Vibrational frequency shifts in NeHF and ArHF complexes

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function, additionally we can analyze the time evolution of the system. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.

Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

Analytical second derivatives in ab initio Hartree–Fock crystal orbital theory of polymers

The reaction of chlorine nitrate with hydrogen chloride catalysed by sulfuric acid molecules and by the hydrogen sulfate anion has been investigated by means of abinitio calculations at Hartree–Fock and MP2 levels of theory. Geometries of reactants, products and transition states have been optimized using 6-31G** and 6-31++G(2D,2P) basis sets. While the reaction barrier of the gas phase reaction does not decrease significantly with sulfuric acid, it vanishes completely if the hydrogen sulfate anion is involved. The reaction occurs in several associative steps which do not have a reaction barrier. Implications of the results for heterogeneous reactions in the stratosphere on sulfuric acid aerosol surfaces or in the bulk are discussed.

A b initio calculations of the static- and frequency-dependent dipole polarizability α and first and second hyperpolarizabilities β and γ of HCl are presented. Static polarizabilities are determined using the self-consistent field (SCF), second-order Mo/ller–Plesset perturbation theory (MP2), the coupled-cluster single and double excitation method (CCSD), and CCSD with a perturbative estimate of triple excitations [CCSD(T)]. The effect of basis set expansion, particularly the addition of diffuse functions up to g type, is explored. It is found that for highly accurate calculations, f functions are necessary on Cl, but g functions have a much smaller effect. The frequency-dependent hyperpolarizabilities for wavelengths of 694.3 and 1319 nm are determined at the SCF and MP2 levels of theory. The CCSD(T) static values, scaled using MP2 dispersion, are found to be in good agreement with experiment. Electron correlation is found to play a significant role in both the static and dynamic quantities. Use of the SCF dispersion as a percentage correction to the static MP2 hyperpolarizability, however, is found to be a good approximation to the total MP2 frequency-dependent hyperpolarizability at the frequencies studied. The effects of vibrational contributions to the polarizabilities are discussed.

On the structure of the 3B 1 excited state of water

Ionic liquids (ILs) hold great promise in many fields including energy storage and generation, mechanical, pharmaceutical, synthetic and separation applications to name just a few. For any given application, the desired physical properties of the ideal IL may differ substantially from others and no widely applicable patterns or trends to facilitate intuitive design. The origins of physical properties lie in the characteristics of the intermolecular energetics, which consist of a complex interplay between electrostatic and dispersion forces. This thesis investigates and develops computational methodologies for calculating a reliable description of the intermolecular interactions for this challenging class of solvents and electrolytes of the future. The electrostatic approximation used in classical molecular dynamics (MD) where atomic partial charges are assigned was investigated in terms of methods based on density matrix partitioning, and the restrained electrostatic potentials (RESP) approaches. It was found that the “geodesic” atomic partial charge scheme, part of the RESP family, produced the most accurate charges. This was measured in terms of (a) charge convergence with increasing basis set size; (b) charge invariance with changes to the coordinate system; (c) insensitivity to minor structural changes on the resulting charges; (d) adequate capture of charge transfer effects; and (e) the preservation of symmetric of charges in symmetric molecules. Although charges can vary dramatically depending on the scheme used, the careful use of atomic partial charge schemes may still produce reliable forcefields, or at least serve as a rapid diagnostic tool to quantify electrostatic interactions and charge transfer. In moving towards unbiased a priori descriptions of IL intermolecular interactions, second-order Moller-Plesset perturbation theory (MP2) was used with the linear-scaling fragment molecular orbital (FMO) framework to assess the extent to which dispersion forces play a role in the intermolecular energetics. ILs of increasing size were examined such that the many-body effects may be captured. The dispersion energy contribution formed up to 20% of the total interaction energy. Furthermore, the interaction energy as produced by FMO was within 1 kJ mol−1 of the full-wavefunction MP2 interaction energy when three-body effects were included. As the dispersion interaction is purely a quantum mechanical phenomenon, correlated quantum mechanical methods, such as MP2 or coupled-cluster approaches, are required to provide an unbiased account of these effects. Ab initio methods such as MP2 and CCSD(T) scale formally as N⁵ an N⁷, respectively, with chemical system size. While the FMO approach provides a marked improvement in efficiency, the counterpoise (CP) approach to correcting the basis set superposition error (BSSE) is not amenable to fragmented approaches and requires each ion in the cluster to be calculated in the basis set of the entire system. In order to remove this bottleneck, the spin-component scaled second-order Moller Plesset perturbation theory (SCS-MP2) methodology was refined by fitting 174 non-CP corrected interaction energies at the MP2/cc-pVTZ level of theory to CP corrected CCSD(T)/CBS benchmark energies. This has resulted in an implicit BSSE correction that may be used within the highly efficient FMO framework, and is shown to yield results on par with or exceeding the accuracy of MP2/cc-pVQZ for clusters of two and four ion pairs (IPs). This new approach as been termed SCS-IL-MP2. An alternative dispersion corrected density functional theory (DFT) approach, DFT- D3, was assessed and refined in view of producing accurate interaction energies at the same CCSD(T)/CBS quality. The same test set of 174 ILs was used to fit the SCS-IL-MP2 approach was used to refit the DFT-D3 approach for both the Hartree-Fock (HF) wavefunction and the PBE and BLYP density functionals (DFs). In most cases, the selection of the DF and associated DFT-D version 3 (DFT-D3) parameters differed negligibly with all reaching within 1 to 2 kJ mol−1 per IP. HF-D3 parameters, on the other hand, showed a substantial improvement, particularly when used with the Becke-Johnson (BJ) damping function. Refitted HF-D3 and the BJ damping function was able to consistently provide interaction energy errors below 5 kJ mol−1 per IP. It would be worthwhile further investigating the application of the refined HF-D3 in its ability to produce reliable energies and geometries over a more diverse set of ILs. Both the SCS-IL-MP2 and new DFT-D3 approaches may be applied to the highly scal- able FMO framework. These form the core elements of the quantum chemistry toolbox for the study and understanding of the physicochemical properties of ILs that have so far been only superficially characterised by electronic structure theory. From this starting point, a rigorous and unbiased a priori understanding of the intermolecular interactions and resulting physicochemical properties may be predicted by means of efficient ab initio molecular dynamics (AIMD) techniques.

Systematic evaluation of method and basis set on the structure and energetics of organocuprate(I) and organocopper(III) species has been carried out. Various structures of organocuprate(I) and organocuprate(III) complexes were optimized with the HF, MP2, and B3LYP methods, and compared with the structures determined by X-ray crystallography (i.e., Me(2)Cu(I)(-), (CF(3))(4)Cu(III)(-)). Both the MP2 and B3LYP methods reasonably reproduce the X-ray structures while the HF method does not. Using larger basis set and incorporating the relativistic effects for Cu afford the best results. In the studies on the energetics of a Libond;Cu cluster model (Me(2)CuLi. LiCl) and Me(3)Cu model with the MP2, MP3, MP4DQ, MP4SDQ, CCSD(T), and B3LYP methods, the B3LYP method gives energetics similar to those obtained with the CCSD(T) method with much less cost, and hence, is judged to be the best practical method. The studies have shown that B3LYP method with the basis set incorporating the relativistic effective core potentials for Cu and the 6-31G* basis set for the rest is the theoretical method that is the most cost-effective for the studies of the structure and energetics of organocuprate(I) and organocopper(III) species.

The potential energy surface (PES) of the water–formaldehyde complex has been examined using ab initio methods. Three energetically low-lying stationary points were located on the potential surface corresponding to one minimum and two transition states. All stationary points were examined using a double-ζ plus polarization (DZP) basis set at the self-consistent field (SCF), single and double excitation configuration interaction (CISD), and single and double excitation coupled-cluster (CCSD) levels of theory. In addition, the minimum was more thoroughly investigated through the use of the triple-ζ plus double polarization (TZ2P) basis set, the TZ2P plus higher angular momentum functions [TZ2P(f,d)] basis, and the TZ2P basis set augmented by a set of diffuse functions (TZ2P+diff) with those same theoretical methods. For each of the stationary points, geometrical parameters, absolute energies, classical binding energies, and zero-point vibrational energy corrections are reported. Additional information concerning the minimum includes vibrational frequencies and corresponding infrared intensities, as well as predicted vibrational frequency shifts of the intramolecular frequencies for the complex and its deuterium substituted isotopomers.

The optimum local-multiplicative exchange potential was found using as input the Hartree–Fock electron density, for the molecular systems: H2, LiH, HF, NH3, CH4, H2O, N2, CO, F2, C2H2 and C2H4. The Zhao and Parr method was used to obtain the local-multiplicative potential where the kinetic energy is minimized using a constrained-search formulation of density functional theory. Two orbital sets were compared, those obtained with the nonlocal Hartree–Fock potential and those obtained with the local-multiplicative potential, both sets yielding the same electron density. As expected, the highest occupied molecular orbital (HOMO) energy was similar in both orbital sets. In contrast, the virtual orbital energies, and in particular the lowest unoccupied molecular orbital (LUMO), exhibited considerable differences. The Hartree–Fock LUMO energy goes to zero in a complete basis set limit and to nearly zero with reasonably large basis sets (e.g., augmented triple zeta) with sufficient diffuse functions added. The LUMO provided by the local-multiplicative potential using the same large basis set goes to a bounded energy not equal to zero. The nonlocal Hartree–Fock potential generates a large gap between the HOMO and LUMO energies; this difference is equal to the negative of the HOMO energy at the complete basis set limit. Contrary to this behavior, the gap obtained with the local-multiplicative potential is a reasonable approximation to the lowest experimental vertical excitation energy. For some of the molecules tested, the ordering of the orbitals corresponding to the HF and local-multiplicative potential are different.

On the improvement of the gauge invariance in finite basis set coupled hartree—fock calculations of molecular magnetic properties

Infrared, and Raman spectra, conformational stability, normal coordinate analysis, ab initio calculations, and vibrational assignment of 1-chlorosilacyclobutane

We address the question of an appropriate choice of basis functions for the self-consistent field (SCF) method of simulation of the N-body problem. Our criterion is based on a comparison of the orbits found in N-body realizations of analytical potential-density models of triaxial galaxies, in which the potential is fitted by the SCF method using a variety of basis sets, with those of the original models. Our tests refer to maximally triaxial Dehnen gamma-models for values of $\gamma$ in the range 0<=gamma<=1. When an N-body realization of a model is fitted by the SCF method, the choice of radial basis functions affects significantly the way the potential, forces, or derivatives of the forces are reproduced, especially in the central regions of the system. We find that this results in serious discrepancies in the relative amounts of chaotic versus regular orbits, or in the distributions of the Lyapunov characteristic exponents, as found by different basis sets. Numerical tests include the Clutton-Brock and the Hernquist-Ostriker (HO) basis sets, as well as a family of numerical basis sets which are `close' to the HO basis set. The family of numerical basis sets is parametrized in terms of a quantity $\epsilon$ which appears in the kernel functions of the Sturm-Liouville (SL) equation defining each basis set. The HO basis set is the $\epsilon=0$ member of the family. We demonstrate that grid solutions of the SL equation yielding numerical basis sets introduce large errors in the variational equations of motion. We propose a quantum-mechanical method of solution of the SL equation which overcomes these errors. We finally give criteria for a choice of optimal value of $\epsilon$ and calculate the latter as a function of the value of gamma.

Raman and vibrational Raman optical activity (ROA) spectra have been calculated for three molecules: H2O2, CHDTF and CHDTOH. The effects of electron correlation on the ROA parameters of these relatively small systems have been investigated by means of the multiconfigurational self-consistent field (SCF) approach. A range of correlation-consistent basis sets has been used in the calculations. The basis set convergence of the calculated ROA parameters is fairly well achieved when sets of at least d-aug-cc-pVTZ quality are used. On the other hand, the aug-cc-pVDZ set seems to be sufficient for a qualitative analysis. Diffuse functions, possibly a double set, are essential to ensure a good quality of the calculated ROA spectrum. In most cases the sign and approximate magnitude of the ROA are correctly predicted at the SCF level, and the corresponding ROA spectra should be considered qualitatively accurate.

Three hydrogen‐bonded minima on the phenol‐water, C6H5OH—H2O, potential energy surface were located with 3–21G and 6–31G** basis sets at both Hartree–Fock and MP2 levels of theory. MP2 binding energies were computed using large “correlation consistent” basis sets that included extra diffuse functions on all atoms. An estimate of the effect of expanding the basis set to the triple‐zeta level (multiple f functions on carbon and oxygen and multiple d functions on hydrogen) was derived from calculations on a related prototype system. The best estimates of the electronic binding energies for the three minima are –7.8, –5.0, and –2.0 kcal/mol. The consequences of uncertainties in the geometries and limitations in the level of correlation recovery are analyzed. It is suggested that our best estimates will likely underestimate the complete basis set, full CI values by 0.1–0.3 kcal/mol. Vibrational normal modes were determined for all three minima, including an MP2/6–31G** analysis for the most strongly bound complex. Computational strategies for larger phenol–water complexes are discussed. © John Wiley &amp; Sons, Inc.