The substituted disilyne molecules, Si2Li2 and Si2HX, where X = Li, F, and Cl, have been investigated using the high-level CCSD(T) and CCSD(T)-F12 ab initio methods. The calculations have found or confirmed the existence of several isomeric forms and transition states for each molecule. Optimized geometries, relative energies, and harmonic vibration frequencies are reported. Bridging structures exist in all cases. Comparisons are made with existing literature results for the related Si2H2, C2X2, and C2HX isomerizing systems. Additionally, CCSD(T) and CCSD(T)-F12 calculations were performed for Si2H2, for which experimental spectroscopic data are available. Results calculated with CCSD(T)-F12 and the cc-pVTZ-F12 basis set are of comparable quality as those computed with CCSD(T) and the much larger cc-pV(6+d)Z basis set, at much less computational cost. We recommend the CCSD(T)-F12/cc-pVTZ-F12 level of theory as a very attractive alternative to conventional CCSD(T).

A (semi-)global, analytical potential energy surface is reported for the ground electronic state of the isomerising disilyne molecule, Si2H2. The surface reproduces well ab initio energies calculated at the CCSD(T) level with a cc-pV(Q+d)Z basis set for over 50000 symmetrically unique molecular geometries. Of these ab initio points, 33000 were used in a least-squares fit to determine the parameters of the analytical surface and the remainder to provide an independent test/validation set. The fitted surface includes: the four known isomeric forms of disilyne, dibridged, monobridged, disilavinylidene and trans-bent; the three most important transition states and four other critical points. The surface reproduces accurately existing experimental spectroscopic data for the dibridged and monobridged isomers and predictions are made for the disilavinylidene and trans-bent forms. The surface has the correct symmetry properties with respect to permutation of like atoms and is suitable for detailed dynamics studies of the isomerising Si2H2 system. Also reported is a systematic investigation of the critical points using the CCSD(T) and MRCI methods and basis sets up to 6-zeta quality: the effects of core-correlation, augmentation with diffuse functions and tight-d functions have been studied. The basis sets include the correlation consistent core-valence, cc-pCV(n+d)Z, basis sets recently developed by Yockel and Wilson [Theor. Chem. Acc., 2008, 120, 119]. Very good agreement is obtained between the theoretical and experimental equilibrium geometries, rotational constants and three available vibration frequencies for the dibridged isomer and for the rotational constants of the monobridged isomer. Multireference character, as measured by the T1 diagnostic, is found to vary significantly across the 12 critical points investigated.

New internal coordinate gradients, -vectors, are derived using geometric algebra. The internal coordinates are based on a completely general description of the molecular geometry in terms of internal vectors. The internal coordinate gradients allow kinetic energy operators to be easily expressed in terms of orthogonal or non-orthogonal coordinate systems. Using this approach, a new exact vibrational kinetic energy operator for centrally-connected penta-atomic systems is derived for an internal polyspherical coordinate system based on orthogonal internal vectors. Difficulties associated with the well known coordinate redundancy in centrally-connected penta-atomic systems are discussed and overcome.

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH3F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH3F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH3F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY3Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C3v symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch–bend calculations of the vibrational energy levels of the CH3F system.

Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Comparison of the two methods is presented in the context of evaluation of matrix elements in a non-direct product basis. If high accuracy of all matrix elements is required then the expansion method is the best choice. If however the accuracy of high order matrix elements is not important (as in variational ro-vibrational calculations where one is typically interested only in the lowest eigenstates), then the method based on the reduced grid offers sufficient accuracy and is much quicker than the expansion method.

A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom–diatom and orthogonal satellite vectors. The method includes all six vibrational dimensions plus three rotational dimensions. Vibration–rotation calculations with reduced dimensionality in the radial degrees of freedom are easily tackled via constraints imposed on the radial coordinates via the input file.Program summaryTitle of program: WAVR4Catalogue number: ADUNProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUNProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: Persons requesting the program must sign the standard CPC nonprofit use licenseComputer: Developed under Tru64 UNIX, ported to Microsoft Windows and Sun UnixOperating systems under which the program has been tested: Tru64 Unix, Microsoft Windows, Sun UnixProgramming language used: Fortran 90Memory required to execute with typical data: case dependentNo. of lines in distributed program, including test data, etc.: 11 937No. of bytes in distributed program, including test data, etc.: 84 770Distribution format: tar.gzNature of physical problem: WAVR4 calculates the bound ro-vibrational levels and wavefunctions of a tetraatomic system using body-fixed coordinates based on generalised orthogonal vectors.Method of solution: The angular coordinates are treated using a finite basis representation (FBR) based on products of spherical harmonics. A discrete variable representation (DVR) [1] based on either Morse-oscillator-like or spherical-oscillator functions [2] is used for the radial coordinates. Matrix elements are computed using an efficient Gaussian quadrature in the angular coordinates and the DVR approximation in the radial coordinates. The solution of the secular problem is carried through a series of intermediate diagonalisations and truncations.Restrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can be practically diagonalised; (2) The DVR approximation for a radial coordinate fails for values of the coordinate near zero—this is remedied only for one radial coordinate by using analytical integration.Typical running time: problem-dependentUnusual features of the program: A user-supplied subroutine to evaluate the potential energy is a program requirement.External routines: BLAS and LAPACK are required.References:[1] J.C. Light, I.P. Hamilton, J.V. Lill, J. Chem. Phys. 92 (1985) 1400. [2] J.R. Henderson, C.R. Le Sueur, J. Tennyson, Comp. Phys. Comm. 75 (1993) 379.

A (semi-)global, analytical potential energy surface is reported for the ground electronic state of the isomerising disilyne molecule, Si2H2. The surface reproduces well ab initio energies calculated at the CCSD(T) level with a cc-pV(Q+d)Z basis set for over 50000 symmetrically unique molecular geometries. Of these ab initio points, 33000 were used in a least-squares fit to determine the parameters of the analytical surface and the remainder to provide an independent test/validation set. The fitted surface includes: the four known isomeric forms of disilyne, dibridged, monobridged, disilavinylidene and trans-bent; the three most important transition states and four other critical points. The surface reproduces accurately existing experimental spectroscopic data for the dibridged and monobridged isomers and predictions are made for the disilavinylidene and trans-bent forms. The surface has the correct symmetry properties with respect to permutation of like atoms and is suitable for detailed dynamics studies of the isomerising Si2H2 system. Also reported is a systematic investigation of the critical points using the CCSD(T) and MRCI methods and basis sets up to 6-zeta quality: the effects of core-correlation, augmentation with diffuse functions and tight-d functions have been studied. The basis sets include the correlation consistent core-valence, cc-pCV(n+d)Z, basis sets recently developed by Yockel and Wilson [Theor. Chem. Acc., 2008, 120, 119]. Very good agreement is obtained between the theoretical and experimental equilibrium geometries, rotational constants and three available vibration frequencies for the dibridged isomer and for the rotational constants of the monobridged isomer. Multireference character, as measured by the T1 diagnostic, is found to vary significantly across the 12 critical points investigated.