Chemistry quantum

Quantum chemistry is the appfication of quantum mechanical principles and equations to the study of molecules. In order to nnderstand matter at its most fundamental level, we must use quantum mechanical models and methods. There are two aspects of quantum mechanics that make it different from previous models of matter. The first is the concept of wave-particle duality that is, the notion that we need to think of very small objects (such as electrons) as having characteristics of both particles and waves. Second, quantum mechanical models correctly predict that the energy of atoms and molecules is always quantized, meaning that they may have only specific amounts of energy. Quantum chemical theories allow us to explain the structure of the periodic table, and quantum chemical calculations allow us to accurately predict the structures of molecules and the spectroscopic behavior of atoms and molecules. 

Quantum mechanical ideas began with studies of the physics of light. By the late nineteenth century, virtually all scientists believed that light behaved as 

Despite this apparent certainty that hght was a wave. Max Planck and Albert Einstein, at the beginning of the twentieth century, showed that some experiments required the use of a particle model for hght, rather than a wave model. Since both models were necessary for an accurate description of all of the properties of light, scientists today use mathematical equations appropriate to both waves and particles in describing the properties of hght. 

Waves and particles are fundamentally different a particle exists at a particular point in space, whereas a wave continues on for (sometimes) a great distance. It defies intuition to think that both of these models might describe the same thing. Nevertheless, an accurate description of light requires the use of both wave and particle ideas. 

It is contrary to our intuition that electrons might behave as waves. The repercussions of this notion are that the electron does not have a definite 

Modern quantum chemistry is strongly dependent on time-consuming computations, so the introduction of the first computers, at the end of the 

initiated a new era in theoretical chemistry. The first all-electron valence bond calculation was performed on the hydrogen fluoride (HF) molecule in 1953. ° The first all-electron SCF studies using molecular orbitals (MO) represented by linear combinations of atomic orbitals (LCAO), still on diatomics, came later. Finally the first ab initio computation using a Gaussian-type function basis set on a polyatomic molecule, hydrazine, was published in 1966.13 

The general tendency that soon appeared in the French community, as elsewhere, vas for the theoretical chemists to split into two categories the methodologists, who were trying to improve the accuracy and the efficiency of the methods, and those who were in contact with experiment. 

In 1968, Alain Veillard moved to Strasbourg, where he started a laboratory that soon became recognized for the study of transition metal compounds. Later, the laboratory, now directed by Elise Kochanski, broadened its interests to include the study of intermolecular interactions. 

In Nancy, Jean Barriol retired in 1974. His successor, Jean-Louis Rivail, started the very early quantum chemical studies of solvated species, and when Bernard Maigret joined the group in 1991, the field of investigation was widened to include biomolecular systems. 

Attributed to Albert Einstein, speaking of quantum mechanics if true, it shows that even geniuses may sometimes be wrong. 

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact appli- 

In 1972 Schaefer described the results of many approximate quantum-mechanical calculations on gas-phase atoms and small molecules that indicated that Dirac s goal was close to being achieved for such species. Around the same time, it became clear that quantum-mechanical theory could also be applied to many categories of more complicated chemical systems in a qualitative manner, leading to substantial advances in the understanding of the structure and reactivity of such complex materials. Contemporaneous with this improved capability of quantum-mechanical theory within chemistry was an expansion in experimental methods that yielded knowledge pertinent to the electronic structure of molecules. 

If theory could provide only exact results for any desired property of any system, it would not be any better than a collection of good experiments. What theory uniquely provides is the qualitative principles responsible for the results from a particular experiment or calculation. With proper understanding of the principles, one can predict how new systems will act in advance of either experiment or quantitative calculations. 

In addition to those groups within quantum chemistry using very accurate and computationally demanding theoretical methods, there are other groups focusing upon simple semiempirical methods that rely upon sym- 

BC bond is fixed. It should be noted that PESs represent the energy of the collection of atoms at absolute zero, i.e., they provide no information on the translational, vibrational, or rotational energies that are normally present. The latter forms of energy clearly must be considered to determine thermochemistry under conditions of practical interest. 

The determination of Ey requires that Schrodinger s equation for the collection of atoms must be solved with all the associated nuclei and electrons in three dimensions. For a molecule with N nuclei and n electrons, the time-independent Schrodinger s equation is given by 

Vj is the Laplacian operator centered around j, Ri and rj are the position vectors for the nuclei i and the electron j, respectively, Eq is the permittivity of vacuum, m is the mass of the electron, is the mass of the jth nucleus, and 4  

IS the total wave function. In shorthand notation Schrodinger s equation can be written as 

For the hydrogen atom, which has one nucleus (charge +e) and one electron (—e), Eq. (2) can be reduced into the following familiar form  

In the late seventeenth century, Isaac Newton discovered classical mechanics, the laws of motion of macroscopic objects. In the early twentieth century, physicists found that classical mechanics does not correctly describe the behavior of very small particles such as the electrons and nuclei of atoms and molecules. The behavior of such particles is described by a set of laws called quantum mechanics. 

Quantum chemistry applies quantum mechanics to problems in chemistry. The influence of quantum chemistry is evident in all branches of chemistry. Physical chemists use quantum mechanics to calculate (with the aid of statistical mechanics) thermodynamic properties (for example, entropy, heat capacity) of gases to interpret molecular spectra, thereby allowing experimental determination of molecular properties (for example, bond lengths and bond angles, dipole moments, barriers to internal rotation, energy differences between conformational isomers) to calculate molecular properties theoretically to calculate properties of transition states in chemical reactions, thereby allowing estimation of rate constants to understand intermolecular forces and to deal with bonding in solids. 

Organic chemists use quantum mechanics to estimate the relative stabilities of molecules, to calculate properties of reaction intermediates, to investigate the mechanisms of chemical reactions, and to analyze NMR spectra. 

Analytical chemists use spectroscopic methods extensively. The frequencies and intensities of lines in a spectrum can be properly understood and interpreted only through the use of quantum mechanics. 

Inorganic chemists use ligand field theory, an approximate quantum-mechanical method, to predict and explain the properties of transition-metal complex ions. 

We have adopted a strategy similar to that used in our development of polymer force fields in parameterization of an atomistic potential function for HMX. Specifically, we have undertaken a systematic investigation of conformational and intermolecular binding energies in model nitramine compounds (i.e., those containing the C2N-NO2 moiety ) using high-level QC calculations. In the case of HMX, a QC-based force field is the only realistic option due to insufficient spectroscopic data that would facilitate force field parameterization. 

Conformer B3LYP/6-311GH t i Geometry t 2 Energy (kcal/mol) BL3YP/6-311G MP2/6-311G  

In the following we describe briefly the procedure for fitting force field parameters, and provide comparisons between force-field and QC predictions. A more detailed discussion of the force field parameterization can be found in Refs. [34] and [35], 

Nonbonded parameters. All dispersion interactions were modeled by an 

Torsional potential function. The torsional parameters were adjusted to give the best representation of the methyl and nitro group rotation in DMNA. 

Peter C. Jurs, Computer-Enhanced Analytical Spectroscopy, Vol. 3, Based on the Third Symposium on Computer-Enhanced Analytical Spectroscopy held June 6-8, 1990, at the Snowbird Resort and Conference Center, Salt Lake City, Utah, Plenum, New York, 1992. 

Charles L. Wilkins, Computer-Enhanced Analytical Spectroscopy, Vol. 4, Plenum, New York, 1993. 

Fausto, Recent Experimental and Computational Advances in Molecular Spectroscopy, Proceedings of the NATO Advanced Study Institute on Molecular Spectroscopy Recent Experimental and Computational Advances, Ponta Delgada, Sao Miguel (Acores), Portugal, August 30-September 11, 1992, in NATO ASI Series, Ser. C, 

George and D. Steele, Computing Applications in Molecular Spectroscopy, Royal Society of Chemistry, Cambridge, UK, 1995. 

Catlow, Computer Modeling in Inorganic Crystallography, Academic Press, San Diego, 1997. 

As mentioned in Section 5.2, every mass spectrometer has a characteristic temporal property and SAT. Although in most cases mass spectrometers are unable to provide 

In MPI, ionization occurs only if the second laser interacts with molecules excited by the first laser before they return to the Sg state or transfer to other electronic states. Ions are produced when a molecule is excited to the ionization continuum. It can happen when the probe laser irradiates the molecule before the electron leaves the state. On the other hand, ion production is not achievable if the delay time between the first and the second laser is longer than the lifetime of the molecule. 

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Ira N. Levine, Quantum Chemistry, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 1991. (Source for density functional theory.)... 

Although a separation of electronic and nuclear motion provides an important simplification and appealing qualitative model for chemistry, the electronic Sclirodinger equation is still fomiidable. Efforts to solve it approximately and apply these solutions to the study of spectroscopy, stmcture and chemical reactions fonn the subject of what is usually called electronic structure theory or quantum chemistry. The starting point for most calculations and the foundation of molecular orbital theory is the independent-particle approximation. 

Levine I N 1991 Quantum Chemistry 4Vn edn (Englewood Cliffs, NJ Wiley)... 

A relatively complete survey of quantum chemistry, written on a level just below that of the Szabo and Ostiund text. Levine has done an excellent job in including up-to-date material in successive editions of this text, which makes for interesting as well as informative reading. 

Szabo A and Ostiund N S 1996 Modern Quantum Chemistry (New York Dover)... 

A comprehensive treatment of density functional theory, an idea that is currently very popular in quantum chemistry. 

Much of the work done on metal clusters has been focused on the transition from cluster properties to bulk properties as the clusters become larger, e.g. the transition from quantum chemistry to band theory [127]. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

In either case, the structure of the solvation shell has to be calculated by otiier methods supplied or introduced ad hoc by some fiirther model assumptions, while charge distributions of the solute and within solvent molecules are obtained from quantum chemistry. 

Quack M 1982 The role of intramolecular coupling and relaxation in IR-photochemistry Intramolecular Dynamics, Proc. 15th Jerusalem Symp. on Quantum Chemistry and Biochemistry (Jerusalem, Israel, 29 March-1 April 1982) ed J Jortner and B Pullman (Dordrecht Reidel) pp 371-90... 

McQuarrie D A 1983 Quantum Chemistry M Valley, CA University Science Books)... 

As a scientific tool, ab initio quantum chemistry is not yet as accurate as modem laser spectroscopic measurements, for example. Moreover, it is difficult to estimate the accuracies with which various methods predict bond energies and lengths, excitation energies and the like. In the opinion of tlie author, chemists who... 

C) All mean-field models of electronic. structure require large corrections. Essentially all ab initio quantum chemistry approaches introduce a mean field potential F that embodies the average interactions among the electrons. The difference between the mean-field potential and the true Coulombic potential is temied [20] the "fluctuationpotentiar. The solutions Ef, to the true electronic... 

B3.1.3 WHAT ARE THE ESSENTIAL CONCEPTS OF AS INITIO QUANTUM CHEMISTRY ... 

The simplest trial fiinction employed in ab initio quantum chemistry is the single Slater detemiinant fiinction in which N spin orbitals are occupied by N electrons ... 

For both types of orbitals, the coordinates r, 0 and cji refer to the position of the electron relative to a set of axes attached to the centre on which the basis orbital is located. Although STOs have the proper cusp behaviour near the nuclei, they are used primarily for atomic- and linear-molecule calculations because the multi-centre integrals which arise in polyatomic-molecule calculations caimot efficiently be perfonned when STOs are employed. In contrast, such integrals can routinely be done when GTOs are used. This fiindamental advantage of GTOs has led to the dominance of these fimetions in molecular quantum chemistry. 

These approaches provide alternatives to the conventional tools of quantum chemistry. The Cl, MCSCF, MPPT/MBPT, and CC methods move beyond the single-configuration picture by adding to the wavefimction more configurations whose amplitudes they each detennine in their own way. This can lead to a very large number of CSFs in the correlated wavefimction and, as a result, a need for extraordinary computer resources. 

The more conventional quantum chemistry methods provide their working equations and energy expressions in temis of one- and two-electron integrals over the final MOs ([Pg.2185]

It was then used within early quantum chemistry in the following references ... 

Szabo A and Ostiund N S 1989 Modern Quantum Chemistry 1st edn (revised) (New York MoGraw-Flill) and also webpage http //www.emsl.pnl.aov 2080/docs/tms/guantummechanics/... 

J0rgensen P and Simons J 1981 Second Quantization-Based Methods in Quantum Chemistry (New York Aoademio) J0rgensen P and Simons J (eds) 1986 Geometrical Derivatives of Energy Surfaces and Molecular Properties (Boston, MA Reidel)... 

Simons J 1991 An experimental chemist s guide to ah initio quantum chemistry J. Phys. Chem. 95 1017-29... 

Pilar F L 1968 Elementary Quantum Chemistry (New York MoGraw-Hill) seotion 11.5... 

Hays E F and Allen L C 1970 Mole. A system for quantum chemistry I. General description Int. J. Quantum Chem. S 3 715-25 Hehre W J, Lathan W A, Ditchfieid R, Newton M D and Popie J A 1971 Program No 236 (Bloomington, IN Quantum Chemistry Program Exchange)... 

J0rgensen P and Simons J 1981 Second Quantization Based Methods in Quantum Chemistry (New York Academic) oh 4... 

Dahl J P and Avery J (eds) 1984 Locai Density Approximations in Quantum Chemistry Soiid State Physics (New York Plenum)... 

First-principles models of solid surfaces and adsorption and reaction of atoms and molecules on those surfaces range from ab initio quantum chemistry (HF configuration interaction (Cl), perturbation theory (PT), etc for details see chapter B3.1 ) on small, finite clusters of atoms to HF or DFT on two-dimensionally infinite slabs. In between these... 

The electron density, pj, of the embedded cluster/adsorbate atoms is calculated using quantum chemistry methods (HF, PT, multireference SCF, or Cl). The initial step in this iterative procedure sets to zero,... 

Flammond B L, Lester W A and Reynolds P J 1994 Monte Cario Methods in Ab initio Quantum Chemistry (Singapore World Scientific)... 

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