Shigeru Obara

Efficient recursive computation of molecular integrals over Cartesian Gaussian functions

Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three‐center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.

General recurrence formulas for molecular integrals over Cartesian Gaussian functions

General recurrence formulas for various types of one‐ and two‐electron molecular integrals over Cartesian Gaussian functions are derived by introducing basic integrals. These formulas are capable of dealing with (1) molecular integrals with any spatial operators in the nonrelativistic forms of the relativistic wave equations, (2) those with the kernel of the Fourier transform, (3) those with arbitrarily defined spatial operators so far as the integrals can be expressed in terms of the basic integrals, and (4) any order of their derivatives with respect to the function centers in the above integrals. Thus, the present formulation can cover a large class of molecular integrals necessary for theoretical studies of molecular systems by ab initio calculations, and furthermore provides us with an efficient scheme of computing them by virtue of its recursive nature.

Abinitio MO studies of electronic states and Mössbauer spectra of high‐, intermediate‐, and low‐spin Fe(II)‐porphyrin complexes

Ab initio LCAO SCF MO calculations were carried out on Fe‐porphine, Fe‐porphine‐pyridine, and Fe‐porphine‐pyridine‐carbonmonoxide which are typical intermediate‐, high‐, and low‐spin complexes, respectively. Mossbauer spectra of ferrous porphyrins were analyzed theoretically by the evaluation of isomer shift (IS), quadrupole splitting (QS), sign and direction of the principal component of electric field gradient tensor, and asymmetry parameter for the complexes. The calculated values have a good agreement with the experimental ones for the low‐ and high‐spin complexes. The ground state of Fe‐porphine, which remains undetermined so far, is assigned as the 3Eg state which is described by mixing of the two configurations, (dxy)2 (dxz,dyz)3 (dz2)1 and (dxy)1 (dxz,dyz)3 (dz2)2. A new relation between Mossbauer spectra and electronic structure is found. The field gradient along the perpendicular axis to the porphyrin plane is determined by two factors, the d‐electron configuration and a constant term depending ...

Intramolecular CH...M interaction: theoretical study of the structure of the six-coordinate ethyldiphosphinetitanium complex EtTi(PH3)2X2Y

Calcul de la geometrie de Ti(I 2 H 5 ) (PH 3 ) 2 Cl 2 H par une methode MO ab initio: presence du groupe C 2 H 5 deforme avec une distance Hβ..Ti courte

Formulation of molecular integrals over Gaussian functions treatable by both the Laplace and Fourier transforms of spatial operators by using derivative of Fourier‐kernel multiplied Gaussians

General recurrence formulas for molecular integrals over Gaussian functions are derived by introducing the derivative of Fourier‐kernel multiplied Gaussians (DFGs). The DFG allows us to formulate on the same ground molecular integrals over the Cartesian Gaussians, modified Hermite Gaussians, and the Gaussians multiplied by phase factors exp[ik⋅(r−R)] with spatial operators including any number of both the Laplace and Fourier transforms for one‐ and two‐electron spatial operators. Thus the present formulation has a wider applicability than that given by Obara and Saika [J. Chem. Phys. 89, 1540(1988)], where the basis functions are the Cartesian Gaussians and the spatial operators are those in the Laplace transform with at most one kernel of the Fourier transform. Furthermore the present formulation inherits the characteristic features of the above one, such as being capable of dealing with (1) molecular integrals with both nonrelativistic and relativistic spatial operators, (2) any order of the derivative ...

Energy gradient with the effective core potential approximation in the ab initio mo method and its application to the structure of Pt(H)2(PH3)2

Abstract The energy gradient method with the effective core potential approximation is proposed. As a demonstration the method is used to determine the structures of Pt(PH 3 ) 2 , cis-Pt(H) 2 (PH 3 ) 2 and trans-Pt(H) 2 (PH 3 ) 2 .

Intramolecular CH…M interaction: Ab initio MO study of the structure of Ti(CH3)(PH3)2(X)2Y

Abstract Ab initio MO calculations indicate that the nature of ligands X and Y and the PTiP angle in Ti(CH3)(PH3)2(X)2Y affect the distortion of its methyl group. For X = Cl, Y = Cl and angle PTiP 75°, the TiCH angle is found to be 100° and the H…Ti distance 2.51 A. The methyl group is distorted, suggesting interaction between the methyl-CH bond and the metal atom. The origin of this distortion is attributed to direct interaction between the CH σ bond and an unoccupied Ti d orbital.

Theoretical studies on low‐lying electronic states of the CCl+, SiCl+, and GeCl+ ions

Potential energy curves for the ground state X 1Σ+ and low‐lying A 1Π and a 3Π states of the CCl+, SiCl+, and GeCl+ ions have been calculated by ab initio LCAO–SCF–MO configuration interaction method. Calculated molecular constants Te, ωe, and ωexe agree well with available experimental data. The assignments of A 1Π–X 1Σ+ and a 3Π–X 1Σ+ bands for CCl+ and a 3Π–X 1Σ+ band for SiCl+ have been confirmed.

Potential-energy surfaces for chemical reactions. Dimerization of CH2 and SiH2, the SN2 reaction in gas-phase clusters and CH activation in transition-metal complexes

We present the results of three applications of the molecular-orbital method to problems of potential-energy surfaces that control chemical reactions. In the first application the dimerization of CH2 and SiH2 in both their singlet and triplet states is investigated in connection with the path of least motion as against the path of non-least motion. Two ground-state (3B1) methylenes in the path of non-least motion give ground-state ethylene with no barrier. The ground-state (1A1) silylenes give a ground-state disilene with a barrier in the path of least motion and no barrier in the path of non-least motion. In the second problem potential-energy surfaces are calculated for an SN2 reaction (H2O)nOH–+ CH3Cl → HOCH3+ Cl–+nH2O, where the reactants are complexed with one or two water molecules. When the hydroxide ion is solvated by two water molecules, the reaction takes place through the first step of reactant complex formation, followed by inversion of the methyl group. The transition state for methyl inversion has an energy comparable to that of the reactants. The migration of water molecules from the hydroxide side to the chloride side is not involved in the rate-determining process. The last problem is concerned with the activation of an inert CH bond in transition-metal complexes. In six-coordinate Ti d0 complexes the optimized geometry shows theoretical evidence that the distortion of the ethyl or methyl ligand, represented by a short M⋯H distance, a small M⋯C—C (or H) angle and a long CH bond, is of electronic origin. Electronegative axial ligands are essential for the existence of an agostic interaction, which is stabilized by CH σ→ Ti dxy charge transfer. A similarly distorted ethyl group has been found in the calculation of a three-coordinate Pd complex. The low-energy transition state for β-elimination lies along a smooth extension of the ethyl distortion.

Efficient and stable method of searching for optimum structures of molecules containing cyclic parts

Abstract An efficient and stable method of searching for optimum structures of molecules containing cyclic parts is proposed, where both the Cartesian and the internal coordinates are improved independently at each iteration of the optimization, and are used for the next geometry of the cyclic parts and of the remaining parts, respectively. The utilization of the Cartesian coordinates at the cyclic parts allows us to avoid the disastrous and irrecoverable distortions, which frequently occur if one uses the internal coordinates. For the remaining parts, the internal coordinates are used, so that an efficient calculation is obtained. The present method is tested in the search for the geometries of pyridine and ethylene oxide in the ground state and compared with the usual methods which employ either the internal coordinates or the Cartesian coordinates as optimization variables; our new method is found to be more efficient and more stable than the usual methods.