Howard D. Cohen

Bio: Howard D. Cohen is an academic researcher. The author has contributed to research in topics: Hartree–Fock method & Polarizability. The author has an hindex of 3, co-authored 3 publications receiving 751 citations.

Electric Dipole Polarizability of Atoms by the Hartree—Fock Method. I. Theory for Closed‐Shell Systems

Abstract: A method for the calculation of the dipole polarizabilities of closed‐shell atomic systems is presented. This method involves the direct calculation of the Hartree—Fock wavefunction of the atom in the presence of the perturbing field. The orbitals are expressed as linear combinations of Slater‐type functions. A large number of carefully chosen and optimized basis functions are used so as to assure a good fit to the true Hartree—Fock wavefunction. The polarizability is then calculated from the limiting value of α=p/F for F=0, where F is the electric field strength, and p is the induced dipole moment.

Electric‐Dipole Polarizability of Atoms by the Hartree—Fock Method. II. The Isoelectronic Two‐ and Four‐Electron Series

Abstract: Results are presented for the electronic‐dipole polarizabilities of the isoelectronic series of helium and beryllium in the presence of a finite electric field. These calculations were done analytically, but large numbers of carefully chosen and optimized basis functions were used in order to assure a good fit to the exact solution for the perturbed Hartree—Fock wavefunction. It was found that the polarizabilities of the helium series increase, and those of the beryllium series decrease, as the field increases.

Electric Dipole Polarizability of Atoms by the Hartree—Fock Method. III. The Isoelectronic 10‐Electron Series

Abstract: Results are presented for the electric dipole polarizabilities of the neon isoelectronic series in the presence of a finite electric field. The calculations were done analytically, but sufficient numbers of carefully chosen and optimized basis functions were used in order to assure a good fit to the exact solution for the Hartree—Fock equations. Shell polarizabilities are given, and these exhibit some interesting relationships. Approximate hyperpolarizabilities are given.

Conceptual density functional theory.

Abstract: I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

Treatment of intershell correlation effects in ab initio calculations by use of core polarization potentials. Method and application to alkali and alkaline earth atoms

Abstract: In the present approach the high reliability of ab initio techniques is combined with the easily amenable phenomenological core polarization concept for an efficient treatment of intershell correlation effects in all‐electron SCF and valence CI calculations. By use of only a single adjustable atomic parameter, which is related to the radius of the core and determines the cutoff at short range, our effective core polarization potential (CPP) accounts quantitatively for dynamical intershell correlation as well as exclusion effects on the correlation energy of the core. The applications refer to alkali and alkaline earth atoms (Li to K and Be to Ca) and a detailed analysis is performed for core polarization effects on ionization energies, electron affinities, oscillator strengths, polarizabilities, van der Waals coefficients, the valence electron density, and spin densities. Very accurate results are obtained for well‐known energetic properties and spin densities at the nucleus. With respect to the other app...

PNO-CI and PNO-CEPA studies of electron correlation effects

Abstract: Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H2O, NH3, CH4 and CO from SCF and correlated wavefunctions. The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.

Molecular vibrational and rotational motion in static and dynamic electric fields

Abstract: For many years the effects of a static or dynamic electric field upon electronic motion in a molecule have been studied. These effects have been described in terms of multipolar electronic polarizabilities and higher-order hyperpolarizabilities. Much less attention, however, has been paid to the effects of an electric field upon vibrational and rotational motion. It is the aim of this review to consider, in some detail, these effects. As in the electronic work, they too will be described in terms of polarizabilities and hyperpolarizabilities (the latter being particularly important for the study of nonlinear optics). The theory will be developed so as to bring together the different methods that have been used in various calculations. Examples drawn from the recent literature will be discussed and it will be seen that in many cases vibrational and rotational changes with an electric field are as important as electronic ones, if not more so. Examples of experimental work relevant to this review include research on the Kerr effect, electric-field-induced second-harmonic generation, and third-harmonic generation.

Atomic and Molecular Polarizabilities-A Review of Recent Advances

Abstract: Publisher Summary This chapter focuses on the recent developments in the experimental and theoretical determination of the polarizabilities of simple atoms and molecules. Polarizability values (related to the “quadratic Stark effect”) are accurately known for the noble gas atoms and for hydrogen, in theory, but the remainder of the periodic table has proven much more difficult to deal with, both theoretically and experimentally. The static electric dipole polarizability of the ground-state hydrogen atom is almost exactly 4.5a30, where a0 is the Bohr radius. Across rows of the periodic table, polarizabilities range from hundreds (of a30 units) for the alkali metal atoms generally monotonically down to a few for noble gas atoms. Excited atoms have much larger polarizabilities; recent polarizability measurements for atoms in Rydberg orbits have yielded values on the order of 1010a30. Further research on molecular polarizabilities can help in the determination of polarizability anisotropies whether through state selection or with beams of different temperatures. Supersonic molecular beams are found to have low internal energies, and the internal energy can be controlled somewhat in “seeded” beams.