One-electron properties of molecules calculated using second-order multireference perturbation theory

A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.     

g-tensor theory for strongly distorted octahedral low-spind 5 complexes

Using the crystal-field theory (CFT), we derive equations for the low-spin d⁵ configuration in the case of an arbitrary ligand field including the configuration interaction correction. Experimental ESR and electronic absorption spectral data of some octahedral Ru(III) and Os(III) complexes with a strong tetragonal distortion are analyzed. It is shown that the contribution of the spin-orbit term of the configuration interaction may be considerably suppressed due to the strong covalency of the σ-bond. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 1, pp. 31–48, January–February, 1994. Translated by L. Smolina     

Perturbational relativistic theory of electron spin resonance g-tensor

We carry out a complete treatment of the leading-order relativistic one-electron contributions, arising from the Breit-Pauli Hamiltonian, to the g-tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the F2(-), Cl2(-), Br2(-), and I2(-) series, using analytical response theory calculations with a multiconfigurational self-consistent field reference state. The results are compared to available experimental data. (c) 2004 American Institute of Physics     

Exact decoupling of the Dirac Hamiltonian. IV. Automated evaluation of molecular properties within the Douglas-Kroll-Hess theory up to arbitrary order

In Part III [J. Chem. Phys. 124, 064102 (2005)] of this series of papers on exact decoupling of the Dirac Hamiltonian within transformation theory, we developed the most general account on how to treat magnetic and electric properties in a unitary transformation theory on the same footing. In this paper we present an implementation of a general algorithm for the calculation of magnetic as well as electric properties within the framework of Douglas-Kroll-Hess theory. The formal and practical principles of this algorithm are described. We present the first high-order Douglas-Kroll-Hess results for property operators. As for model properties we propose to use the well-defined radial moments, i.e., expectation values of r(k), which can be understood as terms of the Taylor-series expansion of any property operator. Such moments facilitate a rigorous comparison of methods free of uncertainties which may arise in a direct comparison with experiment. This is important in view of the fact that various approaches to two-component molecular properties may yield numerically very small terms whose approximate or inaccurate treatment would not be visible in a direct comparison to experimental data or to another approximate computational reference. Results are presented for various degrees of decoupling of the model properties within the Douglas-Kroll-Hess scheme.     

Efficient configuration selection scheme for vibrational second-order perturbation theory

A fast algorithm of vibrational second-order Moller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm(-1).     

Application of second-order SCF perturbation theory to the calculation of mixed-frequency hyperpolarizabilities from time-dependent Hartree-Fock theory

Second-order SCF perturbation theory is used to solve the TDHF equations of Dalgarno and Victor through the introduction of frequency dependent density matrices. Exploratory calculations are reported for the frequency dependent polarizability and hyper-polarizability of LiH.     

One-electron versus electron-electron interaction contributions to the spin-spin coupling mechanism in nuclear magnetic resonance spectroscopy: analysis of basic electronic effects

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. (1)J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas (2)J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of (1)J(C,H) and (2)J(H,H), respectively, for hydrocarbons.     

Self-consistent second-order screening in many-body theory

Self-consistent screening arises in all many-body problems where one-particle equations containing functionals of the solutions are considered. In the theory of simple metals, e.g., these one-particle equations are usually solved to second-order perturbation in the crystal pseudopotential and to first order in the screening. However, higher-order screening terms have a sizable effect on the form factors, the electron charge density, and the screened pseudopotential. The effects of second order are presented for the bcc simple metals Na and Ba. A nonlocal exchange-correlation potential has been used since local density approximations such as ρ^1/3 cause difficulties in the electron–electron dielectric function. © 1994 John Wiley & Sons, Inc.     

Atomic approximation to the projection on electronic states in the Douglas-Kroll-Hess approach to the relativistic Kohn-Sham method

We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n相似文献   

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001     

Accounting for translational invariance in analyzing contributions of perturbation theory to force-constant tensors of molecules

It has been shown that there are an infinite number of modes of representation of force constants in the form of a sum of the contributions of first-order and second-order perturbation theory, depending on the selection of the admixture of translation of the nuclear skeleton as a whole to the displacement of the nuclei. In particular, any force constant can be reprsented in the form of a specially constructed second-order relaxation term (or first-order with zero contribution); a representation has been found in which the first-order contributions for the displacements of all nuclei in the molecule are identical; rules of the sums for the relaxation terms have been derived, relating the changes in the Gel-Mann-Feynman forces on the nuclei in the molecule with displacements of various nuclei. For the electronic ground state of the molecule, the optimal representation of the force constants has been found, in which the minimum in the first-order contribution is combined with the minimum in the absolute magnitude of the second-order relaxation contribution. It has been proven that in the case of an unperturbed electronic state, the first-order contribution to any diagonal force constant is positive.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 3, pp. 280–287, May–June, 1985.     

Application of second-order SCF perturbation theory to the solution of time-dependent Hartree—Fock equations

The self-consistent field based theory of frequency-independent hyperpolarizabilities is adapted to the treatment of the corresponding frequency-dependent quantities. Explicit expressions are given for the double and null frequency polarizations of a molecule in a long-established oscillating electric field.     

Dual-basis second-order Moller-Plesset perturbation theory: A reduced-cost reference for correlation calculations

The resolution-of-the-identity (RI) approximation has placed the onus of the cost of a second-order Moller-Plesset (MP2) calculation on the underlying self-consistent field (SCF) calculation for many moderately sized molecules. A dual-basis approach to the SCF calculation, based on previous methods demonstrated for density functional theory, is combined with RI-MP2 calculations, and small basis subsets for cc-pVTZ, cc-pVQZ, and 6-311++G(3df,3pd) are presented. These subsets provide time savings of greater than 90%, with negligible errors in absolute and relative energies, compared to the associated full-basis counterpart. The method is tested with a series of rotational barriers, relative conformational energies of alanine tetrapeptides, as well as the full G3/99 molecular set. RI-MP2 calculations on alanine octapeptides (40 heavy atoms, 3460 basis functions), using cc-pVQZ, are presented. Results improve upon previous methods that diagonalize the virtual space separately.     

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.Contribution to the Jacopo Tomasi Honorary Issue     

Dilated Weyl theory applied to a set of N-coupled singular second-order differential equations

Weyl's theory for a set of N-coupled singular second-order differential equations is analyzed in relation to S-matrix theory and a dilated version is presented. Applications of this theory to two single channel scattering model problems and a two-channel model problem are given. Some implications of the present theory are discussed.