Molecular orbitals semiempirical quantum-chemistry

Stewart HP. MOPAC A semiempirical molecular orbital program. Quantum Chemistry Program Exchange, 1983. Prog. 455. 

Gubanov VA, Zhukov VP, Litinskii AO (1976) Semiempirical methods of molecular orbitals in quantum chemistry. Nauka, Moscow... 

The extended Hiickel method, which is a semiempirical quantum chemistry method, is often used as a preliminary step in the DFT study of molecular orbital analysis. The acetylide-bridged organometallic dinuclear complexes 5.2 were studied by Halet et al. using the extended Hiickel method for qualitative analysis and DFT for additional electronic properties [97], The extended Hiickel analysis concluded that the main contribution of the Pt-C bond arises from ct type interactions while the n back-donation is very weak. The DFT/BP86 calculation gives a 2.371 eV HOMO-LUMO gap. The electronic communication parameter Hdb between the bis-ferrocene compound linked with platinum acetylide (5.3) was calculated to be 0.022 eV, compared with 0.025 eV obtained experimentally by Rapenne and coworkers using DFT and the extended Hiickel method [98],... 

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

J. N. Murrell and A. J. Harget, Semi-empirical Self-consistent Molecular Orbital Theory of Molecules, Wiley-Interscience, London, 1972 G. H. Wagniere, Introduction to Elementary Molecular Orbital Theory and to Semiempirical Methods, Springer-Verlag, Berlin, 1976 J. Sadleij, Semi-empirical Methods of Quantum Chemistry, Wiley, New York, 1985. 

The semiempirical molecular orbital (MO) methods of quantum chemistry [1-12] are widely used in computational studies of large molecules. A number of such methods are available for calculating thermochemical properties of ground state molecules in the gas phase, including MNDO [13], MNDOC [14], MNDO/d [15-18], AMI [19], PM3 [20], SAMI [21,22], OM1 [23], OM2 [24,25] MINDO/3 [26], SINDOl [27,28], and MSINDO [29-31]. MNDO, AMI, and PM3 are widely distributed in a number of software packages, and they are probably the most popular semiempirical methods for thermochemical calculations. We shall therefore concentrate on these methods, but shall also address other NDDO-based approaches with orthogonalization corrections [23-25],... 

The methods available for computing enthalpies of formation fall into two general groups those based on purely empirical schemes and those founded on quantum chemistry. The quantum chemical methods can be further divided into three types ab initio molecular orbital theory, density functional theory, and semiempirical molecular orbital theory. A summary of the types of method used to calculate enthalpies of formation is given in Table 2, along with some specific examples. This is not meant to be a comprehensive tabulation, but rather a list of some of the more popular approaches in use today. Table 3 names some of the commercially available computer programs having capabilities to calculate thermochemical data. 

Theoretical chemistry at UBC was further strengthened with the arrival of Delano Chong and Keith Mitchell in 1965 and 1966, respectively. Chong s interests in quantum chemistry have spanned the full range from semiempirical to ab initio molecular orbital methods. His long-standing interests in perturbation methods and constrained variations have figured prominently in his publications. He is probably best known for his attempts to calculate the X-ray and UV photoelectron spectra of molecules, often by means of perturbation corrections to Koopmans theorem.40 More recently he has shifted his focus to coupled pair functional methods and density functional methods, with a special interest in polarizabilities and hyperpolarizabilities.41... 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

V. A. Gubanov, V. P. Zhukov, and A. O. Litinskii, Semiempirical Molecular Orbital Methods in Quantum Chemistry, Nauka, Moscow, 1976. 

Recently, semiempirical molecular-orbital methods have been combined with force-field-based molecular-dynamics techniques into hybrid schemes The interesting part of the system is described by quantum chemistry, while the surroundings are treated by a classical force field. These hybrid schemes allow calculation of the energy and gradients fast enough for molecular dynamics simulations of hundreds of picoseconds (10s time steps) duration to be feasible. This provides sufficient sampling for the calculation of many statistical-mechanical properties. A short synopsis is given of work carried out at ETH Zurich on conformational equilibria in solution, reactions in solution and enzyme reactions. 

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

Semiempirical approaches to quantum chemistry are thus characterized by the use of empirical parameters in a quantum mechanical framework. In this sense, many current methods contain semiempirical features. For example, some high-level at initio treatments of thermochemistry employ empirical corrections for high-order correlation effects, and several advanced density functionals include a substantial number of empirical parameters that are fitted against experimental data. We shall not cover such approaches here, but follow the conventional classification by considering only semiempirical methods that are based on molecular orbital (MO) theory and make use of integral approximations and parameters already at the MO level. 

Over the past decades the semiempirical molecular orbital (MO) methods of quantum chemistry have been used widely in computational studies. Self-consistent-field (SCF) tr-electron calculations have been carried out since the 1950s and valence-electron calculations since the 1960s. Several books [1-8] and reviews [9-15] describe the underlying theory, the variants of semiempirical methods, and the numerical results in much... 

This brings us to the present volume, number 10. Here we point out an interesting evolution of pertinent journals in the field of computational chemistry that has been underway for two decades. Back in the old days, the two journals specializing in the field of what we now call computational chemistry were Theoretica Chemica Acta, founded in 1962, and the International Journal of Quantum Chemistry, founded in 1967. Both, as implied by their titles, focused on theoretical (pencil and paper) and computational quantum chemistry. Theoretica Chemica Acta tended to have papers reporting the results erf approximate semiempirical molecular orbital calculations. Routine molecular orbital studies can now be found in many journals, with perhaps one of the highest concentrations in the old issues of THEOCHEM, a journal started in 1981. In the meantime, Theoretica Chemica Acta tried to widen and strengthen its editorial stance by adding the subtitle A Journal for Structure, Dyrtamics, and Radiation in 1985. 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

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