Hybrid Quantum Mechanics Research Articles

Application of a hybrid quantum mechanics and empirical moleculardynamics multiscale method to carbon nanotubes

We present a hybrid multiscale method for coupling quantum mechanicsto empirical molecular dynamics, which is named as hybrid energydensity method. In this approach, quantum mechanical treatment isspatially confined to a small region, surrounded by a largermolecular mechanical region. A unified expression of total energycombining quantum mechanical and molecular mechanical descriptions,is given by employing a localized energy and a weight associatedwith it on each site. And we can perform the dynamical simulationsof entire system according to the given total energy. We use thehybrid energy density method to simulate two models of carbonnanotubes (CNT): one is a long CNT with an open end, and the other along CNT containing a di-vacancy under stretching. Calculations ofthe two CNT models demonstrate that the hybrid multiscale method isrequired to accurately treat the local quantum mechanical regionwith the influence of the larger molecular mechanical region.

Product Specificity and Mechanism of Protein Lysine Methyltransferases: Insights from the Histone Lysine Methyltransferase SET8

Molecular dynamics simulations employing a molecular mechanics (MM) force field and hybrid quantum mechanics (QM) and MM (QM/MM) have been carried out to investigate the product specificity and mechanism of the histone H4 lysine 20 (H4-K20) methylation by human histone lysine methyltransferase SET8. At neutral pH, the target lysine is available to only the enzyme in the protonated state. The first step in the methylation reaction must be deprotonation of the lysine target which is followed by the (+)AdoMet methylation of the neutral lysine [Enz.Lys-CH(2)-NH(3)(+).(+)AdoMet --> H(+) + Enz.Lys-CH(2)-NH(2).(+)AdoMet -->--> Enz.Lys-CH(2)-N(Me)H(2)(+).AdoHcy]. The electrostatic interactions between two positive charges on (+)AdoMet and Lys20-NH(3)(+) decrease the pK(a) of Lys20-NH(3)(+). Upon formation of Enz.Lys-NH(3)(+).(+)AdoMet, a water channel by which the proton escapes to the outer solvent phase is formed. The formation of a water channel for the escape of a proton from Lys20-N(Me)H(2)(+) in Enz.Lys20-N(Me)H(2)(+).(+)AdoMet is not formed because the methyl substituent blocks the starting of the water channel. Thus, a second methylation does not take place. The dependence of the occurrence of methyl transfer on the formation of a water channel in SET8 is in accord with our previous reports on product specificity by histone lysine monomethyltransferase SET7/9, large subunit lysine dimethyltransferase (LSMT), and viral histone lysine trimethyltransferase (vSET). The average value of the experimental DeltaG(E)() for the six lysine methyl transfer reactions catalyzed by vSET, LSMT, and SET7/9 with p53 as a substrate is 22.1 +/- 1.0 kcal/mol, and the computed average (DeltaG(C)()) is 22.2 +/- 0.8 kcal/mol. In this study, the computed free energy barrier of the methyl transfer reaction [Lys20-NH(2) + (+)AdoMet --> Lys20-N(Me)H(2)(+) + AdoHcy] catalyzed by SET8 is 20.8 kcal/mol. This is in agreement with the value of 20.6 kcal/mol calculated from the experimental rate constant (0.43 +/- 0.02 min(-1)). Our bond-order computations establish that the H4-K20 monomethylation in SET8 is a concerted linear S(N)2 displacement reaction.

Role of protein frame and solvent for the redox properties of azurin from Pseudomonas aeruginosa

We have coupled hybrid quantum mechanics (density functional theory; Car-Parrinello)/molecular mechanics molecular dynamics simulations to a grand-canonical scheme, to calculate the in situ redox potential of the Cu(2+) + e(-) --> Cu(+) half reaction in azurin from Pseudomonas aeruginosa. An accurate description at atomistic level of the environment surrounding the metal-binding site and finite-temperature fluctuations of the protein structure are both essential for a correct quantitative description of the electronic properties of this system. We report a redox potential shift with respect to copper in water of 0.2 eV (experimental 0.16 eV) and a reorganization free energy lambda = 0.76 eV (experimental 0.6-0.8 eV). The electrostatic field of the protein plays a crucial role in fine tuning the redox potential and determining the structure of the solvent. The inner-sphere contribution to the reorganization energy is negligible. The overall small value is mainly due to solvent rearrangement at the protein surface.

Prediction of Molecular Weight Distributions Based on ab Initio Calculations: Application to the High Temperature Styrene Polymerization

In this work we used quantum mechanics hybrid models (QM/QM) to investigate the high-temperature polymerization of styrene with the aim of elucidating its elementary chemistry. High and low quality quantum mechanics calculations were performed at the B3LYP/6-31g(d,p) and PM3 levels, respectively. Reaction kinetic constants were calculated for oligomers composed of up to 6 styrene units with classic transition state theory on potential energy surfaces determined at the QM/QM level. The capability of this approach to predict kinetic constants of elementary processes relevant to styrene polymerization was validated through the satisfactory comparison with well-known experimental data. One of the main results of this study is that a new kinetic route is proposed to describe the polymer growth mechanism, in which the succession of backbiting and β scission reactions plays a critical role. In particular we found that the 7:3 backbiting reaction can proceed fast and influence significantly the polymer weight distribution. Finally, the so evaluated kinetic constants were introduced in a polymerization reactor model and used to compare the distribution of the produced oligomers measured experimentally with that predicted from first principles. The agreement with experimental data is good, suggesting that the proposed approach provides a valuable tool to investigate the kinetics of polymerization systems for which experimental data on elementary reactions are not available.

Mechanisms of Amine-Catalyzed Organosilicate Hydrolysis at Circum-Neutral pH

Mono- and polyamines can catalyze the hydrolysis and condensation of organosilicate starting materials in biomimetic silica synthesis pathways at circum-neutral pHs and room temperature. Our study is focused on understanding the mechanistic role of amines in catalyzing the hydrolysis process that precedes condensation. We have conducted (29)Si NMR experimental studies over a range of temperature and pHs for the hydrolysis rates of trimethylethoxysilane (TMES), a model compound with only one hydrolyzable bond, combined with quantum mechanical hybrid density functional theory calculations of putative intermediate and transition-state structures for TMES and tetramethyl orthosilicate (TMOS). Comparison of calculated energies with experimentally determined activation energies indicates that amine catalysis of TMES is primarily a consequence of the amine's acidity at neutral pH. The proton released by the amine is transferred to the organosilicate, producing a protonated ethoxy leaving group that can be displaced by water in an S(N)2 reaction. For TMOS, the activation energy of proton-transfer coupled with S(N)2 substitution is comparable to that for Corriu's nucleophile-activated nucleophilic displacement, such that the mechanism of amine-catalyzed hydrolysis is dependent mostly on the ambient pH conditions as well as the type of amine. The relevance of our results to biological silica precipitation is discussed.

QM/MM and classical molecular dynamics simulation of histidine-tagged peptide immobilization on nickel surface

The hybrid quantum mechanics (QM) and molecular mechanics (MM) method is employed to simulate the His-tagged peptide adsorption to ionized region of nickel surface. Based on the previous experiments, the peptide interaction with one Ni ion is considered. In the QM/MM calculation, the imidazoles on the side chain of the peptide and the metal ion with several neighboring water molecules are treated as QM part calculated by “GAMESS”, and the rest atoms are treated as MM part calculated by “TINKER”. The integrated molecular orbital/molecular mechanics (IMOMM) method is used to deal with the QM part with the transitional metal. By using the QM/MM method, we optimize the structure of the synthetic peptide chelating with a Ni ion. Different chelate structures are considered. The geometry parameters of the QM subsystem we obtained by QM/MM calculation are consistent with the available experimental results. We also perform a classical molecular dynamics (MD) simulation with the experimental parameters for the synthetic peptide adsorption on a neutral Ni(1 0 0) surface. We find that half of the His-tags are almost parallel with the substrate, which enhance the binding strength. Peeling of the peptide from the Ni substrate is simulated in the aqueous solvent and in vacuum, respectively. The critical peeling forces in the two environments are obtained. The results show that the imidazole rings are attached to the substrate more tightly than other bases in this peptide.

DFT ×TB − a unified quantum-mechanical hybrid method

A unified quantum mechanical hybrid method on the basis of density functional theory (DFT) is presented. The method is based on an LCAO-Kohn-Sham ansatz. While a part is treated with standard DFT, for the remaining system non-orthogonal tight-binding (TB) approximations are made for potential and basis functions. This means that it is possible to have covalent bonds in between the DFT and TB parts. The charge fluctuation within the system is controlled by the self-consistent charge technique. Theory, implementation, and first example molecules are presented in this article, and further development is discussed.

Hierarchical Modeling N2 Adsorption on the Surface of and within a C60 Crystal: From Quantum Mechanics to Molecular Simulation

The adsorption of N(2) on the surface of, and within, a C(60) face-centered cubic crystal has been studied using a hierarchical approach. First, an ab initio potential between N(2) and C(60) is obtained from a recently developed quantum mechanical hybrid method, and then the adsorption behavior is predicted using Monte Carlo simulation. On the crystal surface, N(2) adsorption isotherm at 77.3 K is of type II. The adsorption simulated with the ab initio potential is slightly greater than that with the empirical Steele potential derived from experimental N(2) adsorption on planar graphite, and both are in fairly good agreement with measured results. With increasing pressure, N(2) molecules are found to sequentially occupy three favorable sites: the octahedral sites, the tetrahedral sites, and the top of C(60) molecules. Finally multiple layers form and wetting occurs as the bulk N(2) saturation pressure is reached. The isosteric heat of adsorption exhibits two maxima and finally approaches the enthalpy of vaporization of bulk N(2). Within the crystal, the N(2) adsorption isotherm at 77.3 K is of type I, and the use of ab initio potential leads to significantly greater adsorption than the Steele potential. N(2) molecules are observed to intercalate only the octahedral sites, and the isosteric heat of adsorption is nearly a constant. As in our previous work of N(2) and O(2) adsorption in the C(168) schwarzite (Jiang et al. J. Phys. Chem. B 2004, 108, 9852), this work demonstrates the importance of an accurate adsorbate-adsorbent interaction potential in the determination of gas adsorption behavior.

Photophysics of Tryptophan Fluorescence: Link with the Catalytic Strategy of the Citrate Synthase from Thermoplasma acidophilum

The formation of all major intermediates in the reaction catalyzed by the citrate synthase from Thermoplasma acidophilum is accompanied by changes in tryptophan fluorescence. The largest change is the strong quenching observed on formation of the binary complex with substrate, oxaloacetate (OAA). The four tryptophan residues present in the enzyme have been changed to nonfluorescent ones in various combinations without major perturbations in protein stability, enzyme mechanism, or other physical properties. W348, residing in the hydrophobic core of the protein behind the active site wall ca. 9 A from OAA, is responsible for the majority of the protein's intrinsic fluorescence and all of the quenching that accompanies OAA binding. Lifetime studies show that all of the quenching results from excited-state processes. The lack of solvent isotope effects on the quantum yields excludes a quenching mechanism involving proton transfer to an acceptor. There are no significant changes in fluorescence properties in single site mutants of residues near W348 that change conformation and/or interactions when OAA binds. This result excludes these changes from a direct role. Electron transfer from the indole excited state to some acceptor is the major quenching mechanism; the reduced quenching observed in the 5F-W-substituted protein strengthens this conclusion. Using the X-ray structures of the unliganded enzyme and its OAA binary complex, hybrid quantum mechanics-molecular dynamics (QM-MM) calculations show that OAA itself is the most likely quencher with the OAA carbonyl as the electron acceptor. This conclusion is strengthened by the ability of an alpha-keto acid model compound, trimethylpyruvate, to act as a diffusional quencher of indole fluorescence in solution. The theoretical calculations further indicate that the positive electrostatic potential surrounding the OAA carbonyl within the enzymes' active site is essential to its ability to accept an electron from the excited state of W348. These same environmental factors play a major role in activating OAA to react with the carbanion of acetyl-CoA. Since carbonyl polarization plays a role in the catalytic strategies of numerous enzymes whose reactions involve this functional group, tryptophan fluorescence changes might be useful as a mechanistic probe for other systems.

Computation of quantum mechanical hybridization and dipole correlation of the electronic structure of the F3B–NH3supermolecule

AbstractA valence bond description of the electronic structure and the process of the formation of the adduct supermolecule, F3B–NH3by charge transfer interactions between a Lewis acid, BF3, and a Lewis base, NH3, is computed in terms of the quantum mechanical localized molecular orbital (LMO) method. A dipole correlation of electronic structure is also reported. The valence bond description in terms of bond pair and lone pair is transparent in the generated LMOs of the donor, acceptor, and adduct supermolecule. It is transparent in the computed LMOs that the lone pair of N in NH3is actually involved in forming a new dative bond between B and N atoms. The present work reports the evaluated hybridization status of the boron, nitrogen, and fluorine atoms in the interesting donor–acceptor compound, F3B–NH3. It is transparent in the computed results that the quantum mechanical hybridization automatically incorporates the effect of change of environment in the pattern of hybridization perfectly in accordance with Bent's rule. The calculated dipole moment of the supermolecule is high; it is partitioned into contributions resulting from bond moments and atomic dipoles, as contributions from hybrid orbitals accommodating lone pairs of electrons. The magnitude of atomic dipole is small compared with the bond dipole component. A rationale of the bond moment of the molecule is attempted in terms of the charge density distribution on atomic sites and the atomic dipole is correlated in terms of the pattern of hybridization of lone pairs on the F atoms. The generated LMOs reveal that only one lone pair on each F atom is in a hybrid orbital, and the remaining two lone pairs are in pureporbitals. The small lone pair contribution to molecular dipole is thus transparent in computed quantum mechanical hybridization that shows that, out of three, only one lone pair on the F atoms can set in atomic dipole. This study demonstrates that atomic dipole can be used as a descriptor of the hybridization status of lone pairs on atoms in the molecules. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

HM-IE: Quantum Chemical Hybrid Methods for Calculating Interaction Energies

Accurate intermolecular potentials are needed for quantitative molecular simulations, but their calculation from quantum mechanics can be very demanding. We have developed several variations of a procedure, which we collectively refer to as quantum mechanical Hybrid Methods for Interaction Energies (HM-IE), to accurately estimate interaction energies from CCSD(T) calculations with a large basis set (LBS). HM-IE was tested for interaction energies of Ne 2 ,( C 2H2)2, and N2-benzene for many orientations sampling the entire potential energy surface and was found to be in excellent agreement with the CCSD(T)/LBS results while requiring considerably less computational time and resources. Furthermore, for neon, an intermolecular potential fit to interaction energies using HM-IE and a potential fit to CCSD(T)/LBS energies resulted in nearly identical predictions for densities and vapor pressures.

Selective acylation of 2 methoxynaphthalene by large pore zeolites: catalyst selection through molecular modeling

The selective acylation of 2-methoxynaphthalene (2-MON) is commercially very important to produce selectively 2-acyl-6-methoxynaphthalene (2,6-AMON), which is a precursor to Naproxen, an anti-inflammatory drug. Most of the laboratory investigations conducted with different solid acids show that the undesirable products are formed in large quantities. Thus, various molecular modeling techniques were used to investigate selectivity towards desired 2,6-AMON isomer over undesired 1,2-AMON, in four large-pore zeolites, namely, mordenite ( MOR), zeolite L ( LTL), zeolite beta ( BEA) and ITQ-7 ( ISV). The qualitative results were obtained by using simple molecular graphics (MG) and structural fitting approach. The quantitative results were obtained by incorporating the interaction of atoms of the molecules and those of the zeolite frameworks. From diffusion energy profile calculations the diffusion energy barriers for self-diffusion of 2-MON and the acylated isomers were obtained. From these energy barrier values the selectivity offered by zeolites towards desired product was determined and it was found to be in the order of ISV> BEA> MOR>LTL. Hybrid Quantum Mechanics–Molecular Mechanics (QM/MM) approach was used to study the effect of Brønsted acidity on the activity and selectivity offered by zeolites. The interaction of the reactant and product species with the acidic protons at T3 and T9 sites in BEA, having different acidities was studied by this method. The QM energy values indicate that acidity affected the catalytic activity but not the regioselectivity towards the desired 2,6-AMON isomer.

Integral equation treatment of solvated quantum particles

A hybrid quantum-mechanics and molecular-mechanics approach is developed for solvated quantum particles. The method is based on self-consistent field calculations to the wave function of quantum particle and integral equations for solvent structure. The method is applied to evaluate the local solvent structure around a hydrated positronium. The results are consistent with the experimental data.

A Localized Molecular Orbital Study of the Structure and Bonding of Ozone.

The locali zed molecular o rbital th eory and e ne rgy partiti on in g formali sm have been in voked to study th e stru cture and bonding in ozone molecule. The range o f in vestigati o n covers a large numbe r o f confo rmations generated th eore ti cally ove r th e wide range of apical angles between angular (C21.) to linear (0 =11 ) shapes. The results demonstrate that. similar to th e bonding in diborane, th e re are two equi valent three-cente red bonds in ozone embracing three oxygen atoms in all th e conformations . The possibilit y of a triangular struc ture of ozone is ruled out because the computed locali zed mo lecular orbit als demo nstrate that the re is no bonding between the termin a l oxygen atoms and the decomposed e ne rgy compone nt s show that th e interaction between terminal oxyge n atoms is stro ng ly repul s ive. Charge de ns ity di stribution is asy mmetric in th e ho monu c lear mo lecule and it s dipo le mo ment is a n al gebraic sum of bond moment a nd lone pair mo ment a nd lo ne pair o n th e apical oxygen ato m contributes significantl y to the dipo le mo ment. It is de mo nstrated that a ny atle mpt of calculatin g th e apical an g le from the ex perimentall y determined dipole mo me nt would be erroneous and mi s leadin g. Variation of dipo le mo ment as a function of angular to linear reorganization of mo lecular shape is correlated in terms of computed quantum mechanical hybridi zation of the lone pair o n th e apical oxygen a to m. The barrier to in ve rsion of ozone th ro ugh th e lin ear (0=1, ) trans iti o n state originates from a subtl e inte rpla y of one- and two- cente r energy compone nts over the e ntire skeleton of th e molecule.

Density functional and molecular orbital study of physical process of inversion of nitrogen trifluoride (NF3) molecule

Density functional and molecular orbital study of physical process of inversion of nitrogen trifluoride (NF₃) molecule

Quantum chemical study of the umbrella inversion of the ammonia molecule

The physical event of the umbrella inversion of ammonia has been studied in detail by application of the formalisms of frontier orbital theory, the density functional theory, the localized molecular orbital method, and the energy partitioning analysis. An intuitive structure for the transition state and dynamics of the physical process of structural reorganization prior to inversion have been suggested. The computation starts with the CNDO/2 equilibrium geometry, and thereafter the cycle proceeds through all the conformations of ammonia obtained by varying the ∠HNH angle in steps of 2° from its equilibrium value up to the transition state. The geometry of each conformation is optimized with respect to the length of the N–H bond. The glimpses of the charge density reorganization during the movement of the molecule from equilibrium conformation toward the transition state is computed in terms of dipole moment and the quantum mechanical hybridizations of bond pair and lone pair of N atom through the localized molecular orbitals (LMOs) of all the conformations. Results demonstrate that as the geometry of the molecule begins to evolve through the reorganization of structure, the N–H bond length and the dipole moment begin to decrease, and the trend continues up to the transition state. The dipole moment of the molecule at the suggested transition state is zero. The computed nature of quantum mechanical hybridization of bond pair and lone pair of the N atom as a function of reaction coordinates of the ∠HNH angles reveals that the percentage of s character of the lone pair hybrid decreases and that of the bond pair hybrid forming the σ(N–H) bond increases during the process of geometry reorganization from the equilibrium shape to the transition state. The rationale of the zero dipole moment of the transition state for inversion is not straightforward from its point-group symmetry, but is self-evident from its electronic structure drawn in terms of LMOs. The electronic structure of the transition state, which may be drawn in terms of the LMOs, seems to closely reproduce its suggested intuitive structure. The pattern of variation of dipole moment and nature of the changes of the percentage of the s character in the lone pair hybrid creating dipole with the evolution of geometry during the physical process of structural reorganization for the inversion are found to be nicely correlated according to the suggestion of Coulson. The profiles of the increasing strength of the N–H bond and the increasing percentage of s character of the bond pair hybrid of N atom forming this bond as a function of reaction coordinates are also found to be correlated in accordance with the suggestion of Coulson. The profile of global hardness as a function of reaction coordinate seems to demonstrate that the dynamics of the evolution of the molecular structure from equilibrium shape to the transition state following the course of suggested mode of structural reorganization conforms to the principle of maximum hardness (PMH). The profiles of parameters like the energies of highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), the gap in energy between HOMO and LUMO, the global hardness, the global softness, and chemical potential as a function of reaction coodinates of a continuous structural evolution from equilibrium shape to the transition state mimic the potential energy diagram of the total energy. Both the frontier orbital parameters and the density functional quantities are found to be equally effective and reliable to monitor the process of necessary structural reorganization prior to the inversion of mofecules. An energy partitioning analysis demonstrates that the origin of barrier has no unique single source rather as many as four mutually exclusive but interacting one- and two-center energy terms within the molecule entail the origin and the height of the barrier. From a close analysis of the results, it seems highly probable that the necessary structural reorganization prior to umbrella inversion of ammonia most realistically occurs following the course of normal modes of vibration of the molecule. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1–26, 2000

Quantum chemical study of the umbrella inversion of the ammonia molecule

The physical event of the umbrella inversion of ammonia has been studied in detail by application of the formalisms of frontier orbital theory, the density functional theory, the localized molecular orbital method, and the energy partitioning analysis. An intuitive structure for the transition state and dynamics of the physical process of structural reorganization prior to inversion have been suggested. The computation starts with the CNDO/2 equilibrium geometry, and thereafter the cycle proceeds through all the conformations of ammonia obtained by varying the ∠HNH angle in steps of 2° from its equilibrium value up to the transition state. The geometry of each conformation is optimized with respect to the length of the N–H bond. The glimpses of the charge density reorganization during the movement of the molecule from equilibrium conformation toward the transition state is computed in terms of dipole moment and the quantum mechanical hybridizations of bond pair and lone pair of N atom through the localized molecular orbitals (LMOs) of all the conformations. Results demonstrate that as the geometry of the molecule begins to evolve through the reorganization of structure, the N–H bond length and the dipole moment begin to decrease, and the trend continues up to the transition state. The dipole moment of the molecule at the suggested transition state is zero. The computed nature of quantum mechanical hybridization of bond pair and lone pair of the N atom as a function of reaction coordinates of the ∠HNH angles reveals that the percentage of s character of the lone pair hybrid decreases and that of the bond pair hybrid forming the σ(N–H) bond increases during the process of geometry reorganization from the equilibrium shape to the transition state. The rationale of the zero dipole moment of the transition state for inversion is not straightforward from its point-group symmetry, but is self-evident from its electronic structure drawn in terms of LMOs. The electronic structure of the transition state, which may be drawn in terms of the LMOs, seems to closely reproduce its suggested intuitive structure. The pattern of variation of dipole moment and nature of the changes of the percentage of the s character in the lone pair hybrid creating dipole with the evolution of geometry during the physical process of structural reorganization for the inversion are found to be nicely correlated according to the suggestion of Coulson. The profiles of the increasing strength of the N–H bond and the increasing percentage of s character of the bond pair hybrid of N atom forming this bond as a function of reaction coordinates are also found to be correlated in accordance with the suggestion of Coulson. The profile of global hardness as a function of reaction coordinate seems to demonstrate that the dynamics of the evolution of the molecular structure from equilibrium shape to the transition state following the course of suggested mode of structural reorganization conforms to the principle of maximum hardness (PMH). The profiles of parameters like the energies of highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), the gap in energy between HOMO and LUMO, the global hardness, the global softness, and chemical potential as a function of reaction coodinates of a continuous structural evolution from equilibrium shape to the transition state mimic the potential energy diagram of the total energy. Both the frontier orbital parameters and the density functional quantities are found to be equally effective and reliable to monitor the process of necessary structural reorganization prior to the inversion of mofecules. An energy partitioning analysis demonstrates that the origin of barrier has no unique single source rather as many as four mutually exclusive but interacting one- and two-center energy terms within the molecule entail the origin and the height of the barrier. From a close analysis of the results, it seems highly probable that the necessary structural reorganization prior to umbrella inversion of ammonia most realistically occurs following the course of normal modes of vibration of the molecule. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1–26, 2000