Jerome M. Schulman

On symmetrical clusters of carbon atoms: C60

Preliminary results of theoretical calculations on C60 (“Buckminsterfullerene” or “footballene”) and other symmetrical clusters of carbon atoms are reported.

Application of Many‐Body Perturbation Theory to the Hydrogen Molecule

The hydrogen molecule total energy, polarizabilities, and electron‐coupled nuclear spin‐spin Fermi interaction are studied by many‐body perturbation theory. Two potentials, the Hartree and Hartree–Fock, are considered. Through second order the energies are within several kilocalories per mole of the accurate nonrelativistic values. The Hartree–Fock expansion is reasonably accurate through first order for polarizabilities and gives very good agreement with experiment if a rather simple geometric approximation is used. For the spin–spin coupling constant, good agreement with experiment is obtained using the Hartree potential and considering some second‐ and higher‐order diagrams.

Symmetrical clusters of carbon atoms: The C24 and C60 molecules

Abstract We report ab initio and AM1 calculations on C 24 in octahedral symmetry, including geometry optimization and vibrational analysis. The beats of formation and first ionization potentials of C 24 and C 60 are computed.

Recognition of cholinergic agonists by the muscarinic receptor. 1. Acetylcholine and other agonists with the NCCOCC backbone.

A theoretical model is used to deduce the pharmacologically active conformation of acetylcholine and other agonists interacting with the muscarinic receptor of the parasympathetic and central nervous systems. This is accomplished by replacing the usual dihedral angles tau 1 and tau 2, which define the conformations of cholinergic drugs, with two new geometric parameters more suitable for describing the muscarinic pharmacophore: a characteristic distance, [PQ], and a dihedral angle, PNOQ. Values for these parameters are determined by conformational analysis on semirigid muscarinic agonists using molecular mechanics and ab initio molecular orbital methods. In addition to deducing the active conformation of acetylcholine and other agonists, the model also rationalizes the pattern of stereoselectivity in agonists related to 3-acetoxyquinuclidine (aceclidine) and furnishes a geometric criterion for partial agonism and antagonism.

Perturbation Calculation of the Nuclear Spin‐Spin Coupling Constant in HD based on the Bare‐Nucleus Potential

Perturbation calculations of the Fermi contact part of the electron‐coupled nuclear spin‐spin coupling constant (J) in the HD molecule have been performed in the bare‐nucleus potential. A very large Gaussian basis has been employed and, in addition, the effect on J of varying the HD internuclear separation has been considered. The term zeroth order in correlation, J0, is in good agreement with an independent basis set study as is the geometric approximate to the coupled Hartree‐Fock value. The J0 and J1 values reported here differ significantly from those reported in a recent bare‐nucleus perturbation study using numerical H2+ orbitals. We give here a refined value of our previous Hartree perturbative results based on this larger atomic basis set.

A simple formula for the zero-point energies of hydrocarbons

Abstract A simple empirical formula exists for the calculation of accurate zero-point energies of hydrocarbons. The formula is based upon the numbers of C and H atoms present, and not at all upon any structural details. The rms deviation from the predictions of this formula for fifty-five molecules is 1.22 kcal/mol.

AM1, MNDO and MM2 studies of concatenated cyclobutanes: Prismanes, ladderanes and asteranes

Abstract Semiempirical calculations have been performed on a variety of hydrocarbons composed of fused cyclobutane rings using the MNDO, AM1 and MM2 methods. The systems studied include linearly concatenated cyclobutanes (ladderanes), cyclic structures (prismanes) and two “star-shaped” (CH)24 hydrocarbons, helvetane and israelane. The results reported include optimized geometries, heats of formation and vibrational frequencies. The performance of the theoretical models is evaluated and the relative stabilities of the structures are discussed.

Borepin and its valence isomers

Ab initio calculations show borepin to be planar and more stable than its valence isomers boranorbornadiene and boranorcaradiene by a considerable amount; the latter have Cs symmetry.

Orbital Approximation to Spatial Eigenfunctions of the Many‐Electron Hamiltonian

A new procedure is developed for calculating the best wavefunction for an N‐electron atom in terms of N one‐electron orbitals which are eigenfunctions of l2, lz and sz. This is a special case of a method for calculating the best wavefunction in terms of N orbitals unrestricted in angular momentum but restricted in spin component and is thus a partial generalization of Lowdins EHF method. We calculate approximate spatial eigenfunctions of H using the function Φ[α,λ] = Dλλ[α] ∑ i = 1k δiPiφ, where φ is a product of N spatial orbitals and where the Pi are the k permutations out of which k linearly independent projections onto the Young tableau [α,λ] can be obtained. The method gives an improvement to each of Goddards GI solutions in such a way that they all give the same energy when fully minimized, while only involving k−1 additional parameters. For Li atom there is only one additional parameter and calculations are performed using Goddards GI and GF orbitals, obtaining small improvements in the energy. ...

Diamagnetic contributions to the nuclear spin–spin coupling constants of several small molecules. An application of Monte Carlo integration methods to molecular one‐electron properties

A numerical Monte Carlo integration procedure has been developed for calculation of J1a, the diamagnetic contribution to the nuclear spin–spin coupling constant from an arbitrary molecular charge density. The method is applied first to the HD molecule where several previous values of JHD1a are refined and corrected. A test of Brillouin’s theorem for this unusual sum of one‐electron operators is made and the extensive cancellations from different regions of space are examined in detail. Values of J1a are then given for HF, BF, CO, and HCN. It appears that J1a may be the one‐electron property most sensitive to the quality of the wavefunction which has been considered to date. Monte Carlo integration may be employed for the calculation of one‐electron properties when alternatives to analytic integral evaluation are sought.