Semiempirical quantum methods

Recent advances in semiempirical quantum methods (see the chapter... 

K. K. Baldridge, in American Chemical Society Symposium Series, T. Mattson, Ed., Washington, DC, 1994, Chapter 8. Promises and Perils of Parallel Semiempirical Quantum Methods. Also, K. K. Baldridge, unpublished work. 

The original procedure (Miertus et al., 1981) was expressed in the restricted Hartree-Fock (HF) formalism. Extensions to other levels of the quantum theory are easy, and there are versions of the PCM program accepting UHF, ROHF, MPn, CASSCF, SDCI, MRCI, and CASSCF-CI levels of quantum molecular theory. The extension to semiempirical quantum methods has been elaborated by several groups. We quote here Miertus et al. (1988) for CNDO methods, and Luque and Orozco (Luque et al., 1993 1995 Negre et al., 1992) for PM3 and AMI version. Both of them follow this approach. The computational codes are of public domain. The PM3 version has been included in MOPAC package (Stewart, 1990). 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

Bond orders, charges on the atoms in 1 l//-pyrido[2,l-Z)]quinazolin-l 1-one and its protonated form were calculated by quantum chemical calculations by the semiempirical AMI method. According to the results, the equilibrium conformation of the ring in 1 l//-pyrido[2,l-Z)]quinazolin-l 1-one is planar, while l//-pyrimido[l,2-u]quinolin-1-one adopts a conformation close to a half-chair due to the unfavorable interactions between the oxygen atom of the carbonyl group and the ring C-10 atom in the pen-position (97MI22). 

Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence they are divided into quantum, semiclassical and semiempirical. Methods for the calculation of the ionization cross section and experimental techniques developed for the measurement of absolute ionization cross sections will be described in more detail below. Cross sections calculated using the semiempirical additivity method developed by Deutsch and Mark (DM) and their coworkers,12-14 the binary-encounter-Bethe (BEB) method of Kim and Rudd,15 16 and the electrostatic model (EM) developed by Vallance, Harland, and Maclagan17,18 are compared to each other and to experimental data. 

The complete theory of catalysis, which would start with the isolated reaction participants, was not available until now because of the lack of adequate knowledge of the participants themselves (even the complete theory of the isolated participants, starting from the first principles, is still lacking). However, in analogy with the homogeneous chemical reactions one can expect that the quantum chemical approach, based on the semiempirical quantum mechanical methods, could be a prospective one. 

MOPAC is a general-purpose semiempirical molecular orbital program for the study of chemical structures and reactions. It is available in desktop PC running Windows, Macintosh OS, and Unix-based workstation versions. It uses semiempirical quantum mechanical methods that are based on Hartree-Fock (HF) theory with some parameterized functions and empirically determined parameters replacing some sections of the complete HF treatment. The approximations in... 

At the present time, semiempirical quantum calculations applied to a restricted range of fluorine compounds cannot be said to be more successful than other empirical methods, such as Sanderson s, although they yield other molecular properties in addition to enthalpies. 

In a very extensive test of the SM5 method (a type of GBM), Hawkins et al. found the average absolute deviation in AGsoivation to be 0.38 kcal/mole for 260 molecular solutes in water and in 90 organic solvents 131 for ions in water, it was 3.8 kcal/mole, for experimental AGsolvation between -58 and -110 kcal/mole. Semiempirical quantum-mechanical procedures were used. 

In principle there are three methods of calculation the ab initio molecular orbital (MO) method, the semiempirical MO method, and molecular mechanics. The choice depends on a number of factors such as the size of the molecule, the type of information required, and the budget. Whereas the ab initio method is the most basic and reliable quantum mechanical method,t the time requirement is so... 

In Section II,B,8 we discussed the question of determining site densities using high-conversion data. We developed a method applicable in the inter-conversion of three isomers when there is a common surface complex for the three possible reactions. We have tested this method using the conversion of 1-butene to cis- and rrans-2-butene over silica-alumina, a system that, according to Hightower and Hall, proceeds through a common surface complex (111). Their conclusion has been confirmed experimentally (112) and by semiempirical quantum-chemical calculations (113). 

Hypercube, Inc. at http //www.hyper.com offers molecular modeling packages under the HyperChem name. HyperChem s newest version, Hyper-Chem Release 7.5, is a full 32-bit application, developed for the Windows 95, 98, NT, ME, 2000, and XP operating systems. Density Functional Theory (DFT) has been added as a basic computational engine to complement Molecular Mechanics, Semiempirical Quantum Mechanics and ab initio Quantum Mechanics. The DFT engine includes four combination or hybrid functions, such as the popular B3-LYP or Becke-97 methods. The Bio+ force field in HyperChem represents a version of the Chemistry at HARvard using Molecular Mechanics (CHARMM) force field. Release 7.5 of HyperChem updates... 

SemiChem products are available at http //www.semichem.com. AMPAC , available as a stand-alone product with Windows-based and workstation level interfaces, is a semiempirical quantum mechanical program featuring SAMI, AMI, MNDO, MNDO/d, PM3, MNDO/C, MINDO/3 semiempirical methods. AMPAC also includes a graphical user interface (GUI) that builds molecules and offers full visualization of results. The SYBYL/Base program offered by Tripos, Inc. (products described below) provides an interface with interactive graphing and structural display tools that can be used to access AMPAC s calculation tools. 

At present two parallel approaches are being undertaken to determine the PES or the Cj The ab initio and semiempirical quantum mechanical methods. Ab initio methods attempt to undertake the just-mentioned calculations rigorously without relying on the use of any information other than the basis sets resulting accuracy of the calculations large basis sets... 

In summary, computational quantum mechanics has reached such a state that its use in chemical kinetics is possible. However, since these methods still are at various stages of development, their routine and direct use without carefully evaluating the reasonableness of predictions must be avoided. Since ab initio methods presently are far too expensive from the computational point of view, and still require the application of empirical corrections, semiempirical quantum chemical methods represent the most accessible option in chemical reaction engineering today. One productive approach is to use semiempirical methods to build systematically the necessary thermochemical and kinetic-parameter data bases for mechanism development. Following this, the mechanism would be subjected to sensitivity and reaction path analyses for the determination of the rank-order of importance of reactions. Important reactions and species can then be studied with greatest scrutiny using rigorous ab initio calculations, as well as by experiments. 

Small monosaccharides have molecular sizes at the upper limit of the range that is currently treatable with initio methods. An exaiqple of the application of initio calculations to carbohydrates is given in the paper by Garrett and Serianni in this volume. Semiempirical quantum mechanical calculations, which use simplified molecular Hamiltonians with parameters taken from experiment, extend quantum mechanical calculations to larger molecules. However, the reliability is reduced compared to the best ab initio results. 

The electronic coupling of donor and acceptor sites, connected via a t-stack, can either be treated by carrying out a calculation on the complete system or by employing a divide-and-conquer (DC) strategy. With the Hartree-Fock (HF) method or a method based on density functional theory (DFT), full treatment of a d-a system is feasible for relatively small systems. Whereas such calculations can be performed for models consisting of up to about ten WCPs, they are essentially inaccessible even for dimers when one attempts to combine them with MD simulations. Semiempirical quantum chemical methods require considerably less effort than HF or DFT methods also, one can afford application to larger models. However, standard semiempirical methods, e.g., AMI or PM3, considerably underestimate the electronic couplings between r-stacked donor and acceptor sites and, therefore, a special parameterization has to be invoked (see below). 

There is a 3 kcal difference in energy between the energy difference shown in Fig. 38 and the McGrath results. The calculations used for Fig. 38 are based on a lower level, semiempirical quantum mechanics calculation, while the McGarth calculations utilize computationally more expensive ab initio methods. 

A number of papers have appeared recently in which semiempirical quantum mechanical methods, such as the complete neglect of differential overlap (CNDO), incomplete neglect of differential overlap (INDO), or Hiickel methods, have been applied to electron-deficient systems in an attempt to calculate their properties (31, 49, 64, 75, 77, 78, 89, 90, 92). Although the quantitative results of these calculations must be treated with great care, they do provide an indication of some of the parameters that determine formation and stability of electron-deficient bonded systems. 

Figure 2. Experimental and simulated fluorescence Stokes shift function 5(f) for coumarin 343 in water. The curve marked Aq is a classical molecular dynamics simulation result using a charge distribution difference, calculated by semiempirical quantum chemical methods, between ground and excited states. Also shown is a simulation for a neutral atomic solute with the Lennard-Jones parameters of the water oxygen atom (S°). (From Ref. 4.)...

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