Hartree-Fock Perturbation Theory Research Articles

Semiempirical, Hartree-Fock, density functional, and second order Moller-Plesset perturbation theory methods do not accurately predict ionization energies and electron affinities of short- through long-chain [n]acenes

Semiempirical, Hartree-Fock, density functional, and second order Moller-Plesset perturbation theory methods do not accurately predict ionization energies and electron affinities of short- through long-chain [n]acenes

Dirac–Hartree–Fock Perturbation Calculation of Magnetic Shielding Using the External Field-Dependent Restricted Magnetic Balance Condition

Abstract A formulism for four-component Dirac–Hartree–Fock perturbation theory using the restricted magnetic balance (RMB) condition with gauge-including atomic orbitals (GIAOs) is derived at an ab initio level. In this formulation, the zeroth-order Dirac–Hartree–Fock equations are subject only to the usual restricted kinetic balance (RKB) condition, while the external field-dependent RMB condition is introduced in the calculation of the first-order magnetically perturbed orbitals. The magnetic shielding can be divided into a paramagnetic part and a diamagnetic part, as for nonrelativistic (NR) shielding. The present theory is applied to the calculation of hydrogen halide and molecular halogen shieldings.

Rydberg states of the helium atom

AbstractUsing the recently introduced maximum overlap method and Hartree–Fock Perturbation Theory (HFPT), we compute Hartree–Fock (HF) wavefunctions for triplet 1s ns states of the helium atom. Comparison with near‐exact results from Nakatsuji's free ICI method reveals that HF theory provides a simple route to accurate energies of these Rydberg states, especially for large n. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

The extremely flat torsional potential energy surface of oxalyl chloride

The conformational behavior of oxalyl chloride has been investigated using ab initio Hartree-Fock (HF) and second-order Moller-Plesset (MP2) perturbation theories, and the coupled-cluster singles and doubles method appended with a perturbative inclusion of connected triple excitations [CCSD(T)]. Correlation consistent polarized valence quadruple-zeta (cc-pVQZ) and quintuple-zeta (cc-pV5Z) basis sets were used in this research. At the cc-pVQZ and cc-pV5Z HF levels, there is no stationary point corresponding to a stable gauche conformer. On the other hand, at the cc-pVQZ and cc-pV5Z MP2 levels and with the cc-pVQZ CCSD(T) method, the gauche conformer of oxalyl chloride was found at O[Double Bond]C-C[Double Bond]O dihedral angles of 81.9 degrees , 79.4 degrees , and 83.4 degrees , respectively. At the cc-pV5Z MP2 level, the energy barrier from trans to gauche was predicted to be 0.74 kcal mol(-1) and that from gauche to trans to be 0.09 kcal mol(-1). Thus, the potential-energy surface along the O[Double Bond]C-C[Double Bond]O torsional mode is exceedingly flat. The existence of the gauche conformation is mainly due to the minimization of steric repulsion.

On the applicability of deformed jellium model to the description of metal clusters

This work is devoted to the elucidation the applicability of jellium model to the description of alkali cluster properties on the basis of comparison the jellium model results with those derived from experiment and within ab initio theoretical framework. On the basis of the Hartree-Fock and local-density approximation deformed jellium model we have calculated the binding energies per atom, ionization potentials, deformation parameters and the optimized values of the Wigner-Seitz radii for neutral and singly charged sodium clusters with the number of atoms N ≤ 20. These characteristics are compared with the results derived from the ab initio all-electron simulations of cluster electronic and ionic structure based on the density functional theory as well as on the post Hartree-Fock perturbation theory on many-electron correlation interaction. The comparison performed demonstrates the great role of cluster shape deformations in the formation cluster properties and the quite reasonable level of applicability of the deformed jellium model.

Adsorption of water on NaCl(001). I. Intermolecular potentials and low temperature structures

Water adsorption on the NaCl(001) surface has been extensively studied both theoretically and experimentally during recent years. Here we investigate it using intermolecular potentials derived from intermolecular perturbation theory (IMPT). The water–water interactions are described by the recently developed ASP-W4 potential. For the water–NaCl surface, repulsion parameters were developed using IMPT, and C6 dispersion coefficients were calculated using coupled Hartree–Fock perturbation theory. The binding energy between a single water molecule and the NaCl surface is found to be 40 kJ mol−1. A stable tetramer can form on the surface, similar to the water tetramer in the gas phase. At a coverage of one water molecule per NaCl unit, there are several different water monolayer structures with approximately the same energy. Some have all the water oxygens located close to Na+ ions, but others have some water molecules located above the Cl− ions. The latter are farther from the surface, and are hydrogen bonded to water molecules sited above the Na+ ions. Structures were also located with 1.5 water molecules per NaCl unit. Their binding energy per water molecule was similar to the structures with one water molecule per NaCl unit. Experimentally water monolayer structures with (1×1) and (c4×2) unit cells have been suggested. Our results support the conclusion that owing to the small energy differences between different monolayer structures, several different types of monolayer structure can coexist on the surface at low temperatures.

Comparison of the variational and bound perturbation theories in dipole polarizability calculations of molecular complexes

For a model molecular complex, analytical expressions are obtained for the coefficients A3 and A6 of dipole polarizability expansion in a reciprocal power series of intermolecular distances in terms of the variational (VPT) and bound (BPT) Hartree-Fock perturbation theories. It is shown that A3(VPT)<A3(BPT), A6(VPT)<A6(BPT) for weak electron-electron interactions and A3(BPT)<A3(VPT), A6(BPT)<A6(VPT) for strong electron-electron interactions.

Calculation of the NMR shielding of O in MgO at high temperature

17O NMR studies indicate that the O in crystalline MgO becomes less shielded magnetically as the temperature is increased. Over a range of about 1300 °C the shielding decreases by about 10 ppm. Increasing the temperature in MgO also leads to a small increase in the average Mg-O bond length and a large increase in the isotropic temperature factor, corresponding to a large increase in the root mean square deviation of the Mg-O distance from its equilibrium value. Using the gauge-including-atomic-orbital (GIAO) version of coupled Hartree-Fock perturbation theory, implemented at the self-consistent-field (SCF) level using a polarized split valence basis set, we have calculated the NMR shielding at the central O of a cluster OMg6(OH)12 −2, Oh symmetry, for several values of the Mg-O distance within a range of 30% about our calculated equilibrium value. We have also considered some distorted geometries for this cluster. We find that the O NMR shielding decreases nonlinearly as the central Mg-O distance is decreased. For the shortest Mg-O distance studied (1.391 A) in the symmetric geometry the calculated O NMR shielding was 229.4 ppm, while at the equilibrium Mg-O distance calculated for the cluster (1.987 A) the calculated shielding was 317.8 ppm. If the average 17O shielding is estimated by weighting the calculated NMR shieldings at various Mg-O distances by the probability of that distance, as obtained from the experimental isotropic temperature factors, at least a part of the observed deshielding at high temperatures can be reproduced. Calculations on a C4v symmetry OMg6(OH)12 −2 cluster, with the central O displaced from the centre, show even stronger deshielding. Therefore, consideration of such asymmetric motions within the central OMg6 unit could further reduce the calculated 17O shielding.

On the calculation of parity-violating energies in hydrogen peroxide and hydrogen disulphide molecules within the random-phase approximation

It is shown via extended numerical tests that the ab initio calculation of a parity-violating energy term, at the random-phase approximation (or coupled Hartree-Fock perturbation theory) level of accuracy, gives results which are more than one order of magnitude larger than those usually obtained by means of less accurate methods employed so far. These findings make more plausible the hypothesis of electroweak selection of natural enantiomers.

Radially dependent antishielding factor γ(r) of the Sc3+ ion in the solid state

We report the results of our calculation of γ(r), the radially dependent antishielding factor of Sc3+ ion in the crytalline environment. Watson sphere model is used to approximately represent the crystal potential. Differential equations resulting from non-orthogonal Hartree-Fock perturbation theory are solved to obtain perturbations to core electron states. Contribution to γ(r) from electron self-consistency effect has been evaluated by using the latter wave-functions in the many-body expression of Schmidtet al.

Calculation of B and O NMR parameters in molecular models for B 2O 3 and alkali borate glasses

To help in the interpretation of the 11B and 17O magic-angle-spinning (MAS) and double-rotation nuclear magnetic resonance (DOR NMR) spectra of B 2O 3 and related glasses we have calculated NMR parameters from ab initio self-consistent-field MO theory for molecules modeling the local B and O environments of the glasses. The present work employs larger model molecules, larger basis sets, and a better quantum mechanical method (the gauge-including atomic orbital version of coupled Hartree-Fock perturbation theory) than in my previous studies. The calculated 11B shieldings confirm the deshielding of the B atoms within boroxol rings, B 3O 3(-O) 3, compared to corner sharing BO 3 units. The shielding of B atoms within the boroxol rings is almost unchanged when two or even three boroxol rings are linked together, but the shielding of B atoms in the corner-sharing BO 3 units is quite sensitive to the size of the cluster. Calculated O NMR shieldings and quadrupole coupling constants indicate that O in boroxol rings is deshielded and has a smaller coupling constant than O bridging between triangular BO 3 units. Calculated 17O shieldings are smaller for atoms in the middle of a cluster than for chemically similar atoms on the periphery. O atoms bridging between two boroxol rings or between a boroxol ring and a BO 3 unit have intermediate values for both shielding and coupling constant. 17O shieldings show a considerable range and seem more sensitive to distant neighbors than do the 11B shieldings. Perturbations of the boroxol ring model by deprotonation, or by interaction with Na + or OH −, change the 11B shielding by only 1 ppm, while the 17O shieldings and the frequencies of the Raman active symmetric ring O breathing modes show substantial changes. Thus, boroxol ring-like 11B NMR signatures may remain while boroxol-ring Raman spectral signatures disappear.

Coupled Hartree–Fock calculations of molecular magnetic properties annihilating the transverse paramagnetic current density

The reliability of the continuous transformations of origin of the current density method, which makes the transverse paramagnetic current vanish (CTOCD-PZ), for the prediction of nearly gauge-origin independent molecular magnetic susceptibility and gauge-origin independent nuclear magnetic shielding, is proved on the basis of a fairly large number of calculations. It is shown that, within the computational scheme provided by the coupled Hartree–Fock perturbation theory (CHF), convergence towards the presumed Hartree–Fock limit, for magnetic susceptibility and proton magnetic shielding, is systematically reached using basis sets which are smaller than those required by conventional common origin and CTOCD-DZ techniques. For second-row nuclear magnetic shieldings a variant of the CTOCD-PZ method, which shifts the origin of the current towards the nearest nucleus for points close to nuclei, as suggested originally by Keith and Bader with the CSDGT method [T. A. Keith and R. F. W. Bader, Chem. Phys. Lett. 210, 223 (1993)], gives likewise good results with affordable basis sets.

Method of basis set construction in ab initio calculations of molecular magnetic properties

A physically justified method of construction of basis sets of the Slater- and Gauss-type functions for calculations of the molecular magnetic susceptibilities (χ) and NMR shielding constants (σ) is suggested. It is based upon the inclusion of those response functions into the basis set, which were generated from the initial basis set functions by the electron angular momentum operator. The χ and σ test calculations have been carried out for the ten-electron hydride molecules within the coupled scheme of the Hartree-Fock perturbation theory.

Open-shell restricted Hartree–Fock perturbation theory: Some considerations and comparisons

A comparative study is presented of the various recently developed open-shell perturbation theories that are based on a restricted Hartree–Fock reference wave function. Included in this study are issues concerning spin contamination, implementational considerations, and numerical comparisons at the second-order of perturbation theory for equilibrium geometries, vibrational frequencies, and singlet–triplet energy differences. Based on all of these considerations, it is concluded that the z-averaged perturbation theory (ZAPT) method is to be preferred over the other recently devised spin–orbital perturbation theories, while the spin-free OPT2 method possesses some advantages and disadvantages relative to the ZAPT method. In particular, it is shown that OPT2 energies are not invariant to rotations among singly-occupied degenerate molecular orbitals.

Theoretical determination of electric polarizability and hyperpolarizabilities of pyridine N-oxide and 4-nitropyridine N-oxide

Coupled Hartree-Fock perturbation theory has been applied to computing first- and second-order corrections to a molecular wavefunction due to an external electric field, from which the analytic calculation of electric dipole polarizabilities of pyridine N-oxide and 4-nitropyridine N-oxide is performed. The method takes full advantage of molecular symmetry. The results show that the examined molecules possess interesting nonlinear optical properties.

Calculation of molecular magnetic properties in the isoelectronic series PH 2−, PH 3 and PH 4+

Ab initio coupled Hartree-Fock perturbation theory has been used to evaluate magnetic susceptibility and magnetic shielding tensors of 31P and 1H nuclei in PH 2 −, PH 3 and PH 4 +. Good agreement between theoretical and experimental data and a satisfactory degree of origin independence of computed values has been found by adopting large polarized basis sets developed ad hoc for magnetic properties.

An open-shell restricted Hartree—Fock perturbation theory based on symmetric spin orbitals

A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, O 2, NH 2 and CH 2.

Time-dependent Hartree-Fock calculations of the quadratic polarizability dispersion for molecules with pronounced nonlinear optical properties

The quadratic huperpolarizability for the second harmonic generation is calculated at the fundamental frequencies 0, 0.656, 0.941, and 1.165 eV for three classes of organic molecules in the framework of the time-dependent Hartree-Fock perturbation theory. The π-electron approximation used reproduces available experimental data quite satisfactory. It is shown that the computation scheme earlier proposed is readily applicable to molecules of real physical interest.

Convergence properties of coupled Hartree–Fock theory of intermolecular interactions

The interaction between a helium atom and a proton is analyzed using coupled Hartree–Fock perturbation theory in the polarization approximation. It is shown that even for relatively short interatomic separations the perturbation expansion converges and its sum is identical with the supermolecule interaction energy. Similar behavior is observed for molecule–proton complexes although the convergence may be worse and, as an illustration, calculations for H2O–H+ are presented. A detailed analysis of the electrostatic component of the interaction energy between He and H+ shows the failure of a long range multipole expansion in correcting the secondary basis set superposition error. Polarization approximation perturbation theory is also used to analyze interactions for He–Li+ and He–Na+. The results for interatomic distances of 8.0 and 10.0 a0 for both the basis sets of the monomers, and the basis set of the entire complex are in excellent agreement with the counterpoise-corrected interaction energies, and thus show the need to remove the basis set superposition error.

Velocity-gauge formalism in the theory of vibrational circular dichroism and infrared absorption

The first use of velocity-gauge factors in the theory of vibrational circular dichroism (VCD) and infrared absorption intensities is described. The approach involves the exact incorporation of all or part of the dependence of the electronic wave function on an electron-velocity perturbation, such as the vector potential or the velocities of the nuclei, into the atomic orbital basis functions as a gauge transformation. Any remaining dependence of the wave function on these perturbations is carried by the basis-function coefficient derivatives which are determined to first order by coupled Hartree–Fock perturbation theory. The magnetic field perturbation formulations of VCD in the common origin and distributed origin gauges are identified within the new formalism, providing a new direct derivation of the distributed origin gauge theory. The formalism also yields new a priori VCD intensity expressions, derived using nuclear velocity-gauge factors, in the complete adiabatic approximation. Several distinct a priori computational approaches to VCD intensities can now be identified—the vibronic coupling theory implemented with a direct sum over states (VC/SOS), the field adiabatic theory implemented with magnetic field perturbation (FA/MFP), and the complete adiabatic theory implemented with nuclear velocity perturbation (CA/NVP). In addition, basic expressions are presented for an energy gradient theory of VCD that employs both magnetic-field and nuclear-velocity perturbations (EG/MFNVP). It is shown that the CA/NVP theory of VCD possesses a higher Born–Oppenheimer content than the VC/SOS or FA/MFP theories and provides an improved basis for reducing a priori VCD theory to various models of VCD intensity.