John H. Letcher

Theoretical Interpretation of 31P NMR Chemical Shifts. I

An ASP—LCAO—MO quantum‐mechanical calculation of 31P chemical shifts has been made using s, p, and d orbitals and allowing full latitude in the π bonding. This has been accomplished by use of an artfully chosen coordinate notation which allows the chemical‐shift expression to be stated in a particularly simple functional form, using a minimum number of hybridization parameters. Numerical examples of the calculations are presented graphically, and they have been applied to experimental data for the symmetrically substituted 1 phosphines, 2 phosphoryl, 3 thiophosphoryl, and 4 selenophosphoryl derivatives, as well as to the 5 phosphonium salts. The calculations show that the 31P chemical shift is primarily sensitive to asymmetric electronic loading and affords a method for estimating the amount of pπ—dπ bonding to phosphorus.

Localized Orbitals. I. σ Bonds

This paper presents a method for the delineation of a set of truly localized orbitals and uses a nonunitary transformation to convert the localized orbitals into equivalent orbitals which are suitable for molecular quantum‐mechanical calculations. The localized orbitals, which are suitable for describing polyatomic molecules including large nonplanar ones, are generated on the premise that the atomic orbitals used in the construction of two‐center one‐ or two‐electron bonds should be such that, when overlap is totally neglected, each atomic orbital has the same calculated value of angular momentum about its bond axis. The non‐unitary transformation is derived from the modification in the form of the general orthonormality conditions upon a change from overlap metric 1 to a realistic overlap matrix Δ. This approach is applied to methane, ammonia, and water to calculate the equivalent orbitals. System energies and dipole moments are also calculated, and these and the equivalent orbitals are compared with th...

Theoretical Interpretation of 31P NMR Chemical Shifts. II. Unsymmetrical Molecules

An ASP LCAO MO quantum‐mechanical calculation of the 31P chemical shifts has been made for molecules of the form PZ2T and MPZ2T, where M is an electron‐pair‐acceptor atom or group, P is phosphorus, and Z and T are different substituents. The deviations from linearity of the chemical shifts of these mixed species from that predicted by linear interpolation from the shifts of PZ3 and PT3 or of MPZ3 and MPT3 is calculated and used to elucidate molecular parameters such as the extent of π interactions and bond‐angle changes in the mixed as compared to the unmixed molecules.

Ketene in a Gaussian Basis: LCAO–MO–SCF Wavefunction, One‐Electron Properties, and Electron‐Density Maps

An SCF calculation of the wavefunction for ketene is presented. The basis functions are a (73/73/3) uncontracted set of Gaussian 1s and 2p orbitals. Energy components, population analysis, one‐electron properties, and density maps are presented and discussed. A main conclusion is that, opposite to formaldehyde, the total contribution of π orbitals to the radial extent of the charge density in the out‐of‐plane direction in ketene is greater than the total contribution of the σ orbitals. Both second moments of charge and density maps support this conclusion.

Formaldehyde Molecule in a Gaussian Basis. A Self‐Consistent Field Calculation

Accurate LCAO–MO–SCF calculations have been carried out for the formaldehyde molecule using (73/2) and (95/3) Gaussian basis sets. The energy parameters, molecular orbitals, dipole moments, and population analyses are reported. The results are compared to a previous calculation with a minimum Slater basis and to experiment.

Theoretical Interpretation of 31P NMR Chemical Shifts. III. Phosphorus with Five Like Substituents

Using the assumption that the valence orbital hybridization in compounds of the type PZ5 is such that all five fluorines in PF5 are instantaneously magnetically equivalent even though the two axial bond lengths are longer than the three equatorial ones in this trigonal bipyramidal structure, an ASP LCAO MO quantum‐mechanical calculation has been made for the 31P chemical shifts of molecules of the form PZ5. As in the two previous papers of this series, π bonding to the phosphorus is included. On the assumption that the π orbitals of the phosphorus are vacant in the compound P (C6H5)5, the amount of π bonding is estimated for the symmetrically substituted compounds of the type PZ5 on which chemical‐shift data are available.

Characterization of Ground‐State Wavefunctions by Measured Electronic Properties. III. A Gaussian Basis Self‐Consistent‐Field Calculation for Nitrogen Trifluoride

An LCAO MO SCF calculation has been carried out for nitrogen trifluoride using an uncontracted (73 / 73) Gaussian basis set. Energy parameters, dipole moment, field gradient, molecular quadrupole moment, second moments of charge, and population analysis are reported. The calculation is used to evaluate earlier wavefunctions obtained by more empirical methods. Combining experimental quadrupole‐coupling‐constant data with the calculated field gradient gives a nitrogen nuclear quadrupole moment of + 0.018 ± 0.003 × 10−24 cm2 which is in good agreement with earlier, less precise, estimates of this parameter.

Characterization of Ground‐State Wavefunctions by Measured Electronic Properties. I. 119Sn Mössbauer Isomer Shifts

A particular type of LCAO MO wavefunction is applied to the problem of correlating experimental 119Sn Mossbauer isomer shifts with calculated electron densities at the nucleus. The results are found to be sensitive to the choice of basis functions, molecular geometry, and method of setting basis orbital exponents. Because of this sensitivity, only a rough correlation of the isomer‐shft data is obtained when conventional methods of setting orbital exponents are used. A set of wavefunction parameters which result in good correlation of the 119Sn data is found and, for each molecule, a quantitative measure of the sensitivity of the calculated electron densities to each parameter is obtained.

Localized Orbitals. II. Expanded Basis Sets

Two methods are presented to delineate localized orbitals defined on large basis sets. These methods calculate equivalent oribitals for polyatomic molecules which are accurate enough for precise quantum mechanical calculations. The localized orbitals are defined in terms of parameters that can be readily visualized by the chemist, yet allow changes in electronic structure during molecular bond formation and substituent exchange reactions to be determined. It is shown that these equivalent orbitals constitute a foolproof starting point for self‐consistent field (LCAO–MO–SCF) calculations. The results of calculations on the water molecule using Gaussian basis functions are presented along with a discussion of numerical and computational techniques.

The electronic structure of difluoromethane: ab initio studies in several basis sets and semiempirical calculations

LCAO–MO–SCF calculations have been carried out on the difluoromethane molecule, CH2F2, by use of the following basis sets: (31/31/1), (31/31/2), (52/52/2), (52/52/3), (52/73/3), (73/52/3), and (73/73/3), with these orbital listings being in the order of (C/F/H)[the notation (ab/cd/e) corresponds to the assignment of a 1s and b 2p atom-optimized Gaussian-type orbital-exponents to the carbon, c 1s and d 2p to each of the identical fluorine atoms, and e 1s to each of the identical hydrogens]. In addition, CNDO, INDO, and extended Huckel calculations have also been done for this molecule and the energies have been compared to a near-Hartree–Fock Gaussian calculation. Total energies, orbital energies, correlation-corrected binding energies, electron-population analyses, and various physical properties calculated from these wave-functions are compared for the various basis sets. Three-dimensional, electron-density, cross-sectional plots are presented.