Fast semiempirical calculations for nuclear magnetic resonance chemical shifts: a divide-and-conquer approach

A new approach to calculate nuclear magnetic resonance chemical shifts has been implemented at the semiempirical modified neglect of diatomic overlap level using gauge-including atomic orbitals. The perturbed density matrix with respect to the magnetic field is obtained by the diagonalization of the complex Fock matrix using the divide and conquer (DC) method, instead of by solving the computationally expensive coupled perturbed Hartree-Fock equations. Adopting the Patchkovskii and Thiel parameters [S. Patchkovskii and W. Thiel J. Comput. Chem. 20, 1220 (1999)], we were able to reproduce their results for small organic molecules. The errors introduced by DC method are negligible, as shown by the calculations on a series of polyalaine structures. Test calculations on proteins have demonstrated that our approach makes it possible to calculate chemical shifts routinely on systems with hundreds of atoms with good accuracy.     

Comparative semiempirical calculations of tetrazole derivatives

Heats of formation, protonation energies, charge distributions, dipole moments, and geometrical structures of thirty-two 1-, 2-, 1,5-, and 2,5-substituted tetrazoles have been investigated by different semiempirical SCF MO calculations. MNDO and, in some cases, AM 1 methods are the most acceptable for tetrazole derivatives. A number of linear correlations between available experimental data and the calculated energies and charge characteristics have been established. © 1992 John Wiley & Sons, Inc.     

Geometry optimization in semiempirical SCF-MO-CI calculations

It is shown that up to 50% of the computer time needed for geometry optimization on the (semiempirical) CI level by means of gradients calculated as finite differences can be saved by using “corrected noncentral gradients” in combination with a judiciously chosen first estimate of the Hessian in order to assure fast convergence of the procedure.     

Comparison of semiempirical calculations for silicon compounds

A comparison is made of the performance of the MINDO/3, MNDO, AM1, and PM3 methods in calculating the nature of the dimer reconstruction observed on the silicon (100) crystal surface. Based on this case study we conclude that MINDO/3 gives the most realistic results, with PM3 calculations being quite similar but both MNDO and AM1 missing some key features of this system and giving rather unrealistic charge distributions. Hence use of PM3 is recommended for Si containing molecules where a lack of parameters or other restrictions prevent the use of MINDO/3.     

Parallel implementation of divide-and-conquer semiempirical quantum chemistry calculations

We have implemented a parallel divide-and-conquer method for semiempirical quantum mechanical calculations. The standard message passing library, the message passing interface (MPI), was used. In this parallel version, the memory needed to store the Fock and density matrix elements is distributed among the processors. This memory distribution solves the problem of demanding requirement of memory for very large molecules. While the parallel calculation for construction of matrix elements is straightforward, the parallel calculation of Fock matrix diagonalization is achieved via the divide-and-conquer method. Geometry optimization is also implemented with parallel gradient calculations. The code has been tested on a Cray T3E parallel computer, and impressive speedup of calculations has been achieved. Our results indicate that the divide-and-conquer method is efficient for parallel implementation. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1101–1109, 1998     

Molecular conformation of bilirubin from semiempirical molecular orbital calculations

Semiempirical methods were utilized in the computation of a fully optimized structure of bilirubin. Bond lengths and bond angles obtained using either AM1 or PM3 calculations showed excellent agreement with those obtained by X-ray diffraction. This indicated that molecular orbital methods satisfactory reproduced the complex conjugation found in bilirubin. Dihedral angles of the crucial “hinge” and the dihedral angles of the propionic acid side chains agreed well with those found by X-ray diffraction. Calculated hydrogen- bond parameters (distance and angles) showed substantial differences from experimental values, probably due to inherent weakness in the parameterization of the molecular orbital techniques. Conformational studies were carried out using AM1 by rotating the C9? C10 bond in 5° increments showed that the most stable structure exhibited a minimum at about 125° and exhibited a structure similar to those postulated from X-ray and NMR experiments. The hydrogen bonds showed remarkable tenacity during rotation of the C9? C10 bond and resisted breaking until the molecule was under extreme strain. © 1992 John Wiley & Sons, Inc.     

A rapid generalized valence-bond algorithm for semiempirical NDDO calculations

A recently developed algorithm based on the coupled cluster ansatz for the generalized valence-bond perfect-pairing model is adapted for the NDDO class of semiempirical methods. It allows for the calculation of the nondynamic electron correlation and executes as rapidly as the semiempirical molecular orbital method. To assess the interplay of the nondynamic and dynamic electron correlation vs. parameterization, preliminary results are presented for rotation about a double bond, dissociations about single bonds, and the relative stabilities of biradical isomers. © 1995 John Wiley & Sons, Inc.     

On the importance of size-consistency corrections in semiempirical MNDOC calculations

Energies obtained by configuration interaction calculations including all double excitations with regard to the Hartree-Fock reference determinant can empirically be corrected to size consistency using either the Langhoff-Davidson (LD) formula or a formula suggested by Pople, Seeger, and Krishnan (PSK). Semiempirical MNDOC calculations suggest that for molecular systems with a large number of electrons and important correlation effects the PSK correction is superior to the LD correction.     

New method of incorporating nonhorizontal AO in semiempirical quantum-chemical calculations

A previously proposed semiempirical method has been developed for calculating the molecular electron structures and geometries, which explicitly incorporates AOnonorthogonality. The integrals are parametrized in an atomic basis, and then a transfer is made to an orthogonal basis, in which the zero differential overlap approximation is used. The electron-repulsion integral matrix is transformed by a method in which one uses only the Coulomb part. The performance has been evaluated from the number of elementary operations, which is proportional to N³, where N is the basis size. The method is implemented as two schemes that differ in the method of specifying in the atomic basis: -CNDO and -NDDO. Calculations are presented on hydrocarbons by means of the -CNDO scheme, which enables one to calculate the heats of formation and the geometry with an accuracy comparable with that in MINDO/3. The performance is higher in calculations on transitional states, as is demonstrated for the model of nucleophilic substitution (CH₅ ^– anion). The -NDDO scheme has been examined at the level of electron-interaction integral transformation and has considerable advantages over the -CNDO one.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 4, pp. 385–394, July–August, 1987.     

A fast method of large-scale serial semiempirical calculations of docking complexes

A brief survey of the state of the art in methods of calculations of protein—ligand interaction energies in docking complexes is presented. A new computational technique is proposed that allows one to fundamentally improve the performance of large-scale serial calculations of docking complexes using the AM1/PM3 semiempirical methods. The technique explicitly allows for a specific feature of docking problems, viz., the need for calculating numerous ligand complexes with a specified protein whose noninteracting part remains “frozen” during computations. The interaction energies calculated using the new method differ only slightly from the results of complete AM1 calculations and the performance attained is high enough to solve practical drug design problems. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1759–1764, September, 2008.     

Evidence that there is a future for semiempirical molecular orbital calculations

The frequency of use and discussion of semiempirical and ab initio software is traced with bibliometric data from the Current Journals of the American Chemistry Society (JCACS) database, which has complete papers published in 19 journals in various fields of chemistry. Not only is the use of all types of computational chemistry software increasing apace, but also the number of papers mentioning semiempirical programs as a percentage of all papers mentioning quantum chemistry programs is growing. This percentage referring to semiempirical molecular orbital software grew from 29% in 1989 to 34% in 1993.     

Spin density calculations in semiempirical restricted and unrestricted SCF MO methods

In the present paper spin densities are calculated by ten methods on chosen radical systems. - interaction parameters for the individual methods are determined by McConnel's relation a _i =Q _i and by that of Colpa-Bolton a _i =(Q+K _i ) _i and the correlation between the results of the individual methods is studied.

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Zusammenfassung In der vorliegenden Arbeit werden Spindichten anhand von zehn Methoden an ausgewählten Radikalsystemen ermittelt. Die --Kopplungsparameter für die einzelnen Methoden werden nach den McConnell a _i =Q _i - und Colpa-Bolton a _i =(Q+K _i ) _i -Beziehungen bestimmt. Die zwischen den Ergebnissen der einzelnen Methoden bestehende Korrelation wird untersucht.

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Résumé Dans ce travail les densitées de spin sont calculées par dix méthodes sur un système des radicaux choisis. On détermine des parametres - d'interaction pour les méthodes individuelles dans la relation de McConnell a _i =Q _i et celle de Colpa-Bolton a _i =(Q+K _i ) _i et étudie la correlation entre les résultats des méthodes individuelles.

     

Use of semiempirical molecular orbital calculations for the evaluation of force fields

Various methods, employing molecular orbital calculations of varying approximations, for evaluation of force fields of polyatomic molecules have been reviewed. Applications ofcndo/force method for the force field calculations are specially dealt with in detail because of its ease of operation and being economically more viable in terms of computer time. The calculated C=O stretching force constants for a series of organic molecules are shown to have linear relationship with substituent constants.     

Understanding diastereofacial selection in carbohydrate-based domino cycloadditions: semiempirical and DFT calculations

The sequential cycloaddition of nitroalkenes with methyl vinyl ether was investigated by semiempirical (PM3) and density functional methods (B3LYP/6-31G*). The asymmetric version was also examined with a threoconfigured carbohydrate auxiliary. This produces a larger, more flexible system that complicates the calculation. Most transition structures were then fully optimized at the PM3 level and further refinement was done at ab initio levels. This study represents a model case that enables the rationalization of the high facial selectivity observed in carbohydrate-based nitrone- and nitronate-alkene cycloadditions. The selective endo orientation of the [4+2] pathway results from Coulombic attraction and secondary orbital interactions in the transition state. The stereochemical outcome is largely influenced by a combination of steric shielding from the bulky chiral substituent at C4 and the anomeric effect that places the nitronate C6-alkoxy group in a pseudoaxial arrangement. The resulting conformation favors the subsequent exo approach of methyl vinyl ether to the less hindered re face of the nitronate. It is also remarkable to note that solvation energies stabilize significantly a particular transition structure, thereby explaining the marked stereoselection observed in a polar medium.