Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.     

Non-empirical calculations and basis set effects on the inversion geometry of the aniline molecule

The geometry of the amine group and the barrier to internal conversion in aniline have been studied by single-determinantab initio SCF calculations using several basis sets from minimal to double-zeta quality. The results obtained from different types and sizes of basis sets are discussed. Calculations performed with the two most flexible basis sets yield inversion barriers of 0.9–1.1 kcal/mole and angles of pyramidalization at the nitrogen atom of 38–39 ° which are in good agreement with the experimental results (1.3 kcal/ mole and 38 °). Orbital and overlap population analyses are performed and compared with the expected mesomeric and inductive effect. The calculated dipole moment 1.48–1.49 D also agrees with the experimental values (1.48–1.50 D).Dedicated to Professor O. E. Polansky, Mülheim/Ruhr, on the occasion of his 60th birthday.     

Nonempirical calculations of dipole moments of molecules in semifloating gaussian basis sets

For the example of the calculation of the dipole moments of the HF, HCl, H₂O, NH₃, CO, H₂CO, CH₃F molecules in two-exponent and three-exponent Gaussian basis sets, we have studied the effect of including floating functions in the basis, directly giving the effect of polarization of the electron shell of the atom in the molecule. We have established a weak dependence of the calculated dipole moment on the dimensionality of the basis, the number of floating functions, and also the orbital exponents of the hydrogen atoms. The correction introduced by the floating functions in molecules with polar bonds is considerably greater than the correlation correction. The proposed approach allows us to decrease the dimensionality of the orbital basis by a factor of 1.5–2 without making the agreement with experiment worse.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 4, pp. 481–485, July–August, 1990.     

Finite-field many-body perturbation theory. Calculations of the dipole polarizability of the fluoride ion using electric-field-variant gaussian-type orbitals

The dipole polarizability of the fluoride ion, F^–, is calculated using finite-field many-body perturbation theory. The use of electric-field-variant basis sets in such calculations is investigated. Scaling of the zero-order Hamiltonian and the formation of Padé approximants are considered. Empirical and theoretical estimates of the polarizability of F^– are compared.Science Research Council Advanced Fellow.     

Generalized Christoffel–Darboux formulae and the frontier Kohn–Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.     

Constrained anisotropic dipole oscillator strength distribution techniques,and reliable results for anisotropic and isotropic dipole molecular properties,with applications to H2 and N2

Summary Constrained anisotropic dipole oscillator strength distribution techniques are discussed and applied to obtain reliable results for a wide variety of the anisotropic and isotropic dipole properties of H₂ and N₂. These include the dipole oscillator strength sumsS _k, k=2, 1, –1/2(–1/2) –2, –3, –4, ..., the logarithmic dipole sumsL _k and mean excitation energiesI _k, k=2(–1) – 2, and, as a function of wavelength, the dynamic polarizability and the associated anisotropy, the total depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. The anisotropic components of the DOSD for a molecule are obtained from a given recommended isotropic DOSD by using a constrained least squares procedure and a series of known anisotropic constraints. Assuming that sufficient input is available, the constrained DOSD approach used in this paper is the only available method for the reliable evaluation ofall the relevant anisotropic and isotropic dipole properties for a wide variety of atoms and molecules.This research was supported by a grant from the Natural Sciences and Engineering Research Council of CanadaOn leave from Department of Physics, Meerut University, Meerut, India     

Application of quasi-degenerate perturbation theory to the description of potential curves and electronic excitation of molecules

The potential energy functions of the electronic states and the dipole moments of the electronic transitions of the A10 and AlC molecules have been calculated by second-order quasi-degenerate perturbation theory, using the intermediate Hamiltonian technique. Various means are considered for selecting the zero order approximation for the Hamiltonians of the model and intermediate sub-spaces. The results are compared with those obtained by the configuration interaction method. It is shown that this approach is an effective method for analyzing electronic transitions between states of the same symmetry type in the presence of pseudo-crossing of the electronic terms.Moscow University. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 1, pp. 11–16, January – February, 1991. Original article submitted July 21,1988.     

Acetamide, a challenge to theory and experiment? On the molecular structure, conformation, potential to internal rotation of the methyl group and force fields of free acetamide as studied by quantum chemical calculations

The molecular geometry has been optimized without any constraints using different basis sets and levels of theory as: Hartree-Fock with basis sets 6–31+G**, 6–311++G**, cc-pVTZ and aug-cc-pVTZ, MP2 with basis sets 6–311++G** and cc-pVTZ, MP3 with basis set 6–311++G**, and density functional theory with basis sets 6–311++G** and cc-pVTZ. Small basis sets up to 6-31G predict the syn conformation of the methyl group to be the most stable conformation. Larger basis sets predict an unsymmetrical conformation with one of the H atoms perpendicular to the amide skeleton or an anti-like conformation. Dunnings correlation consistent polarized valence triple zeta, cc-pVTZ, basis set including MP2 predict two conformations, one perpendicular and one anti to be the most stable. The DFT calculations predict anti-like conformations. The most accurate calculations predict anti-like conformations which have not been predicted previously. The vibrational frequencies have been calculated for several basis sets and compared to the observed frequencies. The wagging frequency of the NH₂ is very dependent on the basis sets and levels of theory. Most calculations predict a planar NH₂ group in agreement with experiment. A scaled molecular force field has been determined by fitting the calculated frequencies to the observed ones for the perpendicular conformation using MP2/cc-pVTZ. The barrier heights for the methyl group have been calculated. The rotational constants, I_A + I_B − I_C values and dipole moments are compared with experimental values.     

A Continuum Reaction Field Theory of Polarizable, Nondipolar, Quadrupolar Solvents: Ab Initio Study of Equilibrium Solvation in Benzene

A continuum theory to describe solvation in nondipolar quadrupolar solvents is developed by accounting for electronic polarizability. A general Hamiltonian for a solute–solvent system in an arbitrary nonequilibrium configuration is obtained in terms of two field variables—densities of the solvent quadrupole and induced dipole moments. Equilibrium solvation is studied by optimizing this Hamiltonian with account of cavity boundaries. As an application, electronic structures and free energies of small molecules in benzene are examined with ab initio methods. Solvation stabilization due to solvent quadrupole moments is found to be substantial; for the solutes considered here, it is comparable to and often in excess of that arising from solvent-induced dipole moments.     

Energy transfer and migration in highly forbidden transitions of lanthanide ion doped crystals

Förster–Dexter theory for resonant energy transfer is extended to higher order and applied to explain the rates of energy transfer and migration processes in highly forbidden transitions for some solid-state lanthanide (Ln) ion systems for which experimental results are available. The second-order two-body energy transfer mechanism involves two inter-ion correlated dipole electrostatic interactions, i.e. dipole dipole–dipole dipole (dd–dd) energy transfer, also termed Axe–Axe energy transfer in view of the similarity of the theoretical formalism with that for two-photon transitions. Each of the dipolar transitions consists of a transition from the 4fⁿ configuration to an opposite-parity configuration, taken to be 4fⁿ⁻¹5d. dd–dd energy transfer is a short-range (R⁻¹²) interaction so that it is most important in systems with short donor Ln–acceptor Ln separations. The energy transfer formalism is extended to include spin-forbidden transitions at one or two sites, the so-called Axe–Judd–Pooler (Axe–JP) and JP–JP energy transfer. In some cases the dd–dd mechanism is the dominant energy transfer process, as exemplified herein for energy migration in the ⁵D₀ state of Sm²⁺ in SrF₂, and also in the ⁵D₀ state of Eu³⁺ in Cs₂NaEuCl₆.     

Basis set effects on relative energies and HOMO–LUMO energy gaps of fullerene C36

Fifteen C₃₆ isomers were examined to determine the influence that the quality of basis sets has on the geometry parameters, the relative stability and HOMO–LUMO energy gaps of fullerene isomers calculated with density functional theory. It is worthwhile to note that the geometry parameters of all C₃₆ isomers are insensitive to basis sets. On the other hand, one set of d-type polarization functions plays an important role in evaluating relative stability and HOMO–LUMO energy gaps, while diffuse functions are not effective. To obtain reliable energies, at least a double-zeta plus polarization basis set is required, and a triple-zeta plus polarization basis set is suggested to lead to accurate energies at a reasonable computational cost.     

Density functional investigation of high-spin XY (X = Cr, Mo, W and Y = C, N, O) molecules

The performance of a density functional theory approach in calculating the equilibrium bond length, dipole moment, and harmonic vibrational frequency in a series of group 6 (Cr, Mo, W) transition metal-containing diatomic molecules is evaluated. Using flexible basis sets comprised of Slater type functions, a wide range of exchange-correlation functionals is investigated. Comparing with known experimental values and published results from high-level theoretical calculations, the most suitable functional form is selected. The importance of relativistic effects is checked, and predictions are made for several unknown dipole moments. The best agreement with experimental parameters is obtained when using a general gradient approximation, while special and hybrid functional forms give less accurate results.     

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Becke's original three-parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian-type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug-cc-pVTZ (UCC)]. The geometries and dipole moments of over 100 first-row and second-row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double-ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments. © 1997 by John Wiley & Sons, Inc.     

Effect of configurational composition of the wave function on calculated dipole polarizability of molecules

On the basis of the -electron approximation we have investigated the dependence of the calculated dipole polarizability of molecules on the configurational composition of the variational wave function. The values which were closest to the results of complex configurational interaction were obtained for sets including the single-determinant Hartree-Fock function and all the bonding doubly excited configurations constructed from the localized MO, and also from the complete set of singly and doubly excited configurations.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 26, No. 1, pp. 70–73, January–February, 1990.     

Spontaneous Polarization of Thin Water Films in Nonwettable Capillaries by the Data of Numerical Experiment

Abstract–Water films in the flat capillaries with ideal walls were simulated by molecular dynamics method. The profiles of local density and distribution functions of the dipole moment orientations, the directions of valence and H-H bonds were obtained. Profiles of local electric field and electric potential were calculated. Potential jumps at the water–vapor interface were estimated.     

UV, VUV and soft X-ray photoabsorption of dimethyl ether by dipole (e,e) spectroscopies

Absolute UV and VUV photoabsorption oscillator strengths (cross-sections) for the valence shell discrete and continuum regions of dimethyl ether (CH₃OCH₃, DME) have been measured from 5 to 32 eV using high resolution (HR) (0.05 eV f.w.h.m.) dipole (e,e) spectroscopy. A wide-range spectrum, spanning the UV, VUV and soft X-ray regions, from 5 to 200 eV has also been obtained at low resolution (LR) (1 eV f.w.h.m.), and this has been used to determine the absolute oscillator strength scale by employing valence shell Thomas–Reiche–Kuhn (i.e., S(0)) sum-rule normalization. The presently reported HR and LR absolute photoabsorption oscillator strengths are compared with previously published data from direct photoabsorption measurements in those limited energy regions where such data are available. Evaluation of the S(−2) sum using the presently reported absolute differential photoabsorption oscillator strength data gives a static dipole polarizability for dimethyl ether in excellent agreement (within 0.5%) with previously reported polarizability values. Other dipole sums S(u), (u=−1,−3,−4,−5,−6,−8,−10), and logarithmic dipole sums L(u), (u=−1 to −6), are also determined from the presently reported absolute differential photoabsorption oscillator strength data using dipole sum rules.