Jan Wasilewski

Coverage of dynamic correlation effects by density functional theory functionals: Density-based analysis for neon

The problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory (DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A density-based approach directly hinged on difference radial-density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basis-set incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)]. For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy- and density-based perspectives. They indicate the usefulness of density-based criteria for developing new exchange-correlation functionals.

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He2+ ground state and the six lowest excited states of He2 in the range of 1.4 a0 ≤R ≤ 3.5 a0. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He2 by Ginter, except for thec3∑g+ state. This latter discrepancy is probably due to an “obligatory” hump in thec3∑g+ state occurring at 3.5 a0 which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm−1. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He2 excited states which cannot be measured spectroscopically because of the humps in all these states.

Equilibrium structure and harmonic force field of the known PH3 and the unknown PH5

The equilibrium geometries and harmonic force fields of PH3 and PH5 are calculated in an ab initio way including electron correlation. The results for PH3 are in very good agreement with experimental values, whereas those for PH5 have to be regarded as predictions. We find for PH5 in its equilibrium D3h structure rax = 1.47 Å, req = 1.42 Å and the harmonic vibration frequencies in Table 7 given under the heading “CEPA”. The barrier for Berry inversion is 2 kcal/mol. The ab initio calculation of phosphoranes such as PH5 not only requires the inclusion of polarization functions (d on P and p on H) but is also very sensitive to the choice of these polarization functions. This problem is taken care of by a detailed comparison of various basis sets. It is confirmed that a (10/6) basis for P in “double zeta contraction” is better balanced than a (12/9) basis in “double zeta contraction” and that the total energy is not a good criterion for the quality of a basis.

Accurate MR CI studies of the N2 ground state

Abstract Extensive calculations of the ground-state energy of the N 2 molecule have been performed by means of the MC SCF and MR CI(SD) methods which are defined in terms of a 20-configuration reference space including all the configurations required for a correct description of the dissociation of the triple bond. The AO basis contained the 3d2flg polarization set. The whole potential curves have been obtained using the same approach. The calculations yields the lowest total energies and the most accurate results for D e ( = 9.629 eV) and R e ( = 2.078 au) obtained so far in extensive variational calculations. Further evaluation of the quality of our potential curves is made by comparing vibrational intervals, rotational constants and several spectroscopic constants with experimental values. A very satisfactory agreement has been found.

Density functional study of the S0 (X̃1Ag) and T1 (ã3Au) states of the glyoxal molecule

The density functional theory (DFT) calculations in different approximations have been performed for the geometries and vibrational states of the trans-glyoxal molecule in the ground state S0 (X1Ag) and in the lowest excited triplet state T1 (a3Au, n-pi* type). Eight typical combinations of exchange and correlation functionals have been used. Comparative Hartree-Fock (HF) calculations have also been performed. For the open shell a3Au state the standard spin-unrestricted Hartree-Fock and Kohn-Sham approaches (UHF, UKS) as well as the restricted open-shell versions (ROHF, ROKS) have been applied. The calculated frequencies have been compared, among others, with the data resulting from the most recent phosphorescence exicitation spectra of glyoxal cooled in the supersonic molecular beam, recorded with the cooperation of one of us (JH) for the spin-forbidden S0-T1 transition. The most realistic description of the vibrational frequencies, within the unscaled harmonic approximation, can be obtained using the 3-parameter Becke-93 exchange functional (B3), whereas this description practically does not depend on the correlation functional used. Our calculations support the recently reexamined experimental energy of the symmetric CH-rocking fundamental for the T1 state.

Lower vibrational states of SO2. Density functional and discrete variable representation approach

Abstract A set of lower vibrational levels of SO 2 ( 1 A 1 ) has been calculated with inclusion of anharmonic effects. The discrete variable representation of bending coordinate and a two-dimensional distributed Gaussian basis expansion for stretching coordinates have been used. Complete quartic force fields in three dimensions have been constructed, based on density functional theory (BLYP, B3LYP, B3PW91) and CASSCF(14/10) calculations. Our results indicate the B3LYP approach as the best one for reproduction of the observed vibrational excitation energies and a set of Dunham-type spectroscopic constants for the molecule studied.

Some remarks on the calculations of hyperfine splittings in the ESR spectra of conjugated radicals

Some consequences of non-orthogonality of the basic functions of LCAO approximation, on the relations used for calculations of hyperfine splittings in ESR spectra of conjugated radicals, are discussed. Special attention has been paid on the problem of transferability of the hyperfine coupling constants. The discussion is illustrated by some calculations of the hyperfine splittings for radical-ions of naphthalene, and tetracene.ZusammenfassungEinige Folgerungen aus der Nichtorthogonalität der Basis in der LCAO-Näherung für die Beziehungen, die für die Berechnung der Hyperfeinaufspaltung im ESR-Spektrum konjugierter Radikale benutzt werden, werden untersucht. Insbesondere wird die Frage der Übertragbarkeit der Hyperfein-kopplungskonstanten behandelt. Die Diskussion wird durch einige Berechnungen der Hyperfeinaufspaltung für die Radikalionen des Naphtalins und des Tetracens ergänzt.