always lead to an improvement.
Overlap between two Gaussian basis functions, once BASIS=3 has been chosen. The default is 0.75.
Determines the type of orthogonalization within the VSCF program. ORTHO=1 invokes a symmetrical orthogonalization, ORTHO=2 a canonical one and ORTHO=3 uses a canonical one together with an elimination of linear dependencies (see also keyword THRLINDEP. The deafult is ORTHO=1.
Threshold for eliminating linear dependencies in the VSCF procedure (see keyword BASIS=3). The default is THRLINDEP=1e-8.
THERMO=1 allows for the improved calculation of thermodynamical quantities (compare the THERMO keyword in combination with a harmonic frequency calculation). However, the approach used here is an approximation: While the harmonic approximation is still retained in the equation for the partition functions, the actual values of the frequencies entering into these functions are the anharmonic values derived from the VSCF calculation. Default: THERMO=0.
DIPOLE=1 allows for the calculation of infrared intensities. Calculation of infrared intensities requires the calculation of dipole surfaces within the SURF program. By default the intensities will be computed on the basis of Hartree-Fock dipole surfaces.
POLAR=1 allows to compute Raman intensities in addition to infrared intensities, but of course requires polarizability tensor surfaces from the SURF program. By default Raman intensities are switched off.
The expansion of the potential in the VSCF calculation can differ from the expansion in the SURF calculation. However, only values less or equal to the one used in the surface calculation can be used.
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 to NDIM.
Term after which the $n$-body expansions of the polarizability tensor surfaces are truncated. The default is set to 0. Note that NDIMPOL has to be lower or equal to NDIM and must be smaller than 4.
The number of basis functions (distributed Gaussians) to be used for solving the VSCF equations can be controlled by NBAS=n. The default is NBAS=20. This option is only active once a polynomial representation of the potential has been chosen, see the option TYPE=POLY and the POLY program.
By default the expansion of the $\mu$-tensor for calculating the vibrationally averaged rotational constants is truncated after the 2nd order terms, i.e. NVARC=2. This may be altered by the NVARC keyword.
This option provides an extended output. PRINT=1 prints the vibrationally averaged rotational constants for all computed states and the associated vibration-rotation constants $\alpha$. PRINT=2 prints the effective 1D polynomials in case that the potential is represented in terms of polynomials, see the option TYPE=POLY and the POLY program. In addition the generalized VSCF property integrals, i.e. $\left < VSCF \left \vert q_i^r \right \vert VSCF \right >$ are printed. These integrals allow for the calculation of arbitrary vibrationally averaged properties once the property surfaces are available. Default: PRINT=0.
Surface information shall be read from the specified record. This must correspond to the record, to which the potential has been dumped in the SURF program. This option is only of importance within the calculation of vibronic spectra.
Polynomial and other information shall be read from the specified record. This must be the same record, to which the polynomials have been dumped in the POLY program. This option is only of importance within the calculation of vibronic spectra.
This specifies the record, where to dump the VSCF information. Usually this is the same record as specified in the START option. Note that the VSCF information is currently stored in the same record as the polynomial information.
INFO=1 provides a list of the values of all relevant program parameters (options).

The following input example for a grid based calculation of anharmonic frequencies and intensities on the VSCF level (1) optimizes the geometry of water, (2) computes the harmonic frequencies,(3) generates a potential energy surface around the equilibrium structure and (4) computes the nuclear wave function and the infrared intensities at the VSCF level. Vibrational angular momentum terms (VAM) are included. Note, that it is recommended to perform a VCI calculation after a VSCF calculation. The details of the VCI input are described in the next chapter 55.1.

O          0.0675762564        0.0000000000       -1.3259214590
H         -0.4362118830       -0.7612267436       -1.7014971211
H         -0.4362118830        0.7612267436       -1.7014971211


optg                                     !(1) optimizes the geometry
frequencies,symm=auto                   !(2) compute harmonic frequencies


{surf,start1D=label1,sym=auto            !(3) generate potential energy surface
vscf                                     !(4) do a VSCF calculation
put,irspec,irspec.gnu                    !writes a gnuplot file to plot an IR
                                         !spectrum of the VSCF calculation

molpro@molpro.net 2019-06-17