Computational quantum chemistry

D. B. Cook, Handbook of Computational Quantum Chemistry Oxford, Oxford (1998). 

A. Hinchliffe, Computational Quantum Chemistry (Wiley, New York, 1988). 

One of the biggest headaches in computational quantum chemistry is the problem of integral evaluation, so let s spend a few minutes with this very simple problem. 

My little book Computational Quantum Chemistry was published in 1988. In the Preface, I wrote the following ... 

It is interesting to note that all the simple theories (such as Hiickel jr-electron theory) have now reappeared as options in these very same packages Thus, very many scientists now routinely use computational quantum chemistry as a futuristic tool for modelling the properties of pharmaceutical molecules, dyestuffs and hiopolymers. I wrote the original Computational Quantum Chemistry text as... 

It should also be acknowledged that in recent years computational quantum chemistry has achieved a number of predictions that have since been experimentelly confirmed (45-47). On the other hand, since numerous anomalies remain even within attempts to explain the properties of atoms in terms of quantum mechanics, the field of molecular quantum mechanics can hardly be regarded as resting on a firm foundation (48). Also, as many authors have pointed out, the vast majority of ab initio research judges its methods merely by comparison with experimental date and does not seek to establish internal criteria to predict error bounds theoretically (49-51). The message to chemical education must, therefore, be not to emphasize the power of quantum mechanics in chemistry and not to imply that it necessarily holds the final answers to difficult chemical questions (52). 

This line of research has not lost his momentum. One of the reasons is the eontinuing progress in the computer hardware and software. Methods and algorithms are, and will be, continuously updated to exploit new features made available by eomputer seienee, as for example the parallel architectures, or the neuronal networks, to mention things at present of widespread interest, or even conceptually less significant improvements, as the inerease of fast memory in commereial computers. Computer quantum chemistry is not a mere recipient of progresses in eomputer seienee. Many progresses in the software comes from... 

Here, n corresponds to the principal quantum number, the orbital exponent is termed and Ylm are the usual spherical harmonics that describe the angular part of the function. In fact as a rule of thumb one usually needs about three times as many GTO than STO functions to achieve a certain accuracy. Unfortunately, many-center integrals such as described in equations (7-16) and (7-18) are notoriously difficult to compute with STO basis sets since no analytical techniques are available and one has to resort to numerical methods. This explains why these functions, which were used in the early days of computational quantum chemistry, do not play any role in modem wave function based quantum chemical programs. Rather, in an attempt to have the cake and eat it too, one usually employs the so-called contracted GTO basis sets, in which several primitive Gaussian functions (typically between three and six and only seldom more than ten) as in equation (7-19) are combined in a fixed linear combination to give one contracted Gaussian function (CGF),... 

In recent years, density-functional theory has emerged as the computational quantum chemistry method of choice for biological problems of medium size range (up to a few hundreds of atoms) in applications that do not require extensive conformational sampling. The field continues to advance in the accuracy of new functionals, the improvement of algorithms and the functionality and computational performance of software [81]. 

The equation (3) generates the famous BO potential energy hypersurface. The practical power of this concept is well documented and it remains at the foundation of important domains in computational quantum chemistry. The theory of absolute reaction rates is entirely based upon it [32-34, 63] as well as all modem quantum theories of reaction rates [36, 39, 64-80],... 

In the following we shall briefly review some of the recent applications of computational quantum chemistry to zeolites, in particular, some studies on the quantum chemical origin of Loewenstein s aluminum avoidance rule, and on the role of counter ions in stabilizing various structural units in zeolite lattices. These calculations are often extremely time consuming, nevertheless, the scope of their application is continuously expanding. 

The currently available quantum chemical computational methods and computer programs have not been utilized to their potential in elucidating the electronic origin of zeolite properties. As more and more physico-chemical methods are used successfully for the description and characterization of zeolites, (e.g. (42-45)), more questions will also arise where computational quantum chemistry may have a useful contribution towards the answer, e.g. in connection with combined approaches where zeolites and metal-metal bonded systems (e.g. (46,47)) are used in combination. The spectacular recent and projected future improvements in computer technology are bound to enlarge the scope of quantum chemical studies on zeolites. Detailed studies on optimum intercavity locations for a variety of molecules, and calculations on conformation analysis and reaction mechanism in zeolite cavities are among the promises what an extrapolation of current developments in computational quantum chemistry and computer technology holds out for zeolite chemistry. 

Ab initio quantum chemistry has advanced so far in the last 40 years that it now allows the study of molecular systems containing any atom in the Periodic Table. Transition metal and actinide compounds can be treated routinely, provided that electron correlation1 and relativistic effects2 are properly taken into account. Computational quantum chemical methods can be employed in combination with experiment, to predict a priori, to confirm, or eventually, to refine experimental results. These methods can also predict the existence of new species, which may eventually be made by experimentalists. This latter use of computational quantum chemistry is especially important when one considers experiments that are not easy to handle in a laboratory, as, for example, explosive or radioactive species. It is clear that a good understanding of the chemistry of such species can be useful in several areas of scientific and technological exploration. Quantum chemistry can model molecular properties and transformations, and in... 

K. K. Irikura, R. D. Johnson III, R. Kacker. Uncertainty Associated with Virtual Measurements from Computational Quantum Chemistry Models. Metrologia 2004, 41, 369-375. 

T. Daniel Crawford Center for Computational Quantum Chemistry School of Chemical Sciences University of Georgia Athens, GA 30602 USA Christina R. Harris The Sloan-Kettering Institute for Cancer Research Laboratory for Bioorganic Chemistry 1275 York Avenue New York, NY 10021 USA... 

When the uncertainty associated with AHf is 5 kcal/mol, rate and equilibrium constants can be estimated within a factor of 10 at process temperatures, i.e., 500-1,500 K. This level of accuracy may be acceptable for preliminary mechanism development work and for the identification of important reactions in a DCKM. However, it would clearly be desirable to know AHf within 1 kcal/mol, which would lead to the determination of rate and equilibrium constants that are accurate within a factor of two. Since this level of accuracy is very close to the limits of accuracy of most experimental measurements, improvements in AHf are often difficult. Consequently, computational quantum chemistry holds a great promise for the accurate determination of AHf. 

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia... 

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