The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations

We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail.     

改进的相对论量子化学计算ZORA方法

提出一种改进的ZORA(Zeroth-OrderRegularApproximationtotheDiracEquation)方法,其单电子方程为：[σ·p(c^2/2c^2-V~0)σ·p+V(r)]ψ=εψ。式中V~0为空间限域的势能函数：V~0(r=~A∑V~0^A(r~A),r~A=|r-R~A|,V~0^A(r~A)=V^A(r~A){1+exp[α(r~A-r~0^A]}^-^1。其中A表示分子的某个组成原子,R~A为A原子的位置矢量,V^A(r~A)为自由A原子的势函数,α和r~0^A为参数。改进的ZORA方法具有原来方法的所有优点,避免了原有ZORA方法因不满足标度变换不变性带来的缺陷,而且计算过程简单。具体计算表明,通过适当选择参数α和r~0^A,用本研究提出来的方法,在计算分子几何结构和键合能时,基本上消除了ZORA方法由于标度变换依赖性产生的误差。     

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     

On some ways of modifying semiempirical quantum chemical methods

The problems of semiempirical quantum chemical calculations of (a) spin densities in paramagnetic organometallics, (b) hydrogen bonds, and (c) bond energies and the structure of transition-metal compounds are discussed. Some modifications of the existing semiempirical quantum chemical method are presented. An extended NDDO approximation has been developed. This scheme includes explicit symmetric orthogonalization of the core Hamiltonian and the use of Hellmann's effective core potential for core-electron interaction. © 1996 John Wiley & Sons, Inc.     

Reconsideration of solvent effects calculated by semiempirical quantum chemical methods

AM1 and PM3 semiempirical calculations are reported for the solvent effects on the tautomeric equilibria of 2-pyridone/2-hydroxypyridine and 4-pyridone/4-hydroxypyridine in the gas phase and solution. The solvent effects on the tautomeric equilibria were investigated by self-consistent reaction field (SCRF) theory implemented in the AMPAC and MOPAC program in two different ways: one in which all the solvent relaxation is included in the quantum mechanics and the total energy must be corrected for the solvent change in energy, method A; and a second in which the quantum mechanics directly includes this term, method B. The calculated (AM1, method A) tautomeric equilibrium constants (log K₁) for 2-pyridone in the gas phase, cyclohexane, chloroform, and acetonitrile are ?0.3, 0.3, 0.8, and 1.3, respectively, in good agreement with the experimental data (?0.4, 0.24, 0.78, and 2.17, respectively). For 4-pyridone/4-hydroxypyridine differences between calculated log K₁ for the gas phase, chloroform and acetonitrile (?6.0, ?2.6, and ?1.2, respectively) and experimental data (< ?1, 0.11, and 0.66, respectively) are larger but the experimental values are also less certain. The experimental acetonitrile data are disturbed by specific interactions. An extension of the SCRF for aqueous solutions is reviewed. © 1993 John Wiley & Sons, Inc.     

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.     

NANOPACK: Parallel codes for semiempirical quantum chemical calculations of large systems in the sp‐ and spd‐basis

A parallel implementation of the conventionally used NDDO (MNDO, AM1, PM3, CLUSTER‐Z1) and modified NDDO‐WF (CLUSTER‐Z2) techniques for semiempirical quantum chemical calculations of large molecular systems in the sp‐ and spd‐basis, respectively, is described. The atom‐pair distribution of data over processors forms the basis of the parallelization. The technological aspects of designing scalable parallel calculations on supercomputers (using ScaLAPACK and MPI libraries) are discussed. The scaling of individual algorithms and the entire package was carried out for model systems with 894, 1920, and 2014 atomic orbitals. The package speed‐up provided by different multiprocessor systems involving a cluster of Intel PIII processors, Alpha‐21264‐processor‐built machine MBC‐1000M, and Cray‐T3E is analyzed. The effect of computer characteristics on the package performance is discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

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.     

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.     

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method.     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.     

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.     

Fast method for quantum chemical calculations of large molecules with the approximation of the DFT Hamiltonian

The fundamentally new method NESE is proposed for quantum chemical calculations of large molecules, which employs the approximation of the Hamiltonian of the commonly used DFT method and is as fast as the AM1 and PM3 semi-empirical methods or the DFTB method. The parameters for the new method were chosen by the least-squares method based on the comparison of its matrix elements with the reference DFT/PBE Hamiltonian. The initial non-iterative version NESE-0 was computer-implemented and approved on many thousands of various molecules containing H, C, N, and O atoms. The NESE-0 method moderately outperforms the DFTB approach and is an order of magnitude better than the AM1, PM3, and PM6 levels in reproducing the one-electron energies calculated in terms of the DFT/PBE.     

Application of semiempirical quantum chemical methods as a scoring function in docking

A crucial point in docking simulations is the scoring function used for estimation of the target-ligand interaction energy. The usual practice is to employ fast but simplified empirical scoring functions. Rigorous quantum chemical methods are too slow to screen virtual combinatorial libraries consisting of thousands of molecules, but they can be used in the final step of the simulations for assessing the results obtained. At this stage quantum chemical calculations can be performed only for the 10–100 top binders predicted by simplified scoring functions, and only using linear-scaling semiempirical quantum chemical methods such as MOZYME. The possibilities and potentialities of the quantum chemical methods for estimation of the binding affinities in docking simulations are a largely unexplored area, so the main goal of this study is a detailed evaluation of the potential and limitations of the MOZYME methodology for estimation of the target-ligand binding energies and its comparison with available experimental data.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

A new algorithm for molecular fragmentation in quantum chemical calculations

In this study, we present a "black-box" method for fragmenting a molecule with a well-defined Kekulé or valence-bond structure into a significant number of smaller fragment molecules that are more amenable to high level quantum chemical calculations. By taking an appropriate linear combination of the fragment energies, we show that it is possible in many cases to obtain highly accurate total energies when compared to the total energy of the full molecule. Our method is derived from the approach reported by Deev and Collins, but it contains significant unique elements, including an isodesmic approach to the fragmentation process. Using a method such as that described in this work it is in principle possible to obtain very accurate total energies of systems containing hundreds, if not thousands, of atoms as the approach is subject to massive parallelization.     

Smooth solvation method for d-orbital semiempirical calculations of biological reactions. 1. Implementation

The present paper describes the extension of a recently developed smooth conductor-like screening model for solvation to a d-orbital semiempirical framework (MNDO/d-SCOSMO) with analytic gradients that can be used for geometry optimizations, transition state searches, and molecular dynamics simulations. The methodology is tested on the potential energy surfaces for separating ions and the dissociative phosphoryl transfer mechanism of methyl phosphate. The convergence behavior of the smooth COSMO method with respect to discretization level is examined and the numerical stability of the energy and gradient are compared to that from conventional COSMO calculations. The present method is further tested in applications to energy minimum and transition state geometry optimizations of neutral and charged metaphosphates, phosphates, and phosphoranes that are models for stationary points in transphosphorylation reaction pathways of enzymes and ribozymes. The results indicate that the smooth COSMO method greatly enhances the stability of quantum mechanical geometry optimization and transition state search calculations that would routinely fail with conventional solvation methods. The present MNDO/d-SCOSMO method has considerable computational advantages over hybrid quantum mechanical/molecular mechanical methods with explicit solvation, and represents a potentially useful tool in the arsenal of multi-scale quantum models used to study biochemical reactions.     

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.