MNDO force field

Molecular dynamic calculations (on the basis of the semiempirical MNDO force field) were performed for two mutual orientations of a fullerene molecule and the direction of the implanting atom (Fig. 4a). Fig. 4b shows the dependence of the threshold energy of formation of the endohedral complex C C6o (vertical axis) for Orientation I. The obtained results show that the process of formation of endohedral complex proceeds as follows. The implanting atom passes a central part of a five-member (or six-member) ring, cavity of cluster, and is reflected from an opposite side of a cluster. This process continues since the basic part of kinetic energy is not transferred into the vibrational energy of a molecule. The vertical lines of Fig. 4 correspond to the head-on collisions of the implanting atom with the atoms of the five-member face of a molecule. At the top level of Fig. 4 the isolines of the same surface are presented. 

Because of the small difference in total energy between complexes of Type A and B, the question arises of whether the transition of the atom from one stable position into another is possible under the influence of thermal fluctuation. Molecular dynamics calculations (with the MNDO force field model) show that the dynamic barrier of migration is only 0.12 eV for the transition ft-om site A into site B and 0.16 eV for the transition between the sites of type A. 

Table 7 provides the valu of iog /iog term for several types of defect clusters (MNDO force field model) [93]. It is shown that for the defects of types A and B (Fig. 7) these values are rather large, and endohedral clusters significantly influence the properties of the superconductive state. However, utilization of endohedral clusters as the pinning centers requires further research because in the fiame of this approach it is not possible to take into account electron-phonon interactions. 

Owing to the semiempirical nature of the MNDO method, the theoretical force constants are between 10 and 20% larger than the experimental values. Therefore, following Torok and Pulay< empirical scale factors have been calculated in the case of the MNDO force field of butadiene for which molecule enough experimental information is available. The suggestion followed in the computation of these scale factors was that the geometrical mean value of the diagonal force constants be used.< ... 

Before 1980, force field and semiempircal methods (such as CNDO, MNDO, AMI, etc.) [1] were used exclusively to study sulfur-containing compounds due to the lack of computer resources and due to inefficient quantum-chemical programs. Unfortunately, these computational methods are rather hmit-ed in their reliability. The majority of the theoretical studies under this review utilized ab initio MO methods [2]. Not only ab initio MO theory is more reliable, but also it has the desirable feature of not relying on experimental parameters. As a consequence, ab initio MO methods are apphcable to any systems of interest, particularly for novel species and transition states. 

Geometric Optimization. The structure of the molecule as built by CHEMLAB (or a input from other methods) can be optimized through either a full force field molecular mechanics calculation (MMII) or with the semi-empirical molecular orbital methods MINDO-3 and MNDO. 

Molecular Energetics. Molecular energies can be computed in a variety of ways including empirical fixed valence potentials, full force field potentials, and semi-empirical molecular orbital techniques (CNDO-2, INDO, MINDO-3, MNDO, PCILO). 

One example of the use of semiempirical methodology is provided in an article detailing a molecular-dynamics simulation of the beta domain of metallothionein with a semiempirical treatment of the metal core.73 The beta domain of rat liver metallothionein-2 contains three-metal centers. In this study, three molecular variants with different metal contents—(1) three cadmium ions, (2) three zinc ions, and (3) one cadmium ion and two zinc ions—were investigated using a conventional molecular dynamics simulation, as well as a simulation with a semiempirical quantum chemical description (MNDO and MNDO/d) of the metal core embedded in a classical environment. For the purely classical simulations, the standard GROMOS96 force-field parameters were used, and parameters were estimated for cadmium. The results of both kinds of simulations were compared to each other... 

Demiralp E, Cagin T, Goddard WA(1999) Morse stretch potential charge equilibrium force field for ceramics Application to the quartz-stishovite phase transition and to silica glass. Phys Rev l tt 82 1708-1711 Dewar MJS (1977) Ground states of molecules. The MNDO method. Approximations and parameters. J Am Chem Soc 99 4899-4907... 

The strain of 1 has been determined experimentally from silver-ion catalyzed methanolysis to be ca. 68 kcal/mol, and that of cyclopropa[/j]naphthalene to be 65-67 kcal/mol. Combustion calorimetry gave a value of 67.8 kcal/mol. For dicyclopropa[/>,g]naphthalene (115) a lower limit of 166 kcal/mol was found. These energies are well reproduced by ab initio, and even by semiempirical calculations. Thus 3-2IG calculates a strain energy of 70 kcal/mol while 3-2IG gives 71.6. At the MP2/6-31G level the strain of 1 is 71.3 kcal/mol, while that of cyclopropene amounts to 57.4 kcal/mol. This latter value compares well with the experimental one, which is 52.6 kcal/mol. While semiempirical calculations have been found unreliable for cycloproparene structures, the calculated strain energies are usually close to reality for MINDO/3, MNDO, and force-field-SCF calculations. The strain energies of the dicyclopropabenzenes (100, 102) have been predicted to be 133 and 140 kcal/mol, respectively, and that of tricyclo-propabenzene (260) to be 217 kcal/mol (3-21G). ... 

Phillip and Friesner have discussed the development of an ab initio QM/MM method within the Jaguar program [141]. Ryde has presented the COMQUM program [80]. Thiel and coworkers have discussed combinations of MNDO-type methods with the MM3 force field [112,130,147,159]. Several other packages are available [102,103]. 

Molecular geometries may be calculated by means of quantum-chemical semi-empirical valence electron theories, such as Dewar s MINDO/3 , MNDO " or AMl procedures, or by classical molecular force-field methods, such as Allinger s MM2 procedure. Alternatively, inirio Hartree-Fock SCF MO methods allow, by virtue of analytical gradient evaluations , the determination of molecular geometries independent of experimentally adjusted integral values. 

The hybrid scheme used by us has been described in detail (1). Therefore, only a short summary is given here. The system is divided into a primary (QM) part treated quantum-chemically and the environment treated by a force field (MM part). For the QM part, a semi-empirical calculation is carried out. We have used the MOPAC program (2) for this task and have, consequently, employed all NDDO methods (MNDO, AMI, PM3) in the course of our work. The interactions among atoms of the MM part are described entirely by a classical force field. They are evaluated using die GROMOS87 program (3), and the GROMOS force field or close variations of it were used in our work. 

Computational methodology has been used to accompany or to anticipate experimental results for many classes of compounds. Such results are particularly helpful for transient species, for rationalization of physical and structural properties, and for simulation of reaction pathways and transition states. Semiempirical valence electron (CNDO/MNDO), ab initio, and nonquantum mechanical force field (molecular mechanics) calculations have mainly been used for the examination of structure and stability of moderately strained olefins, whereas many-electron quantum-chemical methods have been used for detailed discussion of electronic aspects. Excellent reviews of molecular mechanics calculations, the principal method used to describe geometrical and energy features in distorted double bond systems, have been written by Osawa and Musso (61). 

By the early 1970s, molecular mechanics computer programs such as MMI and MM2 were available, running on the IBM 360. For proteins, ECEPP was developed by Harold A. Scheraga. - Countering the molecular mechanics approach, Michael J. S. Dewar modified John A. Pople s (complete) neglect-of-differential-overlap semiempirical quantum mechanical method (CNDO/2) to calculate quantities such as conformational stability and heats of formation. Such programs (MNDO) were necessarily slower than the empirical force field methods such as MM2 and ECEPP but still had fewer parameters and could account for the effects of polarization in aromatic systems. 

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