Theoretical Chemistry Accounts: New Century Issue

205 Pages·2001·11.347 MB·English

by  Bernd Artur Hess (auth.), Professor Christopher J. Cramer, Professor Donald G. Truhlar (eds.)

C.J. Cramer
D.G. Truhlar
Theoretical
Chemistry Accounts
New Century Issue
Theoretical Chemistry Accounts I New Century Issue
Specialreprintedition ofVol. 103 Number 3-4
Springer-Verlag Berlin Heidelberg GmbH
C. J. Cramer 0. G. Truhlar (Eds.)
Theoretical
Chemistry Accounts
New Century lssue
With contributions by numerous experts
Special reprint edition of Vol. 103 Number 3-4
With Figures and Tables
28 2
i
Springer
J.
PROFESSOR CHRISTOPHER CRAMER
PROFESSOR DONALD G. TRUHLAR
University of Minnesota
Department of Chemistry
207 Pleasant Street SE
55455-0431 Minneapolis, MN
USA
Special reprint edition of Theoretical Chemistry Accounts, Volume 103, Number 3-4, February 2000,
C. J. Cramer, D. G. Truhlar (Eds.)
With contributions by numerous experts
ISSN I432-88IX
ISBN 978-3-540-67867-o
CIP data applied for
Die Deutsche Bibliothek-CIP-Einheitsaufnahme
Theoretical chemistry accounts: new century issue 1 ed.: Christopher ). Cramer; Donald G. Truhlar.
ISBN 978-3-540-67867-0 ISBN 978-3-662-10421-7 (eBook)
DOI 10.1007/978-3-662-10421-7
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Preface
A new century of theoretical chemistry
The end of the century provides a time to look back, and the start of a new century inspires one to look ahead. For
the New Century issue of Theoretical Chemistry Accounts, we asked the advisory editors of the journal to identify a
paper from the first century of theoretical chemistry and discuss its importance for the twentieth century with an
eye towards the twenty-first century. Although we collected 66 such perspectives, they are far from representing a
full set of the papers deserving our reflection. At one point we thought of inviting additional perspectives to fill
some obvious gaps or provide better balance, but we decided that any such attempt would spoil the spontaneity of
the collection, which is part of its interest.
We hope the Theoretical Chemistry Accounts New Century Issue will be entertaining, but even more we hope it will
help younger scientists to see the role that selected creative efforts of the past have played in getting us to the pres
ent. Further, to the extent that this issue inspires members of the theoretical chemistry community to reread the
papers that led to the present state of the art, that is all to the good, because there is still a lot to be learned from the
last century's literature. Finally, taking this issue as prolog, we can all try to make our upcoming efforts as influen
tial for the next century as these papers were for the last.
C. J. Cramer, D. G. Truhlar
Minneapolis, USA
December 31, 1999
Theoretical
Chemistry Accounts
Springer
Theory, Computation, and Modeling
Theoretica Chimica Acta
New Century lssue
PREFACE Frenkel D:
Perspective on "The effect of shape on the interaction
A new century of theoretical chemistry 167 of colloidal particles" 212
Pyykkö P:
PERSPECTIVES
Perspective on Norman Ramsey's theories
Hess BA: of NMR chemical shifts and nuclear
Perspective on "Zur Quantentheorie der Spektrallinien" 168 spin-spin coupling 214
Pettitt BM: Zerner MC:
A Perspective on "Volume and heat of hydration of ions" 171 Perspective on "New developments in molecular orbital
theory" 217
Tully JC:
Perspective on "Zur Quantentheorie der Molekeln" 173 Kato 5:
Perspective on "A molecular orbital theory of reactivity
Frenking G: in aromatic hydrocarbons" 219
Perspective on "Wechselwirkung neutraler Atome und
homöopolare Bindung nach der Quantenmechanik" 177 Hall MB:
Perspective on "The spectra and electronic structure
Helgaker T, Klapper W: of the tetrahedral ions Mn0,4, Cr04, and CI04" 221
Perspective on "Neue Berechnung der Energie des Heliums .
im Grundzustande, sowie des tiefsten Terms Jorgensen WL:
von Ortho-Helium" 180 Perspective on "Equation of state calculations
by fast computing machines" 225
Kutzelnigg W:
Perspective on "Quantum mechanics of many-electron Roos BO:
systems" 182 Perspective on "Quantum theory of many-particle systems
I, II, and 111" 228
Frenking G:
Perspective on "Quantentheoretische Beiträge zum Lluch JM:
Benzolproblem. I. Die Elektronenkonfiguration des Benzols Perspective on "On the theory of oxidation-reduction reactions
und verwandter Beziehungen" 187 involving electron transfer. I" 231
Petersson GA: Frenkel D:
Perspective on "The activated complex in chemical Perspective on "Statistical mechanical theory of irreversible
reactions" 190 processes. I. General theory and simple applications
to magnetic and conduction problems." 234
Tomasi J:
Cavity and reaction field: "robust" concepts. Perspective Miller WH:
on "Eiectric moments of molecules in liquids" 196 Using classical mechanics in a quantum framework.
Perspective on "Semiclassical description of scattering" 236
Garrett BC:
Perspective on "The transition state method" 200 Angyan JG:
Chemical building blocks in quantum chemical calculations.
Catlow CRA: Perspective on "The density matrix in many-electron
Perspective on "Conduction in polar crystals. quantum mechanics I. Generalized product functions.
I. Electrolyte conduction in solid salts" 205 Factorization and physical interpretation
of the density matrices" 238
Tucker SC:
Reaction rates in condensed phases. Perspective Yarkony DR:
on "Brownian motion in a field of force and the diffusion Perspective on "Some recent developments in the theory
model of chemical reactions" 209 of molecular energy Ieveis" 242
Theoretical
Chemistry Accounts
Springer
Theory, Computation, and Modeling
Theoretica Chimica Acta
Table of contents continued
Gordon MS, Jensen JH: Thirumalai 0:
Perspective on "The physical nature of the chemical bond" 248 Two Iandmarks in polymer physics: the Edwards model
and de Gennes' observation 292
Whangbo M-H:
Perspective on "An extended Hückel theory. Schlegel HB:
I. Hydrocarbons" 252 Perspective on "Ab initio calculation of force constants
and equilibrium geometries in polyatomic molecules.
Lavery R: I. Theory" 294
Perspective on "Stereochemistry of polypeptide
chain conformations" 257 Schinke R:
Perspective on "Semiclassical theory of atom-diatom
Ernzerhof M, Scuseria GE: collisions: path integrals and the classical S matrix" 297
Perspective on "lnhomogeneous electron gas" 259
Zhang JZH, Zhang DH:
Rossky PJ: Quantum wavepacket approach to chemical reaction
Perspective on "Correlations in the motion of atoms dynamics. Perspective on "Dynamics of
in liquid argon" 263 the collinear H + H2 reaction. I. Probability density
and flux" 300
Baerends EJ:
Perspective on "Self-consistent equations including exchange Kollman P:
and correlation effects" 265 Perspective on "Molecular dynamics study of liquid water" 306
Schatz GC: Cramer CJ:
Perspective on "Exchange reactions with activation energy. Sugar anomerism - a short and sweet digression
I. Simple barrier potential for (H, H2)" 270 Perspective on "The application of ab initio molecular
orbital theory to the anomeric effect" 308
Bartlett RJ:
Perspedive on "On the correlation problern in atomic and Salahub DR:
molecular systems. Calculation of wavefunction components From Xcx-scattered wave to end-of-the-century
in Urseil-type expansion using quantum-field theoretical applications of density functional theory
methods" 273 in chemistry. Perspertive on "Chemical bonding
of a molecular transition-meta! ion
Kaldor U: in a crystalline environment" 311
Multireference many-body methods. Perspective on "Linked
cluster expansions for the nuclear many-body problem" 276 Jansen AP J, van Santen RA:
Perspertive on "Self-consistent molecular Hartree-Fiock-Siater
Dykstra CE: calculations" 313
Finding the way through intermolecular forces. Perspective on
"Permanent and induced molecular moments Carsky P, Zahradnfk R:
and long-range intermolecular forces" 278 Perspertive on "MO approach to elertronic spertra
of radicals" Carsky P, Zahradnik R (1973)
Kouri DJ, Hoffman DK: Top Curr Chem 43: 1 315
Perspective on "Molecular collisions. VIII" 281
Robb MA:
Jordan KD: Perspective on "Group theoretical approach
Perspective on "Benzynes, dehydroconjugated molecules, to the configuration interartion
and the interaction of orbitals separated by a number and perturbation theory calculations
of intervening u bonds" 286 for atomic and molecular systems" 317
Eisenstein 0: Werner H-J:
Perspective on "lntermolecular orbital theory of the interactions Perspective on "Theory of self-consistent elertron pairs.
between conjugated systems." I General theory; An iterative method for correlated many-electron
II Thermal and photochemical cycloadditions 289 wavefunctions" 322
Theoretical
Chemistry Accounts
Springer
Theory, Computation, and Modeling
Theoretica Chimica Acta
Clary DC: Luque FJ , Löpez JM, Orozco M:
Perspective on "Quantum mechanical reactive scattering Perspective on "Eiectrostatic interactions of a solute
for three-dimensional atom plus diatom systems. with a continuum. A direct utilization of ab initio molecular
II. Aceurate cross sections for H + H/' 326 potentials for the prevision of solvent effects" 343
Gao J: Zhang Y, Yang W:
Perspective on "Theoretical studies of enzymic reactions: Perspective on "Density-functional theory for fractional
dielectric, electrostatic and steric stabilization particle number: derivative discontinuities
of the carbonium ion in the reaction of Iysozyme" 328 of the energy" 346
Houk KN: Truhlar DG:
Perspective on "Theoretical interpretation of 1-2 asymmetric Perspective on "Principles for a direct SCF approach to LCAO-MO
induction. The importance of antiperiplanarity" 330 ab initio calculations" 349
Case DA:
Perspective on "Dynamics of folded proteins" 332 Ayers PW, Levy M:
Perspective on "Density functional approach
Berne BJ: to the frontier-electron theory of chemical reactivity" 353
Perspective on "Statistical mechanics of isomerization dynamics
in liquids and the transition state approximation" 335 Raghavachari K:
Perspective on "Density functional thermochemistry.
Warshel A: 111. The role of exact exchange" 361
Perspective on "The energetics of enzymatic reactions" 337
Chelikowsky JR:
The origin of the pseudopotential density functional method. Online edition in LINK -Chemical Seiences
Perspective on "Microscopic theory of phase transformation and Online Library http://link.springer.de
lattice dynamics of Si" 340 Indexed in Current Conrents
Theor Chem Ace (2000) 103:168-170
Theoretical
DOI I 0.1007 ls002149900081
Chemistry Accounts
©Springer-Verlag 2000
Perspective
Perspective on "Zur Quantentheorie der Spektrallinien"
Sommerfeld A (1916) Ann Phys (Leipzig) 51:1-94, 125--167
Bernd Artur Hess
Lehrstuhl für Theoretische Chemie, Friedrich-Aiexander-Universität Erlangen-Nürnberg, Egerlandstrasse 3, D-91058 Erlangen, Germany
Received: 4 March 1999 I Accepted: 29 July 1999 I Published online: 4 October 1999
Abstract. Among many other results, Arnold thus explained using the "quantized" result of this
Sommerfeld gave in his article the correct expression calculation. The fine-structure constant is introduced
for the relativistic bound-state energy Ievels of the as a measure of the size of the relativistic effects.
hydrogen atom, well before the development of wave It is subsequently used as an expansion parameter for
mechanics, clear ideas about the electron spin, and various quantities, thus defining a "nonrelativistic
Dirac's relativistic wave equation. He correctly Iimit". The separation of kinematical relativistic effects
attributed the fine structure of atomic spectra to and fine-structure splitting is discussed considering the
relativistic effects, and thus published the first paper spherical orbits.
giving a quantitative perspective on relativistic quantum In the third section, X-ray spectra (Röntgenspektren)
chemistry. of the hydrogen atom are discussed. The principles de
veloped in the first two parts of the paper are applied to
Key words: Relativistic quantum chemistry inner-shell spectroscopy. The paper is characterized by a
Sommerfeld transformation quick adaptation and rapid development of the ideas of
the "old quantum theory" introduced by Bohr, which
was vividly discussed in the contemporary Iiterature
[2--4]. The simultaneaus treatment of relativity and
quantum effects is the first of its kind.
Sommerfeld's quantization rules
j
Sommerfeld's paper features three major sections, each p; dq; = 2nn;n, i = 1, ... ,D
presenting new ideas for the explanation of the pheno
menology of the spectra of hydrogen and hydrogen-like for a system with D degrees of freedom are not
atoms. The first section develops the theory of the independent of the coordinate system, and he had to
Balmer series in the spectrum of the hydrogen atom. The carry out an explicit Separation of variables in order to
theoretical method employed is the application of Bohr apply them. Einstein [5] reinvestigated the problern and,
Wilson-Sommerfeld quantization rules to the nonrela besides giving a coordinate-invariant formulation of the
tivistic bound-state Kepler problem, i.e., the physics of a quantum conditions, pointed out that a quantization by
charged body moving in an attractive central potential. means of classical action integrals is possible only for
The extension of previous ad hoc quantization rules to integrable systems. These quantization rules for integr
phase integrals, enabling the application of the "old able systems were later refined by Keller [6] and are
quantum theory" to nonspherical orbits, is introduced in known as Einstein-Brillouin-Keller rules. The method
this section. Sommerfeld uses these new rules to derive of semiclassical quantization was revived in the early
the expressions for the elliptic (bound-state) orbits, in 1980s, when Gutzwiller [7] found a way to apply
particular the ones with nonspherical symmetry, i.e., semiclassical quantization also to nonintegrable systems.
nonvanishing eccentricity, e. His method is based on the Feynman path integral and
The second section deals with the fine structure of the its expansion around closed classical paths in phase
hydrogen spectral lines. The discussion of the bound space, the "periodic orbits", and is nowadays instru
state Kepler problern is extended to the relativistic case. mental in the context of strongly chaotic systems. For an
Following an idea of Bohr [1], who had already account of these developments see the recent monograph
conjectured that the fine structure of the hydrogen by Grosehe and Steiner [8].
spectrum could be a relativistic effect proportional to In the following I shall focus on the second section of
e4 jn2c2, the fine structure of the hydrogen spectrum is the paper, dealing with fine structure, since to some extent