First-principles quantum chemical methods

During the last decade, density-functional theory (DFT)-based approaches [1, 2] have advanced to prominent first-principles quantum chemical methods. As computationally affordable tools apt to treat fairly extended systems at the correlated level, they are also of special interest for applications in medicinal chemistry (as demonstrated in the chapters by Rovira, Raber et al. and Cavalli et al. in this book). Several excellent text books [3-5] and reviews [6] are available as introduction to the basic theory and to the various flavors of its practical realization (in terms of different approximations for the exchange-correlation functional). The actual performance of these different approximations for diverse chemical [7] and biological systems [8] has been evaluated in a number of contributions. 

Figure 2. Illustration of simulation techniques available at various time and length scales. QC means first principles, quantum chemical methods. MD refers to classical molecular dynamics methods. (Monte Carlo methods are useful in roughly the same range of time and distance.) Methods for connecting QC, MD, and continuum methods are indicated in parentheses.

In this chapter, I have provided a brief overview of the QMC method for electronic structure with emphasis on the more accurate diffusion Monte Carlo (DMC) variant of the method. The high accuracy of the approach for the computation of energies is emphasized, as well as the adaptability to large multiprocessor computers. Recent developments are presented that shed light on the capability of the method for the computation of systems larger than those accessible by other first principles quantum chemical methods. 

Cavalli, A., Carloni, P. and Recanatini, M. (2007) Target-related applications of first principles quantum chemical methods in drug design. Chem. Rev., 106, 3497-3519. 

First-principle quantum chemical methods have advanced to the stage where they can now offer qualitative, as well as, quantitative predictions of structure and energetics for adsorbates on surfaces. Cluster and periodic density functional quantum chemical methods are used to analyze chemisorption and catalytic surface reactivity for a series of relevant commercial chemistries. DFT-predicted adsorption and overall reaction energies were found to be within 5 kcal/mol of the experimentally known values for all systems studied. Activation barriers were over-predicted but still within 10 kcal/mol. More specifically we examined the mechanisms and reaction pathways for hydrocarbon C-H bond activation, vinyl acetate synthesis, and ammonia oxidation. Extrinsic phenomena such as substituent effects, bimetallic promotion, and transient surface precursors, are found to alter adsorbate-surface bonding and surface reactivity. 

In this paper, I review the recent advances and developments of first-principle quantum chemical methods and discuss their application to modelling chemisorption, surface reactivity of reactants/intermediates, and the catalytic behavior for a series of relevant commercial chemistries. We focus primarily on the static representation of the surface. 

First principle quantum chemical methods have reached the stage where they can now begin to provide reliable information on the structure, spectral and energetic properties of adsorbates on surfaces. Both the cluster, as well as the periodic band methods, were found to be quite successful. In contrast to early MO-based cluster studies, the DFT cluster methodology provides more accurate predictions, provided that special care is taken to optimize the structural configurations, the geometries, and spin states for all clusters. 

This obvious need for clarifying the relationship between the electronic and geometric stmcture of paramagnetic systems and their g values nowadays can be met with the help of first-principles quantum chemical methods. A theoretical description of electronic g values, based on a relativistic method which accurately treats spin-orbit interaction even in cases when it is too strong to be considered as a perturbation, will be uniformly applicable to systems with both light and heavy atoms. 

Advances in computational chemistry and molecular simulation have also reached the stage whereby they can be used to develop more advanced and robust kinetic models for catalytic systems. First-principle quantum chemical methods, for example, are being used to routinely calculate thermochemistry and kinetics for gas phase chemistry with accuracies on the order of... 

First-principles quantum chemical methods have allowed elucidation of reaction mechanisms for a variety of heterogeneous catalytic reactions. As discussed above, incorporating the nature of the electrochemical double layer into quantum models is limited by the challenges associated with following the structure and dynamics of the electrolyte over the electrode. Further, to capture electro-catalytic reaction mechanisms accurately using DFT methods, the chemical potential of electrons and ionic species that participate in elementary steps must be evaluated. Several DFT modeling approaches have been developed to include the influence of solvent and/or electrochemical potential on surface reactions and to take into account the chemical potential of ionic species. 

It is thus obvious that among numerous computational methods, first principles quantum chemical approach is indispensable. However, initially first principles quantum chemical calculations required the use of models consisting of a few atoms (clusters) and the range of properties was limited. Since the advent of modem computing resources, as well the models could be extended to cover larger variety of structures as the methodology has been... 

Further theoretical studies supported by in situ spectroscopy and high-resolution microscopy are needed to be able to understand this unusually strong bonding between Cu and Ce. To apply such first-principles quantum chemical MD approach, new computational methods accelerating computational time by several orders of magnitude must be developed. 

Undoubtedly, the methods most widely used to solve the Schrodinger equation are those based on the approach originally proposed by Hartree [1] and Fock [2]. Hartree-Fock (HF) theory is the simplest of the ab initio or "first principles" quantum chemical theories, which are obtained directly from the Schrodinger equation without incorporating any empirical considerations. In the HF approximation, the n-electron wavefunction is built from a set of n independent one-electron spin orbitals which contain both spatial and spin components. The HF trial wavefunction is taken as a single Slater determinant of spin orbitals. 

As is evident from these examples, computational quantum mechanics, semiempirical and ab initio methods alike, represent important new tools for the estimation of rate parameters from first principles. Our ability to estimate activation energies is particularly significant because until the advent of these techniques, no fundamentally based methods were available for the determination of this important rate parameter. It must be recognized, however, that these theoretical approaches still are at their early stages of development that is to say, computational quantum chemical methods should only be used with considerable care and in conjunction with conventional methods of estimation discussed earlier in this article, as well with experiments. 

In this review we shall first establish the theoretical foundations of the semi-classical theory that eventually lead to the formulation of the Breit-Pauli Hamiltonian. The latter is an approximation suited to make the connection to phenomenological model Hamiltonians like the Heisenberg Hamiltonian for the description of electronic spin-spin interactions. The complete derivations have been given in detail in Ref. (21), but turn out to be very involved and are thus scattered over many pages in Ref. (21). For this reason, we aim here at a summary that is as brief and concise as possible so that all relevant connections between different levels of approximation are evident. This allows us to connect present-day quantum chemical methods to phenomenological Hamiltonians and hence to establish and review the current status of these first-principles methods applied to transition-metal clusters. 

The nature of the methanol-zeolite interaction has been shown to be sensitive to a number of parameters and as such has proved to be a good benchmark for judging the reliability of quantum chemical methods. Not only are there a number of possible modes whereby one and two molecules interact with an acidic site (245), the barrier to proton transfer is small and sensitive to calculation details. Recent first-principles simulations (236-238) suggest that the nature of adsorbed methanol may be sensitive to the topology of the zeolite pore. The activation and reaction of methane, ethane, and isobutane have been characterized by using reliable methods and models, and realistic activation energies for catalytic reactions have been obtained. 

For He-Ar spectral moments have been computed from first principles, using advanced quantum chemical methods [278] details may be found in Chapters 4 and 5. We quote the results of the ab initio calculations of the moments in Table 3.1, columns 4 and 6. The agreement with measurement is satisfactory in view of the experimental uncertainties. We... 

Highly developed quantum chemical methods exist to compute with an ever increasing precision molecular and supermolecular properties from first principles. For example, attempts to compute intermolecular interaction potentials and, more recently, induced dipole moments, are well known for the simpler atomic and molecular systems. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

Computations. Efforts to compute pair polarizabilities from first principles, using perturbation techniques or modern quantum chemical methods, have been known for many years and are reviewed by Hunt [80] in the desirable detail. Amos s review of ab initio methods applied to the computation of molecular properties considers supermolecular properties, too [2]. 

None of this can be detected by standard geometric criteria. First-principles simulations like CPMD allow for new wave-function-based descriptors [231] as the electronic structure is - in addition to the positions of all atomic nuclei involved -available on the fly . Of course, the above mentioned fundamental problem that the interaction energy is not an observable quantity is in first-principle simulations as apparent as in static calculations. However, the wavefunction naturally tracks all electronic changes in an aggregate. A wavefunction-based descriptor would also be helpful in traditional molecular dynamics because snapshots can be calculated with advanced static quantum chemical methods. 

Modem quantum-chemical methods can, in principle, provide all properties of molecular systems. The achievable accuracy for a desired property of a given molecule is limited only by the available computational resources. In practice, this leads to restrictions on the size of the system From a handful of atoms for highly correlated methods to a few hundred atoms for direct Hartree-Fock (HF), density-functional (DFT) or semiempirical methods. For these systems, one can usually afford the few evaluations of the energy and its first one or two derivatives needed for optimisation of the molecular geometry. However, neither the affordable system size nor, in particular, the affordable number of configurations is sufficient to evaluate statistical-mechanical properties of such systems with any level of confidence. This makes quantum chemistry a useful tool for every molecular property that is sufficiently determined (i) at vacuum boundary conditions and (ii) at zero Kelvin. However, all effects from finite temperature, interactions with a condensed-phase environment, time-dependence and entropy are not accounted for. 

All quantum-chemical methods, even if they are considered as derived from first-principles, make use of at least the first group of parameters. Examples are the atomic masses and atomic heats of formation. Atomic orbital exponents used in all LCAO-based methods are an example of the second group. 

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