Gerhard Herzberg

Bio: Gerhard Herzberg is an academic researcher from National Research Council. The author has contributed to research in topics: Diatomic molecule & Molecule. The author has an hindex of 22, co-authored 32 publications receiving 39073 citations.

Infrared and Raman spectra of polyatomic molecules

Abstract: This present volume represents the continuation of a series on Molecular Spectra and Molecular Structure. Illustrations have been included to make the reader visualize clearly the significance and meaning of results of the theory. A large number of tables have also been included in which theoretical results are summarized, or observed data collected, for the benefit of those carrying out research work in the field of infrared and Raman spectra or related fields.

Generalized Gradient Approximation Made Simple

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

Hybrid functionals based on a screened Coulomb potential

Abstract: Hybrid density functionals are very successful in describing a wide range of molecular properties accurately. In large molecules and solids, however, calculating the exact (Hartree–Fock) exchange is computationally expensive, especially for systems with metallic characteristics. In the present work, we develop a new hybrid density functional based on a screened Coulomb potential for the exchange interaction which circumvents this bottleneck. The results obtained for structural and thermodynamic properties of molecules are comparable in quality to the most widely used hybrid functionals. In addition, we present results of periodic boundary condition calculations for both semiconducting and metallic single wall carbon nanotubes. Using a screened Coulomb potential for Hartree–Fock exchange enables fast and accurate hybrid calculations, even of usually difficult metallic systems. The high accuracy of the new screened Coulomb potential hybrid, combined with its computational advantages, makes it widely applicable to large molecules and periodic systems.

The HITRAN 2008 molecular spectroscopic database

Abstract: This paper describes the contents of the 2016 edition of the HITRAN molecular spectroscopic compilation. The new edition replaces the previous HITRAN edition of 2012 and its updates during the intervening years. The HITRAN molecular absorption compilation is composed of five major components: the traditional line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, infrared absorption cross-sections for molecules not yet amenable to representation in a line-by-line form, collision-induced absorption data, aerosol indices of refraction, and general tables such as partition sums that apply globally to the data. The new HITRAN is greatly extended in terms of accuracy, spectral coverage, additional absorption phenomena, added line-shape formalisms, and validity. Moreover, molecules, isotopologues, and perturbing gases have been added that address the issues of atmospheres beyond the Earth. Of considerable note, experimental IR cross-sections for almost 300 additional molecules important in different areas of atmospheric science have been added to the database. The compilation can be accessed through www.hitran.org. Most of the HITRAN data have now been cast into an underlying relational database structure that offers many advantages over the long-standing sequential text-based structure. The new structure empowers the user in many ways. It enables the incorporation of an extended set of fundamental parameters per transition, sophisticated line-shape formalisms, easy user-defined output formats, and very convenient searching, filtering, and plotting of data. A powerful application programming interface making use of structured query language (SQL) features for higher-level applications of HITRAN is also provided.

General definition of ring puckering coordinates

Abstract: A unique mean plane is defined for a general monocyclic puckered ring. The geometry of the puckering relative to this plane is described by amplitude and phase coordinates which are generalizations of those introduced for cyclopentane by Kilpatrick, Pitzer, and Spitzer. Unlike earlier treatments based on torsion angles, no mathematical approximations are involved. A short treatment of the four-, five-, and six-membered ring demonstrates the usefulness of this concept. Finally, an example is given of the analysis of crystallographic structural data in terms of these coordinates. Although the nonplanar character of closed rings in many cyclic compounds has been widely recognized for many years, there remain some difficulties in its quantitative specification. An important first step was taken by Kilpatrick, Pitzer, and Spitzer in their 1947 discussion of the molecular structure of cyclopentane.' Starting with the normal modes of out-of-plane motions of a planar regular pentagon,* they pointed out that displacement of the j t h carbon atom perpendicular to the plane could be written 2 112 zj = (/'SI 4 COS (2+ + 4 n ( j 11/51 (11 where q is a puckering amplitude and $ is a phase angle describing various kinds of puckering. By considering changes in an empirical potential energy for displacements perpendicular to the original planar form, they gave reasons to believe that the lowest energy was obtained for a nonzero value of q (finite puckering) but that this minimum was largely independent of $. Motion involving a change in fi at constant q was described as pseudorotation. Subsequent refinement of this work has involved models in which constraints to require constant bond lengths are imposed3q4 and extensions to larger rings5-' and some heterocyclic systems are considered.* Although the correctness of the model of Kilpatrick, et a f . , I and the utility of the (q. $) coordinate system is generally accepted, application to a general five-membered ring with unequal bond lengths and angles is not straightforward. Given the Cartesian coordinates for the five atoms (as from a crystal structure), determination of puckering displacements z, requires specification of the plane z = 0. A least-squares choice (minimization of Zz i2) is one possibility, but the five displacements relative to this plane cannot generally be expressed in terms of two parameters q and $ according to eq 1. An attempt to define a generalized set of puckering cordinates which avoids these difficulties was made by Geise, Altona, Romers, and S~ndara l ingam.~l ' Their quantitative description of puckering in five-membered rings involves the five torsion angles 0, rather than displacements perpendicular to some plane. These torsion angles are directly derivable from the atomic coordinates and are all zero in the planar form. They proposed a relationship of the form\