On the effect of molecular structure on the superposition of normal modes of vibration

The normal modes of vibration in cartesian coordinates were calculated for ethylene, C₂H₄, and an ethylene complex, C₂H₄-Tl³⁺-H₂O, which is presumably formed during the catalytic oxidation of C₂H₄. For the CC bond of C₂H₄ as the critical coordinate of this reaction the distortions were then calculated which are caused by superimposing the normal modes. These calculations indicate that the maximum distortion of the CC bond which is attainable by superimposing normal modes in their ground state is larger in some conformations of the complex than in the free molecule. This indicates the general possibility that, depending on proper symmetry, complex formation may increase the reactivity of a compound because, compared to the free molecule, the superposition of a greater number of 3N-6 normal modes can produce greater momentary distortions of internal coordinates. The effect could be of considerable importance for the reactivity of very large systems, like, e.g., enzyme-substrate complexes.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

New vibrational self-consistent field program for large molecules

A recently developed, general computer program that performs vibrational self-consistent field (VSCF) calculations for large molecules is described. The program, which we refer to as VSCF―95, requires as its only input a force field in mass-scaled normal coordinates. Currently, it is limited to a maximum of 200 normal modes, and the force field is limited to coupling terms involving a maximum of six normal modes, with a maximum order of six in any normal mode. As output the program returns VSCF energies for specified quantum states. We illustrate the code with two new applications. The first is to HCO, for which we use a full sixth-order force field. The second is to a model of the fullerene, C₆₀, for which we have calculated a 75,731-term force field, which includes all anharmonic terms up to fifth order, and all two-mode coupling terms up to fourth order. © 1996 by John Wiley & Sons, Inc.     

Pressure and temperature effects on the vibrational frequencies of crystalline polymethylenes. I. Infrared-active rocking modes

The energy level dispersion, along the chain wave vector, of infrared-active methylene rocking modes has been measured as a function of pressure to 40 kbar for a number of polymethylenes. They are crystalline polyethylene and n-paraffins C₂₃H₄₈, C₂₄H₅₀, C₂₈H₅₈, and C₂₉H₆₀. The crystalline factor-group splitting of each chain mode is observed at various pressures, for those polymethylenes which have orthorhombic or monoclinic structures. The effects of crystal structure, intermolecular force field and intramolecular force field on the observed energy levels as well as on the crystalline factor-group splittings are discussed A hydrogen–hydrogen nonbonded repulsion potential has been calculated as a function of interatomic distance r_H??H for 2.3 Å < r_H??H < 3.0 Å from the observed volume dependence of the factor-group splittings of methylene rocking modes. It is shown that the dynamic potential wells along the normal coordinates of the rocking modes are harmonic up to room temperature.     

Extensions and tests of “multimode”: a code to obtain accurate vibration/rotation energies of many-mode molecules

We describe extensions and tests of the code “multimode” which does vibrational self-consistent field method (VSCF) and two types of state-mixing (denoted VSCF-CI and V-CI) for rovibrational energies of many-mode systems. The extensions include an exact treatment of rotation, flexible approaches to perform the CI calculations, and the inclusion of a Davidson diagonalization routine to find low-lying eigenvalues of large matrices. The code is tested against previous exact variational calculations for non-rotating H₂CN, and J=0 and J=1 rovibrational states of H₂CS. The code represents the full potential by a hierarchical n-mode representation, where n is the number of normal coordinates that are coupled together. Tests are presented for the convergence and accuracy of this representation for n equal to 3 and 4, where 4 is the current maximum value. These tests are done at the VSCF and V-CI level, with very encouraging results. Received: 8 June 1998 / Accepted: 11 August 1998 / Published online: 19 October 1998     

Theory of Stereomutation Dynamics and Parity Violation in Hydrogen Thioperoxide Isotopomers 1,2,3HSO1,2,3H

We present quantitative calculations of the mode‐selective stereomutation tunneling and parity violation in chiral hydrogen thioperoxide (‘oxadisulfane') isotopomers XSOY with X, Y=H, D, and T. The torsional tunneling stereomutation dynamics are investigated with a quasi‐adiabatic channel quasi‐harmonic reaction path Hamiltonian approach, which treats the torsional motion anharmonically in detail and all remaining coordinates as harmonic (but anharmonically coupled to the reaction coordinate). We predict how stereomutation is catalyzed or inhibited by excitation of various vibrational modes compared to the corresponding stereomutation dynamics of the vibrational ground state. Parity‐violating potentials were calculated with our recent multiconfiguration linear response (MC‐LR) approach in the random phase approximation (RPA). We find that, in agreement with general scaling expectations, the parity‐violating energy difference for the equilibrium structures of the two HSOH enantiomers (ca. 5×10^?12J mol^?1) is situated intermediate between HOOH and HSSH. Our results on the stereomutation dynamics and the influence of parity violation on these are discussed in relation to investigations for the analogous molecules H₂O₂, H₂S₂, and Cl₂S₂. As expected in XSOY (X, Y=H, D, and T), this influence is much larger than in the corresponding H₂O₂ isotopomers, but smaller than in H₂S₂ or Cl₂S₂.     

Analysis of bonding properties in molecular ground and excited states by a Cohen-type bond order

We propose a Cohen-type bond order analysis in terms of orthogonalized atomic basis functions which can be used to analyze NDO wave functions of large organic and metal–organic molecules. It is shown that for small molecules the results gained with this method are in excellent agreement with the same analysis based on ab initio STO -3G wavefunctions. For large planar aromatic systems these all-valence electron bond orders are found to be a consistent generalization of the π-bond order. A simple relation between these bond orders and the corresponding covalent bond energies is established. The method can be easily extended to study excited state multiconfiguration wave functions. We present calculations for C₂H₂, C₂H₄, C₂H₆, and Mn₂(CO)₁₀. The results indicate that the method can be used to discuss the photochemistry of organic and metal–organic compounds.     

Spectra and structure of organophosphorus compounds: XVII. Infrared and Raman spectra. vibrational assignment and barriers to internal rotation for t-butylphosphine

The infrared spectra of gaseous and solid tertiary-butylphosphine, [(CH₃)₃CPH₂], have been recorded from 50 cm^?1 to 3500 cm^?1. The Raman spectra of gaseous, liquid and solid (CH₃)₃CPH₂ have been recorded from 10 to 3500 cm^?1. A vibrational assignment of the 42 normal modes has been made. A harmonic approximation of the methyl torsional barrier from observed transitions in the solid state gave a result of 4.22 kcal mol^?1 and 3.81 kcal mol^?1 in the gaseous state. Hot band transitions for the phosphino torsional mode have been observed. The potential function for internal rotation about the C-P bond has been calculated. The two potential constants were determined to be: V₃ = 2.79 ± 0.01 kcal mol^?1 and V₆ = 0.07 ± 0.01 kcal mol^?1.     

Determination of mechanisms of the ν1(H–F) band shape formation in the absorption spectra of H-bonded complexes of HF from combined experimental studies and nonempirical calculations

The advantage of combining the spectroscopic experiments and nonempirical calculations in one study is discussed. Based on the results of earlier studies of H-bonded complexes H₂O⋯HF, dimethyl ether⋯HF, and acetone⋯HF and the study of HCN⋯HF performed in this paper, the requirements on the experimental conditions and theoretical approaches that can provide reliable spectroscopic data are generalized for the first time. Detailed recommendations on using the proposed theoretical method in multidimensional anharmonic calculations of other related AH⋯B complexes are also formulated. Comparative analysis of the data calculated for the four complexes shows for the first time that the intensity of shoulders of the ν₁(H–F) band (sum and difference transitions) is governed primarily by perturbations of the wave functions of low-frequency modes.     

Structure and conformation in molecular peroxides

Molecular structures and energies have been calculated in the MINDO approximation for fifteen neutral and anionic peroxides: fully optimized torsional potential functions have been calculated for twelve of these, and torsional potential functions, subject to constrained optimizations, for a further two peroxides. Bond dissociation energies D(R₁O—OR₂) were also calculated. Equilibrium structures and energies were calculated for the polyoxo species H₂O_n, HO_nF, F₂O_n, HO_n and FO_n (n ? 4), and a complete set of bond dissociation energies derived for H₂O_n, HO_nF, and F₂O_n.     

Model calculations of the vibrations of bonded water molecules

Model calculations have been made of the vibrational frequencies and normal modes of a water molecule vibrating in a combined internal and external field. A constant internal force field has been used together with an external central force field from four or three nearest-neighbour atoms to the water molecule. These neighbour atoms have been arranged either tetrahedrally or trigonally around the water molecule. The external force field has been further restricted by the use of five possible site symmetries for the water molecule, C_2v, C₂, C_s(σ_xz, C_s(σ_yz) and C₁. A series of calculations have been made where the external force constants have been varied within the range 1—80 Nm^?1.The nine calculated normal modes can be divided into three groups: intra-molecular, rotational and translational vibrations. Among the rotational vibrations it is found that, in the tetrahedral environment, the rocking mode occurs at lower frequencies than the twisting and wagging modes, whereas the opposite occurs for the trigonal environment. Frequency ratios have been calculated using the isotopic species H₂O, D₂O, HDO and H,¹⁸O. The twisting and wagging modes have the vH₂O/vD₂O ratio in the range 1.35-3-1.41 and the rocking mode in the range 1.26—1.41.     

Spectral effects of the clusterization of greenhouse gases: Computer experiment

Autocorrelation functions of the total dipole moment of clusters composed of H₂O and N₂O molecules are calculated in terms of the molecular dynamics method. The IR absorption and reflection spectra of systems composed of (H₂O)_i, N₂O(H₂O)_i, and (N₂O)₂(H₂O)_i clusters (2 ≤ i ≤ 20) are obtained on the basis of these functions. Frequency-dependent dielectric permittivity of clusters increases after the absorption of N₂O molecules. The absorption coefficient of cluster systems with trapped N₂O molecules increases at low frequencies and decays at frequencies ω > 500 cm^?1. The inclusion of N₂O molecules increases also reflection coefficient R and changes the pattern of R(ω) spectra. The absorption of IR radiation increases with the number of H₂O molecules in clusters. Dielectric losses also increase with an increase in i number upon the absorption of N₂O molecules. The number of electrons interacting with an incident electromagnetic wave increases upon the capture of N₂O molecules.     

Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (k_H/k_D?=?1.075, 368?K) agrees well with the measured value (k_H/k_D?=?1.06, 368?K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the H_ZPE, H_vib, and S_vib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.     

Potential energy surfaces for van der waals complexes of rare gases with H2S and H2S2: Extension to xenon interactions and hyperspherical harmonics representation

This article is an account and extension of a series of recent investigations, which using extensive quantum chemical methods provide analytical hyperspherical representations of the potential energy surfaces for the interactions of rare gases with H₂S as a rigid molecule, and H₂S₂, considered as a floppy molecule with respect to torsional mode. For the H₂S‐rare gas systems, the representation is based on a minimal model, here introduced and discussed. For H₂S₂, the study of the interaction with Xe, not considered previously, completes the series. The results are discussed with reference to the properties and trends expected for interactions of van der Waals type. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Range relaxation

The first of three integral forms of the quantum mechanical variational principle is described and a method introduced for the simultaneous optimisation of the whole of a molecular energy curve, or surface, generated for some adiabatic change. Dimensionless parameters in the wavefunction are expressed as functions of the coordinates and the integral of the energy over the whole surface is minimised with respect to variations in these functions. An integral form of the Virial Theorem is proposed as a test that the wavefunction is in scale for the whole range. A preliminary application is made to the H ⁺₂ , H₂ and He₂ systems.

     

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.     

The role of the torsional potential in relaxation dynamics: a molecular dynamics study of polyethylene

The role of the torsional potential in bulk polymer chain dynamics is investigated via molecular dynamics simulation using polyethylene as a model system. A number of three-fold barrier values, both greater and less than the standard one, were invoked. The one-fold potential that determines the gauche vs trans energy difference was also varied. For each of the selected torsional potentials, the MD volumetric glass transition temperature, T_g, was located. It was found that T_g is quite sensitive to the three-fold barrier magnitude, moving from below 100 K to nearly 400 K as the barrier goes from zero to twice the standard value. However T_g was found to be quite insensitive to the gauche trans energy difference. Details of the conformational dynamics were studied for the case of a zero torsional potential. This included the rate and location of conformational transitions, the decay of the torsional angle autocorrelation function (ACF) and the cooperativity of conformational transitions, all as a function of temperature. The temperature dependence of the conformational transition rate remains Arrhenius at all temperatures. The relaxation time characterizing the torsional angle ACF decay exhibits WLF temperature behavior. The conformational transitions are randomly distributed over the bonds at high temperature, but near T_g they become spatially heterogeneous and localized. The transitions show next-neighbor correlation as well as self-correlated forward-backward transitions. All of these features are similar to those found in previous simulations under the standard torsional potential.     

Generalized quantum mechanical two-centre problems

For the one-electron Schrödinger equation among the solutions of which the Slater-Zener-type functions can be found, it is shown, that it can be generalized to the two-centre case only in one way, if one demands separability in prolate spheroidal coordinates, and if in addition to the Coulomb term of the potential energy there shall be an additional function of the product r ₁ · r ₂ only. The generalized problem with a potential energy of the form V(r) = ? Z₁/r₁ ? Z₂/r₂ ? Q(R)/r₁r₂ is studied for the case of two equal centres Z ₁=Z₂=Z≧0 with regard to the existence and number of bound states. The results are extended as far as possible also to the case with unequal centres. For some examples with equal centres wave functions and correlation diagrams have been computed exactly for the lowest electronic states.