VIBrational CAlculations

        The core of this program was written by Patrick Fowler in the early 80's. In 1989 it was handed to me for further development, when the range of calculated spectroscopic observables was considerably extended.

        The program is limited to the harmonic formulation of the vibrational problem (i.e. only the quadratic force field) and allows calculation of:

  • vibrational frequencies
  • eigenvectors (which can be displayed with VECTOR)
  • various matrices associated with the vibrational problem: B, G, L, and PED (Potential Energy Distribution) matrices
  • Coriolis coefficients
  • quartic centrifugal distortion constants in several reductions of the rotational Hamiltonian
  • harmonic contributions to moments of inertia
  • experimental values of both moments of inertia and centrifugal distortion constants can be brought into the calculation

        VIBCA requires input of force field in internal coordinates, but itself works via mass-weighted Cartesian coordinate type of calculation as described in W.D.Gwinn, J.Chem.Phys. 55, 477 (1971), which avoids the problems inherent in the definitions of symmetry coordinates brought in by the associated reduntant coordinates.

        The main input consists of atomic coordinates, internal coordinate declarations and force constant values. Input deck can either be created by hand, or most usefully, can be generated by means of program FCONV from an appropriate ab initio calculation carried out with the package GAMESS.

        NEW: VIBCA has been extended to deal with up to 100 atoms with associated improvements in readability of output. The PED calculation has also been upgraded as the previously oversimplified version was prone to some spurious results.

VIBCA.FOR The listing - it is recommended that extension .VIB be used for the data files
VIBCA.EXE Win32 executable (VIBCA is a straightforward console program so that the executable can be generated with any contemporary FORTRAN compiler)
MENC.VIB Input file for methyl isocyanide, created from the data in J.L.Duncan et al, J.Mol.Spectrosc. 76, 55 (1979). The force field in the paper is in symmetry coordinates, and the force constants in internals required by VIBCA were generated with FCONV
MENC.RES Output from the above - in comparing with the data in the paper note that you have to compare with the (not explicitly tabulated) calculated values, such as with w-e in Table III.
ANIDFT.VIB Data set for anisole derived with FCONV from B3LYP/6-31G(d,p) calculation performed with PC-GAMESS
ANIDFT.RES VIBCA results file for the data set above, as reported in PCCP 7, 1708-1715 (2005); 7, 2080 (2005)

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Force Constant cONVersions

        This program will carry out the following conversions:

  • internal to symmetry force constants
  • symmetry to internal force constants
  • output from a GAMESS force field run into a VIBCA input deck

        The first two options require declaration of the U matrix and appropriate instructions can be found at the top of the listing.

        FCONV has recently been used almost exclusively as a GAMESS to VIBCA converter, and the H2O example below gives a complete trace of this type of calculation: from ab inito input deck to spectroscopic observables.

        The success of the GAMESS to VIBCA conversion depends on the declaration of internals in GAMESS. Even though GAMESS and VIBCA recognise a common standard set of internals, such declarations are often not straightforward, and some practice is necessary. In general you can be certain of successful conversion only once the calculated vibrational frequencies from GAMESS and VIBCA are in complete agreement.

FCONV.FOR The listing. Note that output will be written to two files: FC.RES and FC.VIB.

For conversion from GAMESS the output file FC.VIB will contain a complete input deck for VIBCA, while for symmetry<->internal force field conversions FC.VIB will contain only a part of the necessary VIBCA deck, namely force constant values and declarations of the potential terms

FCONV.EXE Win32 executable (FCONV is a straightforward console program so that the executable can be generated with any contemporary FORTRAN compiler)
  Symmetry <-> Internal force constants
MENC.F Data for methyl isocyanide necessary for the symmetry->internal force field conversion
FC1.RES The FC.RES file for the above
  GAMESS to VIBCA conversion
H2O.INP GAMESS input deck for calculation of vibrational frequencies of water at the aug-cc-pVDZ/MP2 level.

Note that both a more accurate vibrational calculation and its successful conversion by FCONV are ensured by the following choice of keywords in the $FORCE group:


H2O.OUT Abbreviated GAMESS output for the run above
H2O.VIB VIBCA deck generated automatically by FCONV from the output above
H2O.RES VIBCA output with H2O.VIB as input, compare frequencies with those in H2O.OUT

Try changing isotopic masses in H2O.VIB and compare calculated quartic c.d. constants against Table 8.25 in Gordy&Cook, while remembering that water is a particularly challenging molecule. Note that the bottom lines predict ground state inertial defect of 0.0466, to compare with exptal value of 0.0515 uA**2.

For more rigid, heavier molecules the experimental quartics may be expected to be reproduced/predicted to an accuracy of about 10%. See, for example, results for pyrimidine in J.Mol.Spectrosc. 195, 332 (1999).


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Graphical display of normal coordinate displacement vectors calculated with VIBCA

        This program will graphically display eigenvectors (normal coordinate displacement vectors) calculated with VIBCA by using the option IFVCT=1. The program is derived from PMIFST and works similarly. The previewed eigenvectors can be:

  • toggled through
  • rotated
  • scaled
  • reversed
  • plotted as mass weighted/unweighted
  • NEW: output for the gle program, which allows generation of PostScript, PDF, JPEG etc. publication-quality diagrams
        The development of VECTOR has been on standby since 2001 because there are many excellent programs currently available for displaying normal modes.  Two examples are  MOLDEN and MacMolPlt, both of which will animate modes.  On the other hand there are some features in VECTOR that still make it useful, so that it has recently been upgraded to be more compatible with contemporary versions of Windows and multi-monitor desktops.

VECTOR.FOR The listing, intended for compilation with Intel Visual Fortran 9 or later.
VECTOR.EXE Executable resulting from compilation with IVF9.1. 

Key properties of the graphics, i.e. window size and the display font are now read from the configuration file PMIFST.CFG as used by PMIFST. The PMIFST.CFG file should be placed in the directory C:\ROT. 

VECTOR_MSF5.FOR Listing of the legacy version for Microsoft Fortran 5.  The issues associated with this are discussed separately.
VECTOR_MSF5.EXE Executable from compilation with MSF5 and VGA graphics. It will run on all versions of DOS/WIN which allow full screen MS-DOS mode. Memory requirements of this program (about 250 kB of low DOS memory) are minimal and shouldn't cause any problems.
SNAP1.GIF Snapshot of VECTOR screen for one of the symmetric CH stretching modes in cyclohexane (IVF version).
SNAP2.GIF Snapshot of VECTOR screen for the H2O...HCl stretching mode in the (H2O)2HCl trimer (MSF5 version).

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Energies, eigenvectors and vibrational transitions for a reduced, one-dimensional anharmonic potential

        This is a simple predictive program for the reduced anharmonic potential of the form

V(z) = A ( c2 z2 + c3 z3 + c4 z4 + c6 z6),

which has been most often used in the reduced quartic-quadratic form

V(z) = A ( z4 + B z2)

for double minimum inversion potentials, in which case B is negative. z is a dimensionless coordinate which can be related to the molecular internal coordinate of interest. In the quartic-quadratic form the barrier height is A B2/4, the minima are at -B/2, and two assigned vibrational spacings are sufficient to obtain a good idea of the potential. The matrix elements printed by the program can also be used to set up the dependence of various spectroscopic constants on the vibrational quantum number. A useful description of the reduced quartic-quadratic potential is given in J.Laane, Applied Spectroscopy 24,73-80(1970).

       The original version of this program was developed by Johan Mj÷berg and used, for example, in P.J.Mj÷berg, J.Alml÷f, Chem.Phys. 29,201-208(1978). In that paper the quadratic term is positive and a cubic term is also used.

The program expects to find the data in file ANHARM.INP and writes output to file ANHARM.OUT.

ANHARM.FOR The listing
ANHARM.EXE Executable for Windows 95+ compiled with CVF6 (this is a straightforward console application, so that it can also be compiled with any contemporary FORTRAN compiler)
ANHARM2007.EXE Executable with corrected handling of the z6 term
ANHARM.INP Input file, this contains several example data sets, the results for which can be compared against published data
ANHARM.OUT Output for thietane (trimethylene sulfide). Check frequencies and relative intensities against Table I of T.R.Borgers, H.L.Strauss, J.Chem.Phys. 43,947(1966).

Additional information:

Tables of eigenvalues and expectation values of the quartic-quadratic oscillator as originally produced with ANHARM (can be compared tables in the Laane,1970 paper)
chapter_2.5.pdf Description o the background and some molecular examples of the quartic-quadratic oscillator (see Fig.2.3)

Additional applications:
  • Isotopic scaling of the reduced quartic-quadratic potential and citations of some relevant papers:  Kisiel, Krasnicki, Jabs, Herbst, Winnewisser, Winnewisser, J.Phys.Chem A, 117, 9880-9808(2013)
  • Use of ANHARM and the reduced quartic-quadratic potential for placing energy levels on an ab initio calculated potential surface: Kisiel, Pietrewicz, Fowler, Legon, Steiner, J.Phys.Chem A, 104, 6970-6978 (2000)

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