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576. General Vibrational Analysis System
by Douglas F. McIntosh and Michael R. Peterson, Department of Chemistry, Lash Miller Chemical Laboratories, University of Toronto, 80 St. George St., Toronto, Ontario, Canada M5S 1A1 This package of 4 FORTRAN programs has been designed to allow the user a simple and reliable method for generating a complete vibrational analysis using the GF matrix method of Wilson, Decius and Cross (1). The analysis may be done using either an unsymmetrized or a symmetrized basis set. This new set is meant to be a replacement for our original publication, "General Vibrational Analysis Programs Utilizing The Wilson GF Matrix Method for a General Unsymmetrical Molecule" (QCPE 342). The Wilson methodology requires the definition of a basis set which will be used to construct the normal coordinates. These programs allow for the definition of unsymmetrized or symmetrized basis sets, referred to as Internal and Symmetry Coordinates, respectively. These are related to Cartesian Coordinates via the B and U Matrices through the following relationships: R = BX S = UR = UBX = BSymX where R, S and X represent column vectors of the Internal, Symmetry and Cartesian Coordinates, respectively. The BSym Matrix, which is the product of the U and B Matrices, is referred to as the "Symmetry Adapted B Matrix". Using B or BSym we may determine the Inverse Kinetic Energy Matrices, G and GSym: G = BM1Bt GSym = (BSym)M-1(BSym)t = UMB-1BtUt where the superscript "t" indicates "transpose" and the M-1 is a diagonal matrix which contains the inverses of the masses of the atoms (included 3 times each to account for motions along the x, y and z directions). Using the G or GSym Matrix, the Vibrational Secular Equation may be formulated in either an unsymmetrized or a symmetrized fashion: GFL = Ll GSymFSymLSym = LSym l The problem reduced to the determination of the eigenvector (L or LSym ) and the eigenvalue (l) matrices. The four programs included in this package are: (1) UMAT (Vibrational Analysis Program 1) This is a multi-functional program which is intended to "set-up" the entire analysis. It may be used to: (i) Predict the symbolic form of the Potential Energy (IFF) Matrix (ii) Calculate Orthonormal Symmetry Coordinates (Symmetry Adapted Linear Combinations of Internal Coordinates) (iii) Output the Symmetry Adapted B Matrix (BSym) in a format suitable for input to Programs 2 and 3 (iv) Symmetrize F and IFF to yield the FSym and IFSYM Matrices, the latter being the block-diagonalized, symbolic form of the Potential Energy Matrix Included with the UMAT program are a number of data files which contain the necessary information for a large number of symmetry point groups: Non-Axial Groups: Ci and Cs Axial Groups: Cn and S2n(n = 1 to 8) Cnh and Cnv (n = 2 to 8) Dihedral Groups: Dn, Dnh and Dnd (n = 2 to 8) Cubic Groups: T, Th, Td, O and Oh Icosahedral Groups: I and Ih The Linear Groups, C v and D h, may be conveniently handled by running either C2v or C4v for the former and D2h or D4h for the latter (see documentation for further details). (2) BMAT (Vibrational Analysis Program 1A) This is a modification of the GMAT program of J. H. Schachtschneider (8). BMAT generates an unsymmetrized B Matrix and outputs it in a format suitable for input to Programs 2 and 3. Like UMAT, it allows for the calculation of the following types of Internal Coordinates: (i) Bond Stretch, (ii) Valence Angle Bend, (iii) Out-of-Plane Wag, (iv) Torsion and (v) Linear Bend. Two major innovations have been included in BMAT, namely, Hilderbrandt's normalization of the Torsional Coordinate (9) and the new formulae of McIntosh, Michaelian and Peterson for the Out-of-Plane Wag (10). BMAT is included as a subroutine in the UMAT program, which is intended as its replacement. It is included in the package for those users who prefer to run unsymmetrized basis sets (i.e., internal coordinates) and because of its utility in producing the Bd Matrix (for Root-Mean-Square Amplitude calculations). (3) FTRY-ATOM-RMSA-INTY (Vibrational Analysis Program 2) Program 2 is the "heart" of the package. It is also multi-functional and may be run in one of 4 modes: (i) The FTRY Option will produce the complete set of frequencies for a series of isotopically related molecules. This option may be repeatedly run to manually refine the molecule's General Quadratic Force Field and obtain a better fit between the calculated and observed frequencies. (ii) The ATOM Option will yield a Normal Coordinate Analysis for the first molecule, only, of this series (included are the (a) Eigenvector (L), (b) Potential Energy Distribution (POT), (c) Atomic Displacements (AA) and the (d) Root-Mean-Square Amplitude (äR, äX, äd) Matrices). (iii) The RMSA Option allows the user an alternate method of calculating the R.M.S. Amplitudes of Vibration. (iv) The INTY Option generates the Infrared Intensities of the frequencies of the series of isotopically related molecules. This is based on a point charge model and yields only approximate values. All intensities are ratioed against the largest value (which is arbitrarily assigned a value of 10.00). (4) FFIT (Vibrational Analysis Program 3) Program 3 utilizes the SIMPLEX optimization algorithm of Nelder and Mead (7) to refine the best-guessed force constants via a non-linear least-squares analysis between the calculated and observed frequencies. FORTRAN 77 (VAX) Lines of Code: 6309 |