Viktor Szalay

The barrier to linearity of water

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, explicitly correlated (linear R12) techniques, and full configuration interaction (FCI) benchmarks, with basis sets ranging from [O/H] [3s2p1d/2s1p] to [8s7p6d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best possible value for the barrier to linearity of water. Attention is given to the degree of accord among extrapolations of conventional MP2, CCSD, and CCSD(T) energies to the complete basis set (CBS) limit and corresponding linear R12 schemes for these correlation methods. Small corrections due to one- and two-particle relativistic terms, core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC) have been incorporated. The final electronic (vibrationless) extrapolated barrier height of this study is 11 127±35 cm−1. Anharmonic force fields have been determined at the aug-cc-pCVTZ CCSD(T) level at equilibrium and at a linear reference geometry...

The standard enthalpy of formation of CH2

High-quality ab initio quantum chemical methods, including higher-order coupled cluster and full configuration interaction benchmarks, with basis sets ranging from [C/H] [4s3p1d/2s1p] to [9s8p7d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best technically possible value for the standard enthalpy of formation of X 3B1 CH2 and a 1A1 CH2. Careful extrapolations of finite basis MP2, CCSD, CCSD(T), and CCSDT energies to the complete basis set full configuration interaction limit plus inclusion of small corrections owing to relativistic effects, core correlation, and the diagonal Born–Oppenheimer correction results in the final extrapolated enthalpies of formation of this study, ΔfH0o(X 3B1 CH2)=390.45−0.64+0.68 kJ mol−1 and ΔfH0o(a 1A1 CH2)=428.10−0.64+0.68 kJ mol−1. The computed value for X 3B1 CH2 is in between the best two experimental results of 389.87±0.86 and 390.73±0.66 kJ mol−1. The elaborate calculations leading to these enthalpies of formation also resulted in accurate estimates of the ...

Variational vibrational calculations using high-order anharmonic force fields

A simple variational procedure, termed DOPI for discrete variable representation—Hamiltonian in orthogonal coordinates—direct product basis–iterative diagonalization, is described and applied to compute low-lying vibrational band origins (VBOs) of the triatomic systems H2O, CO2, and N2O, employing published empirical and theoretical sextic force fields. While in these cases no difficulties arise when quartic potentials are used, the limited range of applicability of 6th-order potentials presents difficulties for the variational determination of VBOs, in particular for the higher-lying bending states. For H2O, transformation of quadratic and quartic force fields from simple bond stretching to Simons–Parr–Finlan (SPF) coordinates results in computed VBOs deviating less from experiment. This, however, does not hold for the VBOs computed from the transformed sextic force fields where the two representations provide highly similar results. While use of empirical quartic and sextic force fields result in a much better reproduction of experimental VBOs than that of ab initio force fields, especially at higher (fifth- and sixth-) order the empirical force constants, obtained through different refinement procedures, do not correspond to the associated derivatives of the potential energy surface (PES). Rotational constants characterizing low-lying vibrational states have been evaluated as expectation values using inertia tensor formulas in the Eckart and principal axis frames. Only the Eckart axes should be used for these computations and they yield accurate vibrationally averaged rotational constants.

Discrete variable representations of differential operators

By making use of known properties of orthogonal polynomials the discrete variable representation (DVR) method [J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985)] has been rederived. Simple analytical formulas have been obtained for the matrix elements of DVRs of differential operators which may appear in the rovibrational Hamiltonian of a molecule. DVRs corresponding to Hermite, Laguerre, generalized Laguerre, Legendre, and Jacobi polynomial bases and to the Lanczos basis for Morse oscillator, that is, to basis sets often used in calculating rovibrational energy levels, have been discussed.

The generalized discrete variable representation. An optimal design

The generalized discrete variable representation, as opposed to the discrete variable representation, of a Hamiltonian is such that it can give accurate eigenvalues of the Hamiltonian even if non‐Gaussian quadrature points and weights are used in its construction. A new method of building up the generalized discrete variable representation of a Hamiltonian has been described and its properties have been analyzed. This new method appears to be optimal, meaning that no other design based on the same points, weights, and basis functions can be conceived which would give more accurate eigenvalues. Numerical calculations have revealed that, remarkable accuracy can be achieved even with general, non‐Gaussian quadrature points and weights.

General derivative relations for anharmonic force fields

The brace notation, introduced by Allen and Csaszar (1993, J. chem. Phys., 98 2983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

Ab initio torsional potential and transition frequencies of acetaldehyde

High-level ab initio electronic structure calculations, including extrapolations to the complete basis set limit as well as relativistic and diagonal Born-Oppenheimer corrections, resulted in a torsional potential of acetaldehyde in its electronic ground state. This benchmark-quality potential fully reflects the symmetry and internal rotation dynamics of this molecule in the energy range probed by spectroscopic experiments in the infrared and microwave regions. The torsional transition frequencies calculated from this potential and the ab initio torsional inverse effective mass function are within 2 cm(-1) of the available experimental values. Furthermore, the computed contortional parameter rho of the rho-axis system Hamiltonian is also in excellent agreement with that obtained from spectral analyses of acetaldehyde.

On one-dimensional discrete variable representations with general basis functions

The method of discrete variable representation (DVR) is based on standard orthogonal polynomial bases and the associated Gaussian quadratures. General basis functions correspond either to nonpolynomial expressions or to nonstandard orthogonal polynomials. Although one cannot directly relate any Gaussian quadrature to general basis functions, the DVR-like representation derivable with such basis sets via the transformation (diagonalization) method is, as proved here, of Gaussian quadrature accuracy. The optimal generalized DVR (GDVR) is an alternative to and entirely different from this DVR-like representation. Yet, when built from the same general basis functions and the corresponding quadrature points obtained by the diagonalization method, the two representations are found to give almost identical numerical results. The intricate relationship between the optimal GDVR and the transformation method is discussed.

Symmetry analysis of internal rotation

Research papers and textbooks addressing the problem of internal rotation in a molecule explain symmetry properties of the torsional potential by local geometrical symmetries of the molecule. It is shown here that symmetry properties of a torsional potential derive from permutation inversion symmetry and a peculiar nature of torsional dynamics but have no relation to actual geometrical symmetries. To confirm the validity of our symmetry analysis a minimum energy torsional potential curve has been determined ab initio for acetaldehyde, resulting in exact 2π/3 periodicity that no previous ab initio calculations achieved.

Further extension of the Hougen-Bunker-Johns model

Abstract The method of Hougen, Bunker, and Johns is developed into a unified theory for molecules with one large amplitude internal motion. Examples show how the Nielsen and Hecht-Dennison transformation formulae and also the Hougen-Bunker-Johns formulae for rigid or semirigid large amplitude bending, inversion, and puckering motions follow as special cases from the theory outlined here. The author believes that this theory can also be useful for molecules with more than one large amplitude internal motion. Treating the trimethylene oxide molecule, an example is given for the calculation of effective mass function of small ring molecules.