VSCF,options [vscf]

The VSCF program is exclusively based on the Watson Hamiltonian \begin{align} \hat{H} = \frac{1}{2} \sum_{\alpha\beta} ( \hat{J}_\alpha - \hat{\pi}_\alpha) \mu_{\alpha\beta} (\hat{J}_\beta - \hat{\pi}_\beta) -\frac{1}{8}\sum_\alpha \mu_{\alpha\alpha} -\frac{1}{2}\sum_i \frac{\partial^2}{\partial q_i^2} + V(q_1,\dots,q_{3N-6}) \label{eq:1} \end{align} in which the potential energy surfaces, $V(q_1,\dots,q_{3N-6})$, are provided by the XSURF module. The Watson correction term and the 0D term of the vibrational angular momentum terms are by default (VAM=2) included. As VSCF calculations are extremely fast, these calculations cannot be restarted. For details see:

J. Meisner, P.P. Hallmen, J. Kästner, G. Rauhut, Vibrational analysis of methyl cation - rare gas atom complexes: CH$_3^+$-Rg (Rg=He, Ne, Ar, Kr), J. Chem. Phys. 150, 084306 (2019).
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 following options are available:

• AVERAGE=n By default state-specific VSCF calculations will be performed. AVERAGE=1 allows for configuration averaged VSCF calculations, i.e. CAVSCF. The averaging will be performed for those states being defined by the VIBSTATE program. The vibrational ground state will always be excluded. An identical weight factor will be used for all states, i.e. the inverse of the number of states.
• BASIS=variable BASIS=DGB (default) defines a mode-specific basis of distributed Gaussians and 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. BASIS=HO defines a harmonic oscillator basis. Using this basis together with MAXITER=0 and VAM=0 provides a simple harmonic oscillator basis to be used in all subsequent programs, e.g. in the VCI program.
• INFO=n INFO=1 provides a list of the values of all relevant program parameters (options).
• MAXITER=n This key sets the maximum number of iterations to be performed in the VSCF program.
• MUPLOT=n 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 POT=POLY. The VAM option has to be set accordingly.
• NBAS=n 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=18 for a basis of distributed Gaussians, while its is NBAS=16 for a harmonic oscillator basis. This option is only active once an analytical representation of the potential has been chosen, see the option POT and the POLY program.
• NDIM=n The expansion of the potential in the VSCF calculation can differ from the expansion in the XSURF calculation. However, only values less or equal to the one used in the surface calculation can be used.
• NDIMDIP=n Term after which the $n$-body expansions of the dipole surfaces shall be truncated. The default is set to 3. Note that NDIMDIP has to be lower or equal to NDIM.
• NDIMPOL=n 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.
• ORTHO=n 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 default is ORTHO=1.
• POT=variable VSCF solutions can be obtained using a potential in grid representation, i.e. POT=GRID, or in an analytical representation, POT=POLY, POT=BSPLINE, POT=GAUSS. In the latter case the POLY program needs to be called prior to the VSCF program in order to transform the potential.
• PRINT=n This option provides an extended output. PRINT=1 prints the vibrationally averaged rotational constants for all computed states and the associated vibration-rotation constants $\alpha$. Moreover, the temperature dependence of bond lengths will also be printed, when the potential is represented by a linear combination of basis functions. PRINT=2 prints the effective 1D polynomials in case that the potential is represented in terms of polynomials, see the option POT=POLY and the POLY program. In addition the generalized VSCF property integrals, i.e. $\left < VSCF \left | q_i^r \right | VSCF \right >$ are printed. These integrals allow for the calculation of arbitrary vibrationally averaged properties once the property surfaces are available. Default: PRINT=0.
• SADDLE=n 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 the VSCF program by using SADDLE=1. Currently, the VSCF program can only handle symmetrical double-minimum potentials.
• SOLVER=n 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).
• THERMO=n 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.
• THRBASOVLP=value Overlap between two Gaussian basis functions, once BASIS=DGB has been chosen. The default is 0.75.
• THRLINDEP=value Threshold for eliminating linear dependencies in the VSCF procedure (see keyword BASIS=DGB). The default is THRLINDEP=1e-8.
• VAM=n 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. \eqref{eq:1}) as a pseudo-potential like contribution to the fine grid of the potential (grid version only). Once an analytical representation of the potential is used, the consideration of the Watson correction term is controlled in the POLY program.
• VAM=2 accounts for the 0th order terms of an n-mode expansion of the $\mu$-tensor within the VSCF iterations.
• VAM=3 does not include any VAM terms in the VSCF iterations, but instead accounts for them in the VMP1 energy correction.
• VAM=4 truncates the expansion of the effective moment of inertia tensor after the 1D terms (rather than the 0D term in case of VAM=2 or VAM=3). These terms are only included in the VMP1 energy correction. 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.
• WFPRINT=n This key allows for the printing of the effective potentials and of the n lowest modals. The corresponding gnuplot files will be dumped into the directory plotwf.

The following input example for a polynomial based calculation of anharmonic frequencies and intensities at the VSCF level (1) optimizes the geometry of water, (2) computes the harmonic frequencies,(3) generates a potential energy surface around the equilibrium structure, (4) transforms the grid points to polynomials and (5) 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 the VCI program (VCI).

memory,20,m
basis=vdz
orient,mass
geometry={
3
Water
O          0.0675762564        0.0000000000       -1.3259214590
H         -0.4362118830       -0.7612267436       -1.7014971211
H         -0.4362118830        0.7612267436       -1.7014971211
}

mass,iso

hf
mp2
optg                                     !(1) optimizes the geometry
frequencies,symm=auto                    !(2) compute harmonic frequencies

label1
{hf
start,atden}
{mp2
cphf,1}

{xsurf,sym=auto                          !(3) generate potential energy surface
intensity,dipole=2}
poly                                     !(4) transform to polynomials
vscf,pot=poly                            !(5) do a VSCF calculation

DISK,options

The DISK directive allows to specify explicitly, from where the potential information shall be taken and where it shall be stored to disk. This can also be accomplished in an automated manner. 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.

The following options are available:

• AUTO=n Rather than using the options START and SAVE one may simply assign a label n to a certain PES and all the records will be set automatically.
• SAVE=record 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.
• START=record 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.

VIBSTATE,options [vibstate]

The VIBSTATE program allows to specify the vibrational states to be calculated in the following vibrational SCF and vibration correlation programs. Within the input stream, the VIBSTATE program needs to be called prior to the first call of the VSCF program. By default, the fundamental modes of the molecule are calculated only. In order to define the list of states to be calculated, the following keywords are available:

• COMBI=n 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.
• UBOUND=value The upper energy limit for the generated states is controlled by the keyword UBOUND, i.e. states, for which the harmonic estimate is larger than value, will not be computed. The default is set to 5000 cm$^{-1}$.
• LQUANT=n If the molecule of interest belongs to a non-Abelian point group, real linear combinations of complex basis functions can be used as startvectors for the VCI calculation by setting LQUANT=$1$. For symmetric top molecules the default is LQUANT=$1$ and LQUANT=$0$ for asymmetric top molecules. By using this option, also the mapping between real and complex coordinates will be given in the output.
• VSTATEONLY= n Once additional vibrational states have been defined by using the VSTATE directive, the VSCF program can be forced to compute just these states by the option VSTATEONLY=$1$. Note that the vibrational ground state will always be computed and needs not to be specified explicitly.
• IRREP=string By setting IRREP=string, only states defined by the keywords COMBI, UBOUND, LQUANT and userdefined states via the VSTATE directive with the chosen irreducible representation (irrep) are calculated. Depending on the point group of the molecule, the following irreps are available: A, A, A, A1, A1, A1, A2, A2, A2, Ag, A1g, A2g, Au, A1u, A2u, B, B1, B2, B3, Bg, B1g, B2g, B3g, Bu, B1u, B2u, B3u, E, E, E, E1, E1, E1, E2, E2, E2, Eg, E1g, E2g, Eu, E1u, E2u, T, T1, T2, Tg, T1g, T2g, Tu, T1u, T2u.

VSTATE,options
By this directive, userdefined vibrational states can be defined. It specifies the occupation number vector of the vibrational state to be calculated. If only those vibrational states shall be computed, which are defined by the  VSTATE, VSTATEONLY=$1$ in the VIBSTATE program has to be set.

• MODE(n)=m The $n$th mode of the molecule is supposed to have the quantum number m. If several modes are excited, the option can be repeated accordingly, e.g. VSTATE,MODE(1)=3,MODE(3)=2,MODE(6)=2. All other modes are not excited and thus have the quantum number 0.
• LQUANT(n)=m For symmetric top and linear molecules the specification of the quantum number $l$ is supported by the keyword LQUANT. With LQUANT(n)=l the $n$th mode is supposed to have the quantum number $l$ corresponding to the angular momentum. The occupation number must be set by the keyword MODE(n). E.g., VSTATE,MODE(3)=2,LQUANT(3)=2. All $l$-quantum numbers not set will have a value of zero. Note that this option can only be used for degenerate mode pairs. The counting of modes in this context belongs to the complex representation.
memory,20,m
basis=vdz
orient,mass
geometry={
3
Water
O          0.0675762564        0.0000000000       -1.3259214590
H         -0.4362118830       -0.7612267436       -1.7014971211
H         -0.4362118830        0.7612267436       -1.7014971211
}

mass,iso

hf
mp2
optg                                     !(1) optimizes the geometry
frequencies,symm=auto                    !(2) compute harmonic frequencies

label1
{hf
start,atden}
{mp2
cphf,1}

{vibstate,vstateonly=1                   !(3) only user defined states shall be computed
vstate,mode(3)=1}                            the fundamental of mode(3) shall be computed
{xsurf,sym=auto                          !(4) generate potential energy surface
intensity,dipole=2}
poly                                     !(5) transform to polynomials
vscf,pot=poly                            !(6) do a VSCF calculation

EXCLUDE,options
By this directive, user defined vibrational states can be excluded from the generated list of states. The state to be skipped is defined via MODE as described in the context of the directive VSTATE.