MNDO/d parametrization

The documented successes of MNDO/d (see above) suggest an extension to transition metals. The MNDO/d parametrization has been completed for several transition metals [123] and is in progress for others, but a systematic assessment of the results is not yet feasible. Elsewhere the published MNDO/d formalism for the two-electron integrals [33] has been implemented independently [124] and combined with PM3 in another parametrization attempt for transition metals [125]. Moreover, the SAMI approach is also being parametrized for transition metals [122,126]. Given these complementary activities it seems likely that the performance of MNDO-type methods with an spd basis for transition metal compounds will be established in the near future. 

Apart from the statistical evaluations, the basic MNDO/d papers " also discuss several specific applications to illustrate the performance of MNDO/d in selected areas and to comment on problematic cases. It is important to note in this connection that the MNDO/d parametrization for the heavier elements (Z > 10) cannot remove the limitations arising from the MNDO treatment of the light elements (Z < 10, MNDO/d identical to MNDO). 

The MNDO/d parametrization for the transition metals has proven to be more difficult than for the main-group elements. This is mostly due to the more complicated electronic structure of transition metal compounds, and partly also to the lack of reliable thermochemical reference data. During the parametrization, the proper reproduction of the lowest electronic states of a given transition metal was enforced by a suitable choice of the one-center parameters, and some bond-specific a parameters were introduced for fine tuning. In spite of these measures, the results for elements in the middle of a transition... 

Thiel and Voityuk (1992, 1996) described the first NDDO model with d orbitals included, called MNDO/d. For H, He, and the first-row atoms, the original MNDO parameters are kept unchanged. For second-row and heavier elements, d orbitals are included as a part of the basis set. Examination of Eqs. (5.12) to (5.14) indicates what is required parametrically to add d orbitals. In particular, one needs and /ij parameters for the one-electron integrals, additional one-center two-electron integrals analogous to those in Eq. (5.11) (there are... 

The highly specific behavior of transition metal complexes has prompted numerous attempts to access this Holy Grail of the semi-empirical theory - the description of TMCs. From the point of view of the standard HFR-based semiempirical theory, the main obstacle is the number of integrals involving the d- AOs of the metal atoms to be taken into consideration. The attempts to cope with these problems have been documented from the early days of the development of semiempirical quantum chemistry. In the 1970s, Clack and coworkers [78-80] proposed to extend the CNDO and INDO parametrizations by Pople and Beveridge [39] to transition elements. Now this is an extensive sector of semiempirical methods, differing by expedients of parametrizations of the HFR approximation in the valence basis. These are, for example, in methods of ZINDO/1, SAMI, MNDO(d), PM3(tm), PM3 etc. [74,81-86], From the... 

Modified Neglect of Diatomic Overlap Parametric Method Number 3 (MNDO-PM3) 3.10.6 The MNDO/d Method 88 89 5.5 5.6 5.4.5 Correlation Consistent Basis Sets Extrapolation Procedures Isogyric and Isodesmic Reactions 162 164 169... 

The implementation and the parametrization of the MNDO/d approach are analogous to MNDO (see Section II.A), with only minor and presently irrelevant variations in certain details [33,36]. Optimized final parameters are available [34-36] for the second-row elements, the halogens, and the zinc group elements. MNDO/d employs an spd basis for Al, Si, P, S, Cl, Br, and I but only an sp basis for Na, Mg, Zn, Cd, and Hg. For the latter five elements, parametrizations with an sp and an spd basis yield results of similar quality (as expected in a semiempirical framework) which allows us to adopt the simpler sp basis in these cases [36]. Table III reports a statistical evaluation of extensive test calculations... 

More recent developments in semi-empirical approaches include the treatment of d-orbitals (MNDO/d [36], MND099 [37]), the re-parametrization of established methods such as PM3 [38, 39], RMl [40], and the extension to transition metal compounds (AMI, PM5, PM6) [41, 42]. 

Thiel and Voityuk [W.Thiel and A. A. Voityuk,/. Am. Chem. 5oc., 100,616 (1996)] extended MNDO to include d orbitals for many second-row and later elements, giving the MNDOId method. MNDO/d does not add d orbitals for first-row elements, so for a compound containing only C, H, O, and N, MNDO/d is precisely the same as MNDO. Also, it was found that for Na, Mg, Zn, Cd, and Hg, inclusion of d orbitals made little difference, and MNDO/d uses only an sp basis for these elements (but the MNDO parameters for these five elements must be reoptimized in MNDO/d). MNDO/d parameters have been published for Al, Si, P, S, Cl, Br, and I, and the method has also been parametrized for several transition metals. 

PM5 is a new re-parametrization of the MNDO method. " Currently, PM5 parameters are available for main-group elements and 16 TM elements, however the parameters have not been published yet. Average errors for heats of formation, ionization potentials, and bond lengths in the new parametrization are reduced quite considerably compared to those from MNDO/d, AMl/d, and PM3 calculations. PM5 is available in MOPAC 2002. 

In this article, we summarize the results of our previous OVGF calculations based on the commonly used semiempiri-cal methods (modified neglect of diatomic overlap, MNDO Austin Model 1, AMI and parametric methods, PM3 ) and compare them with the results of the recent semiempirical ab initio method 1 (SAMl) and MNDO/d " semiempirical methods. The focus is on methodology of the method and its performance. 

The established MNDO-type methods, i.e., MNDO, AMl, and PM3 (see AMI MNDO and PM3) employ an sp basis without d orbitals in their original implementation. Therefore, they cannot be applied to most transition metal compounds, and difficulties are expected for hypervalent compounds of main-group elements where the importance of d orbitals for quantitative accuracy is well documented at the ab initio level. To allow for an improved semiempirical description of such compounds, the MNDO formalism has been extended to d orbitals. This extension forms the basis of the MNDO/d method " and the independent PM3/tm parametrization. ... 

In the MNDO/d approach, there are typically 13-16 optimized parameters per element with an spd basis, with 4 parameters related solely to the d orbitals. Hence, MNDO/d is less highly parametrized in the sp part than AMI or PM3 which employ typically 13-16 and 18 parameters, respectively, per element (sp basis). In deliberately restricting the number of optimized parameters, MNDO/d resembles the original MNDO method which uses only 5-7 parameters per element. 

MNDO = modified neglect of diatomic overlap MNDO/d = modified neglect of diatomic overlap with d-type orbitals NLDF = nonlocal density functional PM3/d = parametric method three with d-type orbitals SINDOl = symmetrically orthogonalized intermediate neglect of diatomic overlap parametrization one TM = transition metal UFF = universal force field ZINDO = Zemer s intermediate neglect of diatomic overlap. 

With the intermediate NDO method ZDO is not assumed between a.o. s on the same atom in one-centre electron repulsion integrals. Various other schemes based on different ZDO assumptions together with different schemes of semi-empirical parametrization have been developed. These have become known by their acronyms such as CNDO/1, CNDO/2, INDO, MINDO/3 (m - modified), NDDO (d - diatomic), MNDO etc.. 

Various parameterizations of NDDO have been proposed. Among these are modified neglect of diatomic overlap (MNDO),152 Austin Model 1 (AMI),153 and parametric method number 3 (PM3),154 all of which often perform better than those based on INDO. The parameterizations in these methods are based on atomic and molecular data. All three methods include only valence s and p functions, which are taken as Slater-type orbitals. The difference in the methods is in how the core-core repulsions are treated. These methods involve at least 12 parameters per atom, of which some are obtained from experimental data and others by fitting to experimental data. The AMI, MNDO, and PM3 methods have been focused on ground state properties such as enthalpies of formation and geometries. One of the limitations of these methods is that they can be used only with molecules that have s and p valence electrons, although MNDO has been extended to d electrons, as mentioned below. 

Za and Zg). The SINDOl resonance integrals are also related to overlap integrals, but in a fairly intricate manner [25]. As in MNDO-type methods, the parametrization (d) of SINDOl focuses on ground-state... 

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. 

Because MINDO/3 did not meet Dewar s aims, Dewar and Thiel developed the MNDO (modified neglect of diatomic overlap) method. The MNDO method has been parametrized for nearly all the main-group elements and for Zn, Cd, and Hg. MNDO gives substantially improved results as compared with MINDO/3. For the same sample of C, H, O, N compounds used above for MINDO/3 errors, average absolute MNDO errors are 6.3 kcal/mol in heats of formation, 0.014 A in bond lengths, 2.8° in bond angles, 0.30 D in dipole moments, and 0.5 eV in ionization energies [M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc., 99, 4907 (1977)]. 

Finally, several special MNDO parametrizations are available for certain classes of compounds or for specific properties. These treatments retain the original MNDO approach (a)-(c), but use parameters (d) that have been optimized for the intended applications. It is obvious that such specialized methods ought to be more accurate in their area of applicability than the original general-purpose MNDO method. Samples of this kind include the special MNDO variants for small carbon clusters, fullerenes, and hydrogen-bonded systems as well as special parametrizations for electrostatic potentials. ... 

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