Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n ² operations. No n ³ processes such as matrix diagonalization, matrix multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial “guess” orbitals from optimized molecular orbitals of small systems and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997     

IMiCMO: a new integrated ab initio multicenter molecular orbitals method for molecular dynamics calculations in solvent cluster systems

A new computational scheme integrating ab initio multicenter molecular orbitals for determining forces of individual atoms in large cluster systems is presented. This method can be used to treat systems of many molecules, such as solvents by quantum mechanics. The geometry parameters obtained for three models of water clusters by the present method are compared with those obtained by the full ab initio MO method. The results agree very well. The scheme proposed in this article also intended for use in modeling cluster systems using parallel algorithms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1107–1112, 2001     

On the suitability of strictly localized orbitals for hybrid QM/MM calculations

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. II. Two‐center expansion method

Using expansion formulas for the charge‐density over Slater‐type orbitals (STOs) obtained by the one of authors [I. I. Guseinov, J Mol Struct (Theochem) 1997, 417, 117] the multicenter molecular integrals with an arbitrary multielectron operator are expressed in terms of the overlap integrals with the same screening parameters of STOs and the basic multielectron two‐center Coulomb or hybrid integrals with the same operator. In the special case of two‐electron electron‐repulsion operator appearing in the Hartree–Fock–Roothaan (HFR) equations for molecules the new auxiliary functions are introduced by means of which basic two‐center Coulomb and hybrid integrals are expressed. Using recurrence relations for auxiliary functions the multicenter electron‐repulsion integrals are calculated for extremely large quantum numbers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 117–125, 2001     

A Terminal Chlorophosphinidene Complex

Terminal, electrophilic phosphinidene complexes (M=PR) are attractive platforms for PR-transfer to organic substrates. In contrast to aryl- or alkylphosphinidene complexes terminal chlorophosphinidenes (M=PCl) have only been proposed as transient intermediates but isolable example remain elusive. Here we present the transfer of PCl from chloro-substituted dibenzo-7λ³-phosphanorbornadiene to a square-planar osmium(II) PNP pincer complex to give the first isolable, terminal chlorophosphinidene complex with remarkable thermal stability. Os=P bonding was examined computationally giving rise to highly covalent {Os^II=P^ICl} double bonding.     

Development of minimized mixing molecular orbital method for designing organic ferromagnets

Predicting the high spin stability of organic radicals correctly for designing organic ferromagnets remains a significant challenge. We have developed a method with an index (L_min) for predicting the high spin stability of conjugated organic radicals at the restricted open‐shell Hartree–Fock level. Unitary transformations were performed for localizing the coefficients of nonbonding molecular orbitals, and subsequently the localized coefficients were used to calculate L_min that indicates the high spin stability of conjugated organic radicals. This method can be combined with the elongation method to treat huge high spin open‐shell systems. Thus, this method is useful for designing organic ferromagnets. © 2015 Wiley Periodicals, Inc.     

Synthesis of (3,6-dihydro-2H-pyran-2-yl)phosphonate derivatives and investigation of catalyst effect on frontier molecular orbitals using DFT method

Hetero Diels-Alder (HDA) reactions between 2,3-dimethyl-1,3-butadiene and diethyl ester of aroyl phosphonates catalyzed by AlCl₃ to afford (3,6-dihydro-2H-pyran-2-yl) phosphonate derivatives were investigated. Aroyl phosphonates with electron-withdrawing groups generally resulted in better isolated chemical yields. A stoichiometric amount of AlCl₃ rather than a catalytic amount was necessary to activate the cycloaddition reaction. The amount of AlCl₃ catalyst and its effect on LUMO of ethyl ester benzoyl phosphonate were also investigated by performing density functional theory (DFT) (B97D/6-31+G(d,p)) computations in dichloromethane. An increased loading of AlCl₃ induced a considerable decrease in the LUMO energy of ethyl ester of benzoyl phosphonate. The computed Gibbs free activation energy is 17.03 kcal/mol in DCM at 0°C using the same computational level.     

Computationally efficient canonical molecular dynamics simulations by using a multiple time‐step integrator algorithm combined with the particle mesh Ewald method and with the fast multipole method

An efficient implementation of the canonical molecular dynamics simulation using the reversible reference system propagator algorithm (r‐RESPA) combined with the particle mesh Ewald method (PMEM) and with the macroscopic expansion of the fast multipole method (MEFMM) was examined. The performance of the calculations was evaluated for systems with 3000, 9999, 30,000, 60,000, and 99,840 particles. For a given accuracy, the optimal conditions for minimizing the CPU time for the implementation of the Ewald method, the PMEM, and the MEFMM were first analyzed. Using the optimal conditions, we evaluated the performance and the reliability of the integrated methods. For all the systems examined, the r‐RESPA with the PMEM was about twice as fast as the r‐RESPA with the MEFMM. The difference arose from the difference in the numerical complexities of the fast Fourier transform in the PMEM and from the transformation of the multipole moments into the coefficients of the local field expansion in the MEFMM. Compared with conventional methods, such as the velocity‐verlet algorithm with the Ewald method, significant speedups were obtained by the integrated methods; the speedup of the calculation was a function of system size, and was a factor of 100 for a system with 3000 particles and increased to a factor of 700 for a system with 99,840 particles. These integrated calculations are, therefore, promising for realizing large‐scale molecular dynamics simulations for complex systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 201–217, 2000     

Investigation of the change in the electronic properties of FeF3 by the introduction of oxygen using a molecular orbital method

FeF₃ has attracted interest as a conversion‐reaction‐based positive electrode material in applications to lithium ion batteries. However, slow reaction kinetics is a major drawback due to its poor electrical conductivity. The electronic features of FeF₃ were examined using the DV‐Xα molecular orbital method. This article reports the effects of oxygen doping on the bonding characteristics and electrical conductivity. An analysis of the bond overlap population and spatial distribution of electrons showed that the Fe? O bond has a more covalent nature than the Fe? F bond. New energy levels were generated in the original band gap region through an interaction between the Fe3d and O2p orbitals with the introduction of oxygen. The electrical conductivity of FeF₃ is expected to be increased by the partial substitution of oxygen for fluorine due to the higher covalent character and the formation of new energy levels. © 2013 Wiley Periodicals, Inc.     

Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method

The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.Acknowledgement We thank the National Institutes of Health for support of this research.Contribution to the Jacopo Tomasi Honorary Issue     

Exploration of the (ethanol)4–water heteropentamers potential energy surface by simulated annealing and Ab initio molecular dynamics

A DFT electronic structure study of the (ethanol)₄–water heteropentamers at the B3LYP/6‐31+G(d) model chemistry was carried out. To get determine possible configurations, the potential energy surface (PES) was explored with two methods: simulated annealing and ab initio molecular dynamics. The results suggest that the PES is very flat. A total of 81 stable structures were determined. These structures were classified into 16 different geometric patterns according to geometric criteria like the number of hydrogen bonds and their spatial arrangement: cyclic, bicyclic, or lineal patterns. Thermodynamic stability was used for defining the order of such classification. Hydrogen bonds are mutually disturbed due to the existence of cooperative effects. Cooperativity affects the nature of the hydrogen bonds and the overall stability of the ethanol–water system given that the strongest interactions are markedly covalent and the most stable geometric pattern corresponds to the pentagonal arrangement. These observations were supported by the analysis of the loss of atomic charge of the hydrogen atoms involved in hydrogen bonds. These hydrogen bonds were classified as primary and secondary hydrogen bonds: O? H ··· O and C? H ··· O, respectively. For comparative purposes, some (ethanol)₅, (methanol)₅, and (methanol)₄–water clusters were characterized in this study. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A new hierarchical parallelization scheme: generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method (FMO)

A two-level hierarchical scheme, generalized distributed data interface (GDDI), implemented into GAMESS is presented. Parallelization is accomplished first at the upper level by assigning computational tasks to groups. Then each group does parallelization at the lower level, by dividing its task into smaller work loads. The types of computations that can be used with this scheme are limited to those for which nearly independent tasks and subtasks can be assigned. Typical examples implemented, tested, and analyzed in this work are numeric derivatives and the fragment molecular orbital method (FMO) that is used to compute large molecules quantum mechanically by dividing them into fragments. Numeric derivatives can be used for algorithms based on them, such as geometry optimizations, saddle-point searches, frequency analyses, etc. This new hierarchical scheme is found to be a flexible tool easily utilizing network topology and delivering excellent performance even on slow networks. In one of the typical tests, on 16 nodes the scalability of GDDI is 1.7 times better than that of the standard parallelization scheme DDI and on 128 nodes GDDI is 93 times faster than DDI (on a multihub Fast Ethernet network). FMO delivered scalability of 80-90% on 128 nodes, depending on the molecular system (water clusters and a protein). A numerical gradient calculation for a water cluster achieved a scalability of 70% on 128 nodes. It is expected that GDDI will become a preferred tool on massively parallel computers for appropriate computational tasks.     

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

DFT‐based QSAR study and molecular design of AHMA derivatives as potent anticancer agents

A quantitative structure–activity relationship (QSAR) of 3‐(9‐acridinylamino)‐5‐hydroxymethylaniline (AHMA) derivatives and their alkylcarbamates as potent anticancer agents has been studied using density functional theory (DFT), molecular mechanics (MM+), and statistical methods. In the best established QSAR equation, the energy (E_NL) of the next lowest unoccupied molecular orbital (NLUMO) and the net charges (Q_FR) of the first atom of the substituent R, as well as the steric parameter (MR₂) of subsituent R₂ are the main independent factors contributing to the anticancer activity of the compounds. A new scheme determining outliers by “leave‐one‐out” (LOO) cross‐validation coefficient (q) was suggested and successfully used. The fitting correlation coefficient (R²) and the “LOO” cross‐validation coefficient (q²) values for the training set of 25 compounds are 0.881 and 0.829, respectively. The predicted activities of 5 compounds in the test set using this QSAR model are in good agreement with their experimental values, indicating that this model has excellent predictive ability. Based on the established QSAR equation, 10 new compounds with rather high anticancer activity much greater than that of 34 compounds have been designed and await experimental verification. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Intra- and intermolecular interactions between cyclic-AMP receptor protein and DNA: ab initio fragment molecular orbital study

The ab initio fragment molecular orbital (FMO) calculations were performed for the cAMP receptor protein (CRP) complexed with a cAMP and DNA duplex to elucidate their sequence-specific binding and the stability of the DNA duplex, as determined by analysis of their inter- and intramolecular interactions. Calculations were performed with the AMBER94 force field and at the HF and MP2 levels with several basis sets. The interfragment interaction energies (IFIEs) were analyzed for interactions of CRP-cAMP with each base pair, DNA duplex with each amino acid residue, and each base pair with each residue. In addition, base-base interactions were analyzed including hydrogen bonding and stacking of DNA. In the interaction between DNA and CRP-cAMP, there was a significant charge transfer (CT) from the DNA to CRP, and this CT interaction played an important role as well as the electrostatic interactions. It is necessary to apply a quantum mechanical approach beyond the "classical" force-field approach to describe the sequence specificity. In the DNA intramolecular interaction, the dispersion interactions dominated the stabilization of the base-pair stacking interactions. Strong, attractive 1,2-stacking interactions and weak, repulsive 1,3-stacking interactions were observed. Comparison of the intramolecular interactions of free and complexed DNA revealed that the base-pairing interactions were stronger, and the stacking interactions were weaker, in the complexed structure. Therefore, the DNA duplex stability appears to change due to both the electrostatic and the CT interactions that take place under conditions of DNA-CRP binding.