Orthogonalization corrections

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],... 

Weber, W. and Thiel, W., Orthogonalization corrections for semiempirical methods, Theor. Chem. Acc., 103, 495-506, 2000. 

Tlie bands have long been interpreted as LCAO d bands, crossed by and hybridized with a free-electron-like band (Saffren, 1960 Hodges and Ehrenreich, 1965 and Mueller, 1967). By including some eleven parameters (pseudopotential matrix elements, interatomic matrix elements, orthogonality corrections, and hybridization parameters), it is possible to reproduce the known bands very accurately. We shall also make an LCAO analysis of the bands but shall take advantage of recent theoretical developments to reduce the number of independent parameters to two for each metal, each of which can be obtained for any metal from the Solid State Table. These two parameters will also provide the basis for understanding a variety of properties of the transition metals. 

The MNDO method has been continually modified and improved by Thiel et al. The most important aspects of these modifications are the use of Zerner s [62] elfective core potential and the inclusion of orthogonalization corrections in a way similar to the INDO method SINDOl (see the last section) leading to the two models OM1 and OM2 (orthogonalization models 1 and 2), respectively [3,71,72], These corrections have been found to be important for the description of torsion angles in organic compounds. So far, it has been parameterized for elements H, C, N, and O. 

To conclude this section, we mention an article [68] that discusses desirable features for next-generation NDDO-based semiempirical methods. Apart from orthogonalization corrections and effective core potentials that are already included in some of the more recent developments (see above) it is proposed that an implicit dispersion term should be added to the Hamiltonian to capture intramolecular dispersion energies in large molecules. It is envisioned that dispersion interactions can be computed self-consistently from an additive polarizability model with some short-range scaling [68]. 

The discussion in Section II.A has shown that many of the currently accepted semiempirical methods for computing potential surfaces are based on the MNDO model. These methods differ mainly in their actual implementation and parametrization. Given the considerable effort that has gone into their development, we believe that further significant overall improvements in general-purpose semiempirical methods require improvements in the underlying theoretical model. In this spirit we describe two recent developments The extension of MNDO to d orbitals and the incorporation of orthogonalization corrections and related one-electron terms into MNDO-type methods. 

From a computational point of view, - H could be evaluated analytically ab initio) and then be added to the semiempirical core Hamiltonian matrix. This procedure, however, introduces an imbalance between the one- and two-electron parts of the Fock matrix as long as the two-electron integrals are not subjected to the same exact transformation (J)), which would sacrifice the computational efficiency of semiempirical methods and is therefore not feasible. Hence the orthogonalization corrections to the one-electron integrals must instead be represented by suitable parametric functions. Their essential features can be recognized from the analytic expressions for the matrix elements of in the simple case of a homonuclear diatomic molecule with two orbitals at atom A, at atom B) ... 

Conformational properties such as rotational barriers and energy differences between conformers are often poorly reproduced by existing semiempirical methods [19-22, 37]. These problems have been attributed to the neglect of orthogonalization corrections to the resonance integrals. 

The introduction of orthogonalization corrections for the one-center part of the core Hamiltonian matrix [37] generates improved excitation energies by correcting for deficiencies inherent to the ZDO approximation. 

As expected theoretically [136,137], better predictions for conformational properties become possible [38] when including orthogonalization corrections also for the two-center resonance integrals. 

Recognizing the importance of orthogonalization effects (see Section 2.38.2.6), which are neglected in many semiempirical SCF MO methods, INDO-based methods with orthogonalization corrections, SINDO, SINDO1 and MSINDO, " have been developed. The orthogonalization models... 

The most important modifications of the MNDO method are the use of effective core potentials for the inner orbitals and the inclusion of orthogonalization corrections in a way as was suggested and implemented a long time ago in the SINDOl method [249] at first developed for organic compounds of first-row elements and later extended to the elements of the second and third row [250,251]. 

Table 2 Orthogonalization Correction Terms AH Version of SINDOl in the Present ...

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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