Semiempirical electronic structure theory

The principal parameterization of the MNDO, AMI, and PM3 models is for s and p functions. Though they have parameters for some metals, these are often based on very limited experimental data and, thus, may be very unreH-able. Thiel and co-workers have developed MNDO/d, which more accurately represents metals. With s, p, and d functions, MNDO/d typically employs 15 parameters per atom. MNDO/d is one of the MNDO methods in the computer program package MND097. OMl and OM2 methods, which go beyond MNDO methods by employing orthogonalization corrections, are also included in MND097. 

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In excerpt 3Y, the authors refer to computational results performed with the Gaussian suite of programs, a computational package used to calculate molecular ab initio or semiempirical electronic structure theory. Computational parameters (e.g., the basis set and level of theory) are included in the description. Do not worry if you do not understand the content of excerpt 3Y the language is intended for chemists with a computational or theoretical background. 

The earliest place where the quantity (/ - A) has made its appearance and played the role of a prominent character is the semiempirical electronic structure theory, which is known for its richness in scientific content, particularly for the physical basis in choosing the parameters and using the approximations. This theory provides one of the simplest and transparent models through the smiiempirical Hamiltonian as proposed by the Pariser-Parr-Pople (PPP) theory to approximate the total energy of a molecular system. In one of its simplest forms, the PPP Hamiltonian can be expressed as... 

Direct dynamics was first applied by Wang and Karplus in a study of the CH2 + H2 CH4 reaction. The CNDO semiempirical electronic structure theory was used for this calculation. Two years later, Warshel and... 

Semiempirical direct dynamics was used to study trimethylene s unimo-lecular dynamics and the thermal stereomutation of cyclopropane.The semiempirical model used in these simulations is AMI with specific reaction parameters (SRPs see discussion of semiempirical electronic structure theory in the section on BO direct dynamics) chosen to fit the CASSCF PES. In choosing the SRPs, the AMI barrier for propene formation was lowered by... 

The classical trajectory simulations were carried out with VENUS interfaced with the semiempirical electronic structure theory computer program MOPAC. To simulate experimental conditions for (gly-H) -I-diamond collisions, the center of a beam of (gly-H)+ ion projectiles is aimed at the center of the surface, with fixed incident angle 0, and fixed initial translational energy, E,. The radius of the beam was chosen so that the beam overlapped a unit area on the surface. For each trajectory, the projectile was randomly placed in the cross section of this beam and then randomly rotated about its center of mass so that it had an initial random orientation with respect to the surface. The azimuthal angle, %, between the beam and a fixed plane perpendicular to the surface, was sampled randomly between 0 and 2n. Such a random sampling of X simulates collisions with different domains of growth on the diamond surface. 

Finally, some attention has been paid to the quality of the complete electrostatic potential about the molecule at the NDDO level. This topic is discussed in Chapter 9, as are additional details associated with the performance of semiempirical models in comparison to other levels of electronic structure theory for a variety of more specialized properties. 

Figure 13.5 An application of a hybrid MO/MO philosophy to the indicated RNA trimer proceeds using correlated levels of electronic structure theory for various tautomers and protonation states of the central base pair, this parr then representing the small system in the MO/MO analog of Eq. (13.6), and semiempirical theory for both die small system and the frozen-geometry larger system... 

In contrast to molecular mechanics force fields, modern semiempirical methods are classified as an SCF electron-structure theory (wave function-based) method [8]. Older (pre-HF)... 

Figure 12-3. IR-UV double resonance spectrum of GC (structure C) in the mid-IR frequency range (recorded at the FELIX free electron laser facility), compared with three types of ab intio calculations. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces [30]...

Modern electronic structure theory employs two levels of simplification. The use of various mathematical approximations is dictated by the limitations of computer hardware and the need for keeping the cost of quantum-chemical calculations within reasonable limits. In contrast, the avoidance of quantum-mechanical treatment of nuclei is deeply rooted in the aforementioned conceptual prejudices. While the severity of mathematical approximations is on a constant decrease thanks to the ever-increasing speed and availability of computers (note the gradual disappearance of semiempirical calculations from the chemical literature ), the validity of views that regard molecules as quasi-rigid assemblies of nuclei held together by electron clouds is rarely questioned by the majority of researchers. 

Before beginning our discussion of wave function-based electronic structure theory, we note that an alternative, rigorous approach to electronic structure is provided by DFT (this volume, chapter by Ayers and Yang). DFT is based on the premise that all information about the electronic system can be extracted from the electron density, rather than from the electronic wave function. The attraction of DFT is that the electron density is a much simpler entity than the wave function, depending on just three spatial coordinates rather than on the An spatial and spin coordinates of n electrons. However, a difficulty of DFT is that no accurate, non-empirical method has yet been devised to extract the necessary information from the electron density. Current DFT calculations are therefore, to a large extent, based on semiempirical functionals [12], in which a set of parameters is fitted to experimental data. Nevertheless, the fitted parameters are universal in the sense that they are not atom-dependent or molecule-dependent. Also, the accuracy achieved in this manner is often high, surpassed only by the most elaborate wave function methods [13]. 

Flanigan, M. C., Komornicki, A., Mclver, J. W., Semiempirical Methods of Electronic Structure Theory, in Modern Theoretical Chemistry. Vol. 8, Segal, G. A. (ed.) Plenum Press, New York, 1977... 

Since hardness measures the HOMO-LUMO gap in Huckel or in Hartrec-Fock theories [37] it is natural to look for ways to incorporate the hardness in simple electronic structure theories. Thus, the new ideas of bond electronegativity and bond hardness have been introduced and a semiempirical density functional theory of molecular electronic structure and chemical binding outlined [39], To illustrate the energy expressions in PPP theories including electron repulsion terms are given by [40]... 

At the same time, molecular orbitals were used in simplified treatments of the pi-electrons in conjugated organic molecules. Similar empirical or semiempirical electron-structure models were developed and successfully applied in other areas of chemistry. They have been described in other chapters of this book. The field was therefore open for development of a nonempirical HF theory for molecules. A key paper was published by Roothaan in 1951. Albeit not the first to do so, he gave a clear and detailed description of an HF procedure for molecules that could almost be used as a manual for the development of a computer code. The computers were not quite ready, though, and it was to take another 10 years before the first general-purpose codes were produced. 

The HF method represents a point of departure in electronic structure theory. One direction involves improvement of the accuracy by including electron correlation (see Section n.B.3.). Semiempirical methods, however, try to provide moderate accuracy, but at much lower cost than that of ab initio methods. Therefore, only valence electrons are treated explicitly and core electrons are replaced by an effective core (covering nucleus plus core electrons) and a minimal basis of orthogonal Slater-type orbitals (usually only s and p types) is chosen to describe the valence electrons. 

Common language of electronic structure theory, validating density functional theory, standardization of Gaussian basis sets, semiempirical methods, B3LYP functional (Becke s three-parameter hybrid functional using the LYP correlation functional), well-defined procedures for QM algorithms... 

In contrast to molecular mechanics force fields, modern semiempirical methods are classified as an SCF electron-structure theory (wavefunction-based) method [12]. Older (pre-HF) semiempirical approaches such as extended Hvickel theory, which can be classified as a one-electron effective Hamiltonian approach, involve drastic approximations but rely on the researcher s intuition and ability to extrapolate from simple computations to meaningful chemistry. This method is not used much these days but still plays a role in determining the band structures of organic polymers, most of which are carbon-rich by definition [13]. 

Because the electronic energy Ee(q) in Eq. [8] and its derivatives must be calculated at each integration step of a classical trajectory, a direct dynamics simulation is usually very computationally intense. A standard numerical integration time step is /St = 10 " s. Thus, if a trajectory is integrated for 10 s, 10" evaluations of Eq. (8) are required for each trajectory. An ensemble for a trajectory simulation may be as small as 100 events, but even with such a small ensemble 10 " electronic structure calculations are required. Because of such computational demands, it is of interest to determine the lowest level of electronic structure theory and smallest basis set that gives an adequate representation for the system under study. In the following parts of this section, semiempirical and ab initio electronic structure theories and mixed electronic structure theory (quantum mechanical) and molecular mechanical (i.e. QM/MM) approaches for performing direct dynamics are surveyed. 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

The solvation models are used to predict the properties of small molecules and large biomolecules employing different levels of theory. In the prediction of solvent effect using electronic structure calculation, semiempirical, HF, post-HF, and DFT-based hybrid methods have been widely used [2-11], Since a wealth of literature is... 

The semiempirical models mentioned above allow an estimation of the stability of binary hydrides provided that the rigid band theory can be applied. However, the interaction of hydrogen with the electronic structure of the host metal in some binary hydrides and especially in the ternary hydrides is often more complicated. In many cases, the crystal structure of the host metal and therefore also the electronic structure... 

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