PM3 methods

Calculations using the semiempirical PM3 method with standard convergence criteria of 0.0003 aii on the maximum component of the gradient vector and either an energy change from the previous cycle of < 10 hartree or a maximum predicted displacement for the next step of < 0.0003 au. 

Using Cl may not necessarily improve the calculation of ground slate cn crgics. Pararn eters for th e MINDO/3, MNDO,. AM I, and PM3 methods already iricltide the effects of Cl. Cl calculation s retjuire m ore corn pii ting time. 

Tl le popularity of the MNDO, AMI and PM3 methods is due in large part to their implementation i n the MOPAC and AMP AC programs. The programs are able to perform many kinds of calculation and to calculate many different properties. 

The modihed neglect of diatomic overlap (MNDO) method has been found to give reasonable qualitative results for many organic systems. It has been incorporated into several popular semiempirical programs as well as the MNDO program. Today, it is still used, but the more accurate AMI and PM3 methods have surpassed it in popularity. 

PM3/TM is an extension of the PM3 method to include d orbitals for use with transition metals. Unlike the case with many other semiempirical methods, PM3/TM s parameterization is based solely on reproducing geometries from X-ray diffraction results. Results with PM3/TM can be either reasonable or not depending on the coordination of the metal center. Certain transition metals tend to prefer a specific hybridization for which it works well. 

PM3/TM is an extension of the PM3 method to transition metals. Unlike the parameterization of PM3 for organics, PM3/TM has been parameterized only to reproduce geometries. This does, of course, require a reasonable description of energies, but the other criteria used for PM3 parameterization, such as dipole moments, are not included in the PM3/TM parameterization. PM3/TM tends to exhibit a dichotomy. It will compute reasonable geometries for some compounds and completely unreasonable geometries for other compounds. It seems to favor one coordination number or hybridization for some metals. 

Note Configuration Interaction significantly increases computing time. For calculations of ground-state energies, MINDO/3, MNDO, AMI, and PM3 methods may already include in their parameters some effects of Configuration Interaction. 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

Thus, HyperChem occasionally uses a three-point interpolation of the density matrix to accelerate the convergence of quantum mechanics calculations when the number of iterations is exactly divisible by three and certain criteria are met by the density matrices. The interpolated density matrix is then used to form the Fock matrix used by the next iteration. This method usually accelerates convergent calculations. However, interpolation with the MINDO/3, MNDO, AMI, and PM3 methods can fail on systems that have a significant charge buildup. 

Figures 17A and 17B (p. 183) show energy as a function of rotation for a series of 1-substituted acetaldehydes, with 6 = 0° in the syn conformation and 6 = 180° in the anti conformation. The calculations were done using the PM3 method. Figure 17A for a vacuum, whereas Fig. 17B is for a solvent cavity with a dielectric constant of 4." The table gives the calculated barriers. Discuss the following aspects (a) rationalize the order Br > Cl > F for syn conformers (b) rationalize the shift to favor the am. conformation in the more polar environment. 

The MNDO, AMI and PM3 methods are parameterizations of the NDDO model, where the parameterization is in terms of atomic variables, i.e. referring only to the nature of a single atom. MNDO, AMI and PM3 are derived from the same basic approximations (NDDO), and differ only in the way the core-core repulsion is treated, and how the parameters are assigned. Each method considers only the valence s- and p-functions, which are taken as Slater type orbitals with corresponding exponents, (s and... 

Each of the MNDO, AMI and PM3 methods involves at least 12 parameters per atom orbital exponents, Cj/pi one-electron terms, II /p and j3s/p two-electron terms, Gss, Gsp, Gpp, Gp2, Hsp, parameters used in the core-core repulsion, a and for the AMI and PM3 methods also a, b and c constants, as described below. 

MNDO has been parameterized for the elements H, B, C, N, O, F, Al, Si, P, S, Cl, Zn, Ge, Br, Sn, I, Hg and Pb. The G s, Gsp, Gpp, Gp2, H p parameters are taken from atomic spectra, while the others are fitted to molecular data. Although MNDO has been succeeded by the AMI and PM3 methods, it is still used for some types of calculation where MNDO is known to give better results. 

Some typical errors in heat of formation for the MNDO, AMI and PM3 methods are given in Table 3.1. The exact numbers of course depend on which, and how many, compounds have been selected for comparison, thus the numbers should only be taken as a guideline for the accuracy expected. Some typical errors in bond distances are given in Table 3.2. 

Tire heats of formation of the intermediate methylamino-transition states of the SnFI methylamination reaction of these nitro-1,8-naphthyridines were calculated by the PM3 method. Tire agreement between the calculated and observed results was found to be satisfactory (97LAR2601,97MI4). 

Semiempirical calculations on the interaction between [Me2Sn(IV)] and a dinuclide triphosphate duplex (DD), mimicking a DNA model system, were performed with the PM3 method and published by Barbieri et al. The results indicate that the [Me2Sn(IV)] moiety binds to two adjacent phosphate groups. 

Current AMI and PM3 methods use an alternative core repulsion function which differs from that used in MNDO in that an additional term involving one to four Gaussian functions is used (defined by parameters a-c, Eq. 5-6) [20, 21], These extra terms help to reduce the excessive core-core repulsions just outside bonding distances. 

This strategy has been found to be more efficient than using Gaussian functions and has now been used to extend the NDDO-based family of methods to the remaining main group elements [22], the AMI parameterisation of second row elements [39] and the transition metals titanium and zirconium [40] as well as our work extending the PM3 method to iron [26, 32],... 

The modification of the semi-empirical Hamiltonian thus required the development of a new set of parameters for use within the PM3 method. Rather than develop a new reference database we chose to use the high-level ab initio calculations recently reported by Hobza and co-workers [1]. These calculations have been collected together in a database which can be used to judge the accuracy of less rigorous, but... 

The results of the various semi-empirical calculations on the reference structures contained within the JSCH-2005 database (134 complexes 31 hydrogen-bonded base-pairs, 32 interstrand base pairs, 54 stacked base pairs and 17 amino acid base pairs) are summarised in Table 5-10. The deviations of the various interaction energies from the reference values are displayed in Figure 5-5. As with the S22 training set, the AMI and PM3 methods generally underestimate the interactions whereas the dispersion corrected method (PM3-D) mostly over-estimates the interactions a little. Overall the PM3-D results are particularly impressive given that the method has only... 

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

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