Computational quantum chemistry methods

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]. 

Potential energy diagram for the decomposition of the methylmethoxy radical, an important intermediate in the combustion of diethyl ether. Highly accurate computational quantum chemistry methods were used to calculate the configurations and the relative energies of the species shown. 

The new computational quantum chemistry methods make it possible to directly simulate biochemical processes, which involve large molecules. In this work the interaction of silver and copper ions with chitin dimers was modeled using the DFT theory. 

Organometallic chemistry is possibly one of the fields in which the application of computational quantum chemistry methods has been most successful [1-3]. Indeed, it is now common practice to complement synthetic or spectroscopic studies with the computational characterization of putative species present in reaction mixtures [4-6]. Detailed mechanistic studies, employing state-of-the-art electronic structure methods (notably, density functional theory, DFT), may also be performed to rationalize experimental outcomes [7, 8]. Many of these studies are based on reduced model systems, in which the reactive moieties are represented explicitly and environmental effects are included by means of mean field theories [9-11]. The approach has turned out to be successful in many instances and may be routinely performed on general-purpose hardware. 

The combined approach of low-temperature scanning tunneling spectroscopy and DFT computations (LDA and HSE periodic computations) was used to study hexadecafluoro-phthalocyanine CuFjgPc and epitaxial graphene on 6H-SiC(0001) (Table 11.9) [154]. Since a dispersion-stabilized system was investigated, computational quantum chemistry methods that properly treat vdW-interactions were desired for such a study. These may correct the computed adsorption- and diffusion-related energetic characteristics. 

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),... 

The understanding of the catalytic function of enzymes is a prime objective in biomolecular science. In the last decade, significant developments in computational approaches have made quantum chemistry a powerful tool for the study of enzymatic mechanisms. In all applications of quantum chemistry to proteins, a key concept is the active site, i.e. a local region where the chemical reactivity takes place. The concept of the active site makes it possible to scale down large enzymatic systems to models small enough to be handled by accurate quantum chemistry methods. 

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... 

Computational quantum chemistry has emerged in recent years as a viable tool for the elucidation of molecular structure and molecular properties, especially for the prediction of geometrical parameters, kinetics and thermodynamics of highly labile compounds such as nitrosomethanides. However, they are difficult objects for both experimental (high toxicity, redox lability, high reactivity, explosive character etc.) and computational studies, even with today s sophisticated techniques (e.g. NO compounds are often species with open-shell biradical character which requires the application of multi-configuration methods). 

The aforementioned progress in NMR spectroscopy (and other experimental methods as well) in combination with computational chemistry has reached a stage in which an understanding of the most general features of organic reactions on solid acids may reasonably be expected in several years. This does not yet quite exist this report is written in a time at which the sophisticated application of NMR and computational quantum chemistry to solid acids is becoming widespread, and specialists in various areas are suddenly having to evaluate evidence from other specialties. 

Any mechanistic study undertaken using quantum chemistry methods requires considerable physical and chemical insight. Thus for a thermal reaction, there is no method that will generate automatically all the possible mechanistic pathways that might be relevant. Rather, one still needs to apply skills of chemical intuition, and it is necessary to make sensible hypotheses that can then be explored computationally. In excited state chemistry, these problems are even more difficult, and we hope the examples given in the last section provide a bit of this required insight. However, the DBH example shows just how complex these problems can become when many electronic excited states are involved. 

Since his appointment at the University of Waterloo, Paldus has fully devoted himself to theoretical and methodological aspects of atomic and molecular electronic structure, while keeping in close contact with actual applications of these methods in computational quantum chemistry. His contributions include the examination of stability conditions and symmetry breaking in the independent particle models,109 many-body perturbation theory and Green s function approaches to the many-electron correlation problem,110 the development of graphical methods for the time-independent many-fermion problem,111 and the development of various algebraic approaches and an exploration of convergence properties of perturbative methods. His most important... 

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

The theoretical tools of quantum chemistry briefly described in the previous chapter are numerously implemented, sometimes explicitly and sometimes implicitly, in ab initio, density functional (DFT), and semi-empirical theories of quantum chemistry and in the computer program suits based upon them. It is usually believed that the difference between the methods stems from different approximations used for the one- and two-electron matrix elements of the molecular Hamiltonian eq. (1.177) employed throughout the calculation. However, this type of classification is not particularly suitable in the context of hybrid methods where attention must be drawn to the way of separating the entire molecular system (eventually - the universe itself) into parts, of which some are treated explicitly on a quantum mechanical/chemical level, while others are considered classically and the rest is not addressed at all. That general formulation allows us to cover both the traditional quantum chemistry methods based on the wave functions and the DFT-based methods, which generally claim... 

The study of van der Waals and hydrogen bonded molecules is one of the very important fields of chemistry where computational quantum chemical methods have increased our understanding both in a quantitative and qualitative way. The interest in the subject is emphasised by the impressive number of reviews, monographs and books that have recently appeared [1]. An accurate knowledge of the interaction potential between the individual molecules is in fact essential to the treatment of both finite clusters and condensed matter properties in the broad field of computer simulations. 

The recent developments in generalized Valence Bond (GVB) theory have been reviewed by Goddard and co-workers,13 and also the use of natural orbitals in theoretical chemistry,14 15 and the accuracy of computed one-electron properties.18 The Xa method has been reviewed by Johnson,17 and Hurley has discussed high-accuracy calculations on small molecules.18 Several other reviews of interest have appeared in Advances in Quantum Chemistry.17 Localized orbital theory has been reviewed by England, Salmon, and Ruedenberg,19 and the bonding in transition-metal complexes discussed by Brown et a/.20 Finally, the recent developments in computational quantum chemistry have been reviewed by Hall.21... 

Regarding TDDFT benchmark studies of chiroptical properties prior to 2005, the reader is referred to some of the initial reports of TDDFT implementations and early benchmark studies for OR [15,42,47,53,98-100], ECD [92,101-103], ROA [81-84], and (where applicable) older work mainly employing Hartree-Fock theory [52,55, 85,104-111], Often, implementations of a new quantum chemistry method are verified by comparing computations to experimental data for relatively small molecules, and papers reporting new implementations typically also feature comparisons between different functionals and basis sets. The papers on TDDFT methods for chiroptical properties cited above are no exception in this regard. In the following, we discuss some of the more recent benchmark studies. One of the central themes will be the performance of TDDFT computations when compared to wavefunction based correlated ab initio methods. Various acronyms will be used throughout this section and the remainder of this chapter. Some of the most frequently used acronyms are collected in Table 1. 

Shavitt, I., 1979, "New Methods in Computational Quantum Chemistry and their Application on Modern Supercomputers ,... 

Any application of the methods of computational quantum chemistry and the broader field of computational chemistry is based on the available knowledge and although this is contained in the primary literature it is at its most accessible in textbooks. There are a number of textbooks at various levels from undergraduate to research frontier. In reverse chronological order, these are ... 

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