A. Saika

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.

An NMR relaxation study on the proton transfer in the hydrogen bonded carboxylic acid dimers

We have studied the proton spin‐lattice relaxation times (T1) of a series of benzoic acid (BAC) derivatives and decanoic acid (DAC) over a wide range of temperature and analyzed the results in terms of the double proton switching along the hydrogen bonds. The proton T1 in the high temperature region are analyzed using the classical jump model and the barrier heights for the proton transfer are determined. The thermodynamic parameters for the equilibria between the two configurations in the solid state are also determined by the FT–IR measurements. It is shown that the energetics and dynamics of the proton transfer in DAC and the para‐ and meta‐substituted BAC are all similar, but they are very different in the ortho‐substituted ones. It is suggested that the low temperature behavior of the proton T1 of the dimers of carboxylic acid is due to the tunneling and the asymmetry of the potential brings in a small activation energy.

A study on the proton transfer in the benzoic acid dimer by 13C high-resolution solid-state NMR and proton T1 measurements

Abstract By a solid-state 13 C and proton NMR study of the hydrogen bonded dimer of benzoic acid, the rate of proton transfer, the height of the potential barrier for the transfer and the relative population of two different configurations were determined.

Switching-angle sample-spinning NMR spectroscopy for obtaining powder-pattern-resolved 2D spectra: Measurements of 13C chemical-shift anisotropies in powdered 3,4-dimethoxybenzaldehyde

Abstract A general method is proposed which allows us to obtain individual powder patterns of chemically distinct nuclei. As an example, the measurement of 13 C chemical-shift anisotropies in powdered 3,4-dimethoxybenzaldehyde is reported.

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.

Dipolar SASS NMR spectroscopy: Separation of heteronuclear dipolar powder patterns in rotating solids

Two‐dimensional sample‐spinning NMR techniques for separately obtaining heteronuclear dipolar powder patterns of chemically distinct nuclei are proposed, which involve switching the spinning axis on and off the magic angle. Procedures for the computation of dipolar spectra obtained by this method are described, and various features of such spectra are discussed using simulated spectra. Practical applications of this method are demonstrated with 13C spectra of calcium formate, β‐quinol‐methanol clathrate, and urea‐trans‐4‐octene clathrate, providing information on the absolute sign and magnitude of the indirect dipolar couplings, 13C–1H distances, and dynamics of trapped molecules in clathrates.

High‐resolution J‐resolved NMR spectra of dilute spins in solids

A technique for obtaining J‐resolved NMR spectra of dilute spins in solids has been developed. It is based on the observation that a combination of magic‐angle irradiation and magic‐angle spinning removes dipolar broadening, but leaves indirect spin–spin coupling. A preliminary application of this technique to adamantane clearly reveals the AX (J = 121 Hz) and AX (J = 135 Hz) multiplets in the methylene and methyne 13C spectrum, respectively.

Perturbational Calculations of the Nuclear Spin—Spin Coupling Constant for the Hydrogen Fluoride Molecule

Most of previous perturbational calculations of nuclear spin—spin coupling constants either made the mean excitation energy approximation or took account of only a few lower excited states. We have examined these approximations by including higher excited states, taking as an example the hydrogen fluoride molecule, for which several molecular‐orbital wavefunctions are available. Contributions from the orbital and spin dipolar terms besides the Fermi contact term are also calculated with due regard to two‐center integrals. The present results indicate that the calculated values of the coupling constant are extremely sensitive to the wavefunctions employed, and the estimates by these approximate wavefunctions available at present cannot be fully trusted as yet.

Unified analytical evaluation of two‐center, two‐electron integrals over Slater‐type orbitals

A unified analytical expression is given for all types of two‐center electron‐repulsion integrals over Slater‐type atomic orbitals. By means of the Neumann expansion of the inverse interelectronic distance (1/r12) in prolate spherical coordinates, Coulomb, hybrid, and exchange integrals are expressed in terms of the function W1‖ m ‖ introduced by Kotani. The present formulation allows a preliminary estimation of the number of terms in the expansion to be retained for a desired accuracy, resulting in a significant saving of computation time and working storage. The method is implemented on a computer for various type atomic orbitals from 1s to 4f with an accuracy of 12 decimal places.

Study of static and dynamic structure of β‐quinol‐methanol clathrate by 13C high‐resolution solid‐state NMR and proton T1 measurements

13C high‐resolution solid‐state NMR spectra and proton spin‐lattice relaxation times T1 have been measured for β‐quinol clathrate with trapped methanol molecules over a wide temperature range of 4.2–363 K. Above the transition point (∼67 K), a single and axially‐symmetric 13C chemical shift tensor is observed for the trapped methanol, demonstrating that the molecules reorient themselves among three potential minima in the cavity. Its anisotropy allows us to obtain a temperature‐dependent angle ϑ between the CO bond and the crystallographic c axis. Analysis of the T1 results gives the motional parameters (Ea = 0.7±0.2 kcal/mol, τ0 = 3.7×10−12 s for C3‐ reorientation and Ea = 2.4±0.1 kcal/mol, τ0 = 4.5×10−14 s for inversion about the cavity center) and the position of the methanol molecule in the cavity. Each 13C absorption line for both methanol and quinol is found to split into three below the transition point. This splitting indicates that the methanol molecules are settled down in any of the six orienta...