The vibrational bound states of isomerising disilyne.

Full-dimensional variational calculations are reported for the isomerising disilyne molecule, Si2H2. Large-scale calculations using coordinates based on orthogonal satellite vectors permitted the computation of excited vibrational state energies and wavefunctions for all four isomeric forms: dibridged Si(H2)Si, monobridged Si(H)SiH, disilavinylidene H2SiSi, and trans-bent HSiSiH. Energies and wavefunctions have been determined for the lowest 2400 totally symmetric vibrational states; this set includes highly excited states above all three chemically relevant isomerisation barriers--up to about 8300 cm(-1) above the (dibridged) ground state. States strongly localised in the dibridged, monobridged, and disilavinylidene regions of the potential energy surface have been found as well as many partially or fully delocalised states. For the trans-bent form, only partially localised states have been identified. Comparisons are made with similar literature calculations on the isovalent acetylene-vinylidene system HCCH/H2CC.

Computational Studies of Bridging Structures and Isomerism in Substituted Disilynes.

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).

The potential energy surface of isomerising disilyne.

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 50 000 symmetrically unique molecular geometries. Of these ab initio points, 33 000 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.

Infrared spectra of CF(2)=CHD and CF(2)=CD(2): scaled quantum-chemical force fields and an equilibrium structure for 1,1-difluoroethylene.

Infrared (IR) spectra in the gas phase are reported for CF(2)=CHD and CF(2)=CD(2) in the region 350-4000 cm(-1). Ab initio calculations of an harmonic force-field and anharmonicity constants have been made with an MP2/aug-cc-pVTZ model. These enable a number of Fermi resonances in each species to be analyzed and a complete set of "observed" harmonic frequencies to be derived. The latter are combined with similar data for CF(2)=CH(2) in a scaling of the model harmonic force field to both anharmonic and harmonic frequencies. Inspection of the scale factors reveals minor defects of the model, evident in the out-of-plane wagging modes and in the CF stretch/CF stretch interaction force constant. Fermi resonance treatments involved in all isotopomers studied are compatible with the overall force-field refinement results. The treatment leaves a small anomaly in the (13)C shift on nu(1). Improved microwave spectra are reported for five isotopic species, and a semiexperimental equilibrium structure for F(2)C=CH(2) is determined and compared favorably with the structure obtained from new high-level ab initio calculations. Centrifugal distortion constants are predicted for the five isotopic species, and those for F(2)C=CH(2) are compared with values fit to microwave spectra.

Infrared spectra of (12)CF(2)=(12)CH(2) and (12)CF(2)=(13)CH(2), quantum-chemical calculations of anharmonicity, and analyses of resonances.

Infrared spectra obtained in gas and liquid argon phases are reported for (12)CF(2) horizontal line(12)CH(2) and (12)CF(2) horizontal line(13)CH(2). These spectra firmly establish the positions of nu(3)(A(1)) and nu(6)(A(2)) for both isotopomers. Using anharmonicity constants from MP2 calculations, Fermi resonances affecting nu(1)(A(1)), nu(2)(A(1)), nu(3), and nu(8)(B(1)) are analyzed. Deperturbed fundamental frequencies from these analyses are used in conjunction with unaffected fundamentals and ab initio anharmonicity data to predict all 12 "observed" harmonic frequencies. A Darling-Dennison type resonance between 2nu(6) and nu(11) + nu(12) is diagnosed, the calculation of which from ab initio data requires modification of the existing second-order treatment of such constants, where Fermi resonance type terms are also present. Predictions are made of many overtone and combination band frequencies, aiding assignment of observed spectra. From the isolated CH stretching frequency obtained here of 3125.4 cm(-1), the C-H equilibrium bond length is predicted to be 1.0762(11) A.

Vibrational anharmonicity and harmonic force fields for dichloromethane from quantum-chemical calculations.

Anharmonic and related constants have been calculated for CH2Cl2, CD2Cl2, and CHDCl2 by using the program Gaussian03 and B3LYP and MP2 models. Bases used were 6-311++G** and cc-pVTZ. The size of grid used in the B3LYP/6-311++G** model had a noticeable effect on resulting data. Features of the MP2/6-311++G** calculations suggested a deleterious effect of the absence of f functions in this basis set. The need for the replacement of second-order terms in the perturbation theory formulas for the vibrational anharmonic constants x ij in the presence of Fermi resonance was explored, and minor resonances were found associated with the cubic constants varphi 122 and varphi 299 (d 0 isotopomer), phi122 and phi849 (d2), and phi278 (d1). Computed xij values for nuCH and nuCD motions agree quite well with earlier experimental data. Observed anharmonic frequencies, nu obsd, were corrected to "observed" harmonic frequencies, omega obsd, by using computed differences Delta = omegaQC-nuQC. These differences Delta are larger for the antisymmetric nuasCH2 mode than for symmetric nusCH2 motion. This fact made it necessary to use differing scale factors for the two kinds of CH stretching force constants in a subsequent scaling of the harmonic force field to nuobsd. Force field scaling was also carried out by refining to omega obsd. In both approaches, the B3LYP models required differing scale factors for symmetric and antisymmetric CCl stretching force constants, indicating a failure to compute an accurate C-Cl stretch-stretch interaction force constant. The MP2/cc-pVTZ force field was preferred. Both scaled and unscaled harmonic force fields were used to calculate centrifugal distortion constants (CDCs) and contributions to the vibrational dependence of the rotational constants (alphas). Variations in the CDCs can, in part, be explained by the magnitudes of the frequencies used in the scaling process.

Scaled quantum chemical force fields for 1,1-difluorocyclopropane and the influence of vibrational anharmonicity.

Potential functions and harmonic (omega(i)) and anharmonic (nu(i)) fundamental frequencies have been calculated for 1,1-difluorocyclopropane (DFCP) and its d4 and d2 isotopomers using the program Gaussian 03. B3LYP and MP2 models were employed, each with the bases 6-311++G** and cc-pVTZ. Anharmonicity corrections Delta(i) = omega(i) - nu(i) are listed and shown to be different for symmetric and antisymmetric CH stretching modes in situations where Fermi resonance appears to be absent. The same effect is missing in C2H4, for which similar calculations were made. The quadratic force fields for DFCP have been scaled in symmetry coordinate space with 15 scale factors both to observed frequencies nu(obsd)and also to omega (obsd), where omega(obsd) = nu(obsd) + Delta. With nu(obsd) especially, different scale factors are needed for the symmetric and antisymmetric CH stretching force constants due to their differing anharmonicities. The source of the latter in the quartic and cubic force field is explored. MP2 calculations of valence interaction force constants involving the stretching of bonds on a common carbon atom are preferred to those from a B3LYP model. In either model, scaling to omega(obsd) rather than to nu(obsd) does not remove the necessity of varying scale factors for differing types of motion in the same group. Theoretical values of the five quartic centrifugal distortion constants are listed for the normal species and compared with new experimental data. The predictions are sufficiently good to be useful in fitting pure rotational transitions. A weakness is identified in the current Gaussian 03 code for the calculation of vibration-rotation quantities, and limitations are noted in the manner in which Fermi resonance is handled.

General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I.

New internal coordinate gradients, s-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.

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II.

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F 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 CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) 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 CH(3)F system.

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene.

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.