Quantum chemists

By its nature, the application of direct dynamics requires a detailed knowledge of both molecular dynamics and quantum chemistry. This chapter is aimed more at the quantum chemist who would like to use dynamical methods to expand the tools at theh disposal for the study of photochemistry, rather than at the dynamicist who would like to learn some quantum chemishy. It hies therefore to introduce the concepts and problems of dynamics simulations, shessing that one cannot strictly think of a molecule moving along a trajectory even though this is what is being calculated. 

Quantum chemists have devised efficient short-hand notation schemes to denote the basis set aseti in an ab initio calculation, although this does mean that a proliferation of abbrevia-liijii.s and acronyms are introduced. However, the codes are usually quite simple to under-sland. We shall concentrate on the notation used by Pople and co-workers in their Gaussian aerie-, of programs (see also the appendix to this chapter). 

Ldwdin population analysis avoids the problem of negative populations or populations greater than 2. Some quantum chemists prefer the Ldwdin approach to that of Mulliken as the charges are often closer to chemically intuitive values and are less sensitive to basis set. 

There may be as many basis sets defined for polyatomic calculations as there are quantum chemists One would like to define, in advance, the standard basis sets that will be suitable to most users. However, one also wants to allow sophisticated users the capability to modify existing basis sets or define their own basis sets. We have thus defined a HyperChem basis set file format and included with HyperChem a number of these. BAS files that define standard basis sets. Users, however, can define as many of their own basis sets as they like using this file format. The details of the HyperChem basis set file format are described in the HyperChem Reference manual. 

Sq can be calculated from the theoretically derived U(r) curves of the sort described in Chapter 4. This is the realm of the solid-state physicist and quantum chemist, but we shall consider one example the ionic bond, for which U(r) is given in eqn. (4.3). Differentiating once with respect to r gives the force between the atoms, which must, of course, be zero at r = rg (because the material would not otherwise be in equilibrium, but would move). This gives the value of the constant B in equation (4.3) ... 

Some large basis sets specify different sets of polarization functions for heavy atoms depending upon the row of the periodic table in which they are located. For example, the 6-311+(3df,2df,p) basis set places 3 d functions and 1 f function on heavy atoms in the second and higher rows of the periodic table, and it places 2 d functions and 1 f function on first row heavy atoms and 1 p function on hydrogen atoms. Note that quantum chemists ignore H and Ffe when numbering the rows of the periodic table. 

In the beginning, quantum chemists had pencils, paper, slide rules and log tables. It is amazing that so much could have been done by so few, with so little. 

The sixth article in this collection takes up the story from where paper 4 left off. If the n + (Madelung) rule can be fully reduced, then it might rightly be claimed that the periodic table reduces fully to quantum mechanics. This is a question that has been asked in a much-quoted paper by Per-Olov Lowdin, the influential quantum chemist who for many years led the Quantum Chemistry project at the University of Florida. 

The discrepancy between the two sequences of numbers representing the closing of shells and the closing of periods occurs, as is well known, due to the fact that the shells are not sequentially filled. Instead, the sequence of filling follows the so-called Madelung rule, whereby the lowest sum of the first two quantum numbers, n + 1, is preferentially occupied. As the eminent quantum chemist Lowdin (among others) has pointed out, this filling order has never been derived from quantum mechanics (2),... 

My project is not to critique of the power of quantum chemistry that I regard to be a self-evident fact. But with the triumph of quantum mechanics I believe there has been some tendency to exaggerate its success, especially on the part of some practicing quantum chemists and physicists. As a philosopher of chemistry I have the luxury of being able to examine the field as an outsider and of asking the kinds of questions which true practitioners might not even contemplate. The approach I take in this article is a philosophical one in the sense that I am concerned with principles and not just with technical details, although I try to be as accurate as possible with the latter. 

It Is something of a miracle that quantum mechanics explains the periodic table to the extent that It does we should not let this fact seduce us into believing that It Is a deductive explanation. Attempts to explain the details of the periodic table continue to challenge the Ingenuity of quantum physicists and quantum chemists, and the periodic table will continue to present a test case for the adequacy of new methods developed in quantum chemistry. 

The definitions given by Coulson to quantum ehemists belonging to this group (electronic computers, or ab initio-ists) is surely outdated. Every quantum chemists is now an "electronic computer" and the differenee between ab-initioists and non ab-initioists is rather... 

A crisis similar to that felt by Coulson in 1959 is probably impending now. Our fathers have been able to close the gap between groups I and 11 offering on the one side methods, computational tools, and confidence in numerical quantum chemist and on the other side accepting this offering and exhibiting the capability to re-formulate in a new form concepts and approaches. 

I have tried to sketch a partition of the variotts approaches in Quantrrm Chemistry into four groups. This taxonomy is open to criticism and does not imply, in my intention, an exclusive assignation of each quantum chemist to one of the four groups. 

Then appeared the time of computers. Quantum chemists developed semi-empirical codes that rapidly evolved into ab-initio complex systems of programs. According to their optimistic or pessimistic views, colleagues have seen this period either as that of semi -quantitative or of semi-qualitative theoretical chemistry. Very recently came the age of super computers, and a generation of quantum chemists have seen their dream come true at last, the quality of the calculation is in harmony with the quality of the concepts. 

Although the broad spectrum of Quantum Chemistry represented by the thirty or so articles contained in this volume only partially reflects the variety and richness of Berthier s preoccupations, it should convey to the coming generation of quantum chemists and to all readers the useful lesson of an outstanding chemist maintaining wide interests and resisting the drift of fashion. 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

Some substituents induce remarkably different electronic behaviors on the same aromatic system (8). Let us consider, for example, the actions of substituents on an aromatic electron system. Some substituents have a tendency to enrich their electronic population (acceptors), while others will give away some of it (donors). Traditionaly, quantum chemists used to distinguish between long range (mesomeric) effects, mainly u in nature, and short range (inductive) effects, mainly a. The nonlinear behavior of a monosubstituted molecule can be accounted for in terms of the x electron dipole moment. Examples of donor and acceptor substituents can be seen on figure 1. 

Instead of a theory to elucidate the important unsolved problems of chemistry, theoretical chemistry has become synonymous with what is also known as Quantum Chemistry. This discipline has patently failed to have any impact on the progress of mainstream chemistry. A new edition of the world s leading Physical Chemistry textbook [4] was published in the year that the Nobel prize was awarded to two quantum chemists, without mentioning either the subject of their work, nor the names of the laureates. Nevertheless, the teaching of chemistry, especially at the introductory level, continues in terms of handwaiving by reference to the same quantum chemistry, that never penetrates the surface of advanced quantum theory. 

From a computational view point, chemical reactions in solution present a yet not solved challenge. On one hand, some of the solvent effects can be approximated as if the solute molecule would be in a continuum with a given dielectric characterization of the liquid, and this view point has been pioneered by Bom [1], later by Kirkwood [2] and Onsager [3] and even later by many computational quantum chemists [4-9], On the other hand, the continuum model fails totally when one is interested in the specific... 

Quantum chemists have developed considerable experience over the years in inventing new molecules by quantum chemical methods, which in some cases have been subsequently characterized by experimentalists (see, for example, Refs. 3 and 4). The general philosophy is to explore the Periodic Table and to attempt to understand the analogies between the behavior of different elements. It is known that for first row atoms chemical bonding usually follows the octet rule. In transition metals, this rule is replaced by the 18-electron rule. Upon going to lanthanides and actinides, the valence f shells are expected to play a role. In lanthanide chemistry, the 4f shell is contracted and usually does not directly participate in the chemical bonding. In actinide chemistry, on the other hand, the 5f shell is more diffuse and participates actively in the bonding. 

Physical chemistry began to prosper partly from institutional and industrial causes. Some students who set out to study organic chemistry in the late nineteenth century were dissuaded from their aim by overcrowded conditions in the instructional and research laboratories. One example is Arthur A. Noyes, who was to establish the first physical chemistry research laboratory in America at the Massachusetts Institute of Technology. He set out for Germany in 1888 with his friend Samuel Mulliken, father of the later theoretical and quantum chemist, Robert Mulliken. 

At the same time that Heisenberg was formulating his approach to the helium system, Born and Oppenheimer indicated how to formulate a quantum mechanical description of molecules that justified approximations already in use in treatment of band spectra. The theory was worked out while Oppenheimer was resident in Gottingen and constituted his doctoral dissertation. Born and Oppenheimer justified why molecules could be regarded as essentially fixed particles insofar as the electronic motion was concerned, and they derived the "potential" energy function for the nuclear motion. This approximation was to become the "clamped-nucleus" approximation among quantum chemists in decades to come.36... 

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