Combined Quantum Mechanics Research Articles

Spintronics

LATER this year physicists will be celebrating the centenary of Paul Dirac's birth. One of the most influential scientists of the 20th century, Dirac combined quantum mechanics and special relativity to explain the strange magnetic or “spin” properties of the electron. What Dirac could not have foreseen, however, is how the spin of the electron could change the field of microelectronics.

Sampling Phase Space by a Combined QM/MM ab Initio Car−Parrinello Molecular Dynamics Method with Different (Multiple) Time Steps in the Quantum Mechanical (QM) and Molecular Mechanical (MM) Domains

This study considers a scheme for sampling phase space in large molecules based on Car−Parrinello ab initio molecular dynamics. The scheme makes use of a combined quantum mechanics and molecular mechanics (QM/MM) method augmented with a multiple-time-step technique. This scheme makes it possible to oversample the computationally less expensive MM region relative to the QM domain. The goal here is to provide better ensemble averaging in the MM region that is usually larger in size and therefore typically has a higher degree of configurational variability. It is shown that the multiple-time-step integrator will generate the same trajectory as a standard molecular dynamics integrator. Moreover, with a gradual rescaling of masses, the energy conservation of a multiple-time-step simulation can be satisfied to the same extent as a standard simulation. Finally, it is demonstrated that the multiple-time-step QM/MM method can accelerate the equilibration and configurational sampling of a molecular dynamics simulation as it is used in thermodynamic integration. The scheme is not intended as a tool for generating trajectories in actual dynamics.

A comparative study of two QM/MM methods testing the validity of the mean field approximation

We compared the performances of two methods that combine quantum mechanics and molecular mechanics for the study of liquid systems. They differ in the description of the solute–solvent interaction. One makes use of the mean field approximation and the other does not. We show that the introduction of this approximation does not introduce significant errors into the induced dipole moment of the solute, the interaction energy or the solvent structure, while it permits a considerable reduction (from several thousand to four or five) of the number of quantum calculations and hence of the computational demands.

Energetically most likely substrate and active-site protonation sites and pathways in the catalytic mechanism of dihydrofolate reductase.

Despite much experimental and computational study, key aspects of the mechanism of reduction of dihydrofolate (DHF) by dihydrofolate reductase (DHFR) remain unresolved, while the secondary DHFR-catalyzed reduction of folate has been little studied. Major differences between proposed DHF mechanisms are whether the carboxylate group of the conserved active-site Asp or Glu residue is protonated or ionized during the reaction, and whether there is direct protonation of N5 or a proton shuttle from an initially protonated carboxylate group via O4. We have addressed these questions for both reduction steps with a comprehensive set of ab initio quantum chemical calculations on active-site fragment complexes, including the carboxyl side chain and, progressively, all other polar active-site residue groups including conserved water molecules. Addition of two protons in two steps was considered. The polarization effects of the remainder of the enzyme system were approximated by a dielectric continuum self-consistent reaction field (SCRF) model using an effective dielectric constant (epsilon) of 2. Optimized geometries were calculated using the density functional (B3LYP) method and Onsager SCRF model with the 6-31G basis. Single-point energy calculations were then carried out at the B3LYP/6-311+G level with either the Onsager or dielectric polarizable continuum model. Additional checking calculations at MP2 and HF levels, or with other basis sets or values of epsilon, were also done. From the results, the conserved water molecule, corresponding to W206 in the E. coli DHFR complexes, that is H-bonded to both the OD2 oxygen atom of the carboxyl (Asp) side chain and O4 of the pterin/dihydropterin ring, appears critically important and may determine the protonation site for the enzyme-bound substrates. In the absence of W206, the most stable monoprotonated species are the neutral-pair 4-enol forms of substrates with the carboxyl group OD2 oxygen protonated and H-bonded to N3. If W206 is included, then the most stable forms are still the neutral-pair complexes but now for the N3-H keto forms with the protonated OD2 atom H-bonding with W206. A second proton addition to these complexes gives protonations at N8 (folate) or N5 (DHF). Calculated H-bond distances correlate well with those for the conserved W206 observed in many X-ray structures. For all structures with occluded M20 loop conformations (closed active site), OD2-N3 distances are less than OD2-NA2 distances, which is consistent with those calculated for protonated OD2 complexes. Thus, the results (B3LYP; epsilon = 2 calculations) support a mechanism for both folate and DHF reduction in which the OD2 carboxyl oxygen is first protonated, followed by a direct protonation at N8 (folate) and N5 (DHF) to obtain the active cation complexes, i.e., doubly protonated. The results do not support a proposed protonated carboxyl with DHF in the enol form for the Michaelis complex, nor an ionized carboxyl with protonated enol-DHF as a catalytic intermediate. However, as additional calculations for the monoprotonated complete complexes show a reduction in the energy differences between the neutral-pair keto and ion-pair keto (N8- or N5-protonated) forms, we are extending the treatment using combined quantum mechanics and molecular mechanics (QM/MM) and molecular dynamics simulation methods to refine the description of the protein/solvent environment and prediction of the relative stabilization free energies of the various (OD2, O4, N5, and N8) protonation sites.

A QM/MM/continuum model for computations in solution: Comparison with QM/MM molecular dynamics simulations

AbstractWe propose a model for fast quantum mechanical computations of molecules and processes in solution. The chemical system is described quantum mechanically (QM) using density functional theory. A few discrete solvent molecules are described using molecular mechanics (MM) force fields. The bulk solvent is described through a dielectric continuum model. The interaction between the QM/MM aggregate and the continuum is computed by using a multipole moment development of the charge distribution of the former. This is an intermediate model between the standard continuum approach and the combined quantum mechanics and molecular mechanics (QM/MM) technique, in which a large number of MM solvent molecules is considered and a statistical simulation of the solution is performed. The method may also be used to estimate long‐range interactions in combined QM/MM Monte Carlo or molecular dynamics simulations. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Combined Quantum Mechanics: Interatomic Potential Function Investigation of rac-meso Configurational Stability and Rotational Transition in Zirconocene-Based Ziegler−Natta Catalysts

The relative energetic stability of the “rac” and the “meso” rotational isomers of metallocene-based Ziegler−Natta (ZN) catalysts plays an important role in determining the structural, physical and...

A multiconfiguration self-consistent field/molecular dynamics study of the (n→π*)1 transition of carbonyl compounds in liquid water

A model is presented for the electrostatic component of solvatochromic shifts in vertical electronic excitation energies. The model, which makes use of the mean-field approximation, combines quantum mechanics (QM) in the description of the solute molecule and molecular mechanics (MM) in the description of the solvent. The method is implemented at the multiconfigurational self-consistent field level. We present illustrative applications to the (n→π*)1 transitions of formaldehyde, acetaldehyde, and acetone in liquid water. The solvent shifts obtained compare well with other ab initio QM/MM calculations and when the electron correlation components are included with the experimental solvent shift, but differ from the results obtained with semiempirical QM/MM and continuum models.

New approaches to the description of short-range repulsion interactions in hybrid quantum/classical systems

We discuss some limitations of combined quantum mechanics and molecular mechanics methods, which are becoming popular when working with large chemical and biochemical systems. More precisely, we focus on the treatment of the short-range interaction between a quantum molecule and a classical system. Generally, this short-range energy is handled by a sum over atom pairs of A/ R 12 terms, where R is the atom–atom separation, as in Lennard–Jones potentials. We illustrate the limitations of this approach and propose two other methods. The first one consists in the use of a Buckingham-type formula which, compared to the A/ R 12 term, is mathematically more flexible and physically more adequate. The second one is based on the use of a pseudopotential for describing the classical atoms that interact with the electronic cloud of the quantum system. The transferability of these potentials is discussed.

Towards solvation simulations with a combined ab initio molecular dynamics and molecular mechanics approach

The combined quantum mechanics and molecular mechanics method has been implemented within the framework of the Projector Augmented Wave Car-Parrinello method for explicit solvent simulations. The approach has been evaluated for its ability to represent the ‘true’ intermolecular interaction potential and its ability to perform energy conserving dynamics. The combined QM/MM potential has been parameterized to reproduce 27 hydrogen bonded bimolecular interactions between a water molecule and a set of organic molecules calculated wholly at the density function theory level. For this training set, a root-mean-square deviation of 0.8kcal/mol was achieved for the interaction energies that ranged from −0.3 to −29.3kcal/mol.

Solvent effects by means of averaged solvent electrostatic potentials: Coupled method

In this article we propose a mean field theory that permits the calculation of solvent effects in a direct way by combining quantum mechanics and molecular dynamics simulations. Because of the reduced number of necessary quantum calculations, it is possible to get the same level of theory used for molecules in vacuo. The electronic structure of the solute in solution and the solvent structure around it are optimized in a self-consistent way. The main characteristics of the proposed method are high-level quantum calculations in the representation of the solute, a detailed description of the solvent structure through molecular dynamics calculation, inclusion of the mutual polarization of the solute and solvent molecules, and an accurate description of the solute–solvent interaction energy. As an application of the model we studied the polarization of quantum mechanically treated water and methanol molecules in the liquid phase. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 705–715, 2000

Finding transition structures in extended systems: A strategy based on a combined quantum mechanics–empirical valence bond approach

A method for efficient localization and description of stationary points on the potential energy surface of extended systems is presented. It is based on Warshel’s empirical valence bond approach, for which we propose a modification, and combines the potential function description of the total system with a quantum mechanical description of the reaction site (QM-Pot). We describe the implementation of the method in the QMPOT program, which is basically an optimizer for minima and saddle points and has interfaces to existing quantum mechanical (e.g., TURBOMOLE, GAUSSIAN94) and interatomic potential function codes (e.g., GULP, DISCOVER). The power of the method is demonstrated for proton transfer reactions in zeolite catalysts, which may have as many as 289 atoms in the unit cell. As a test case the zeolite chabazite is considered in this study. Its limited unit cell size (37 atoms) makes comparison with the full periodic ab initio limit possible. The inclusion of long-range effects due to the periodic crystal structure by the QM-Pot method proves crucial in obtaining reliable results. The combined quantum mechanics–interatomic potential function calculations yield reaction barriers within 6 kJ/mol and reaction energies within 3.5 kJ/mol of the periodic ab initio limit. The zero-point vibrational energy corrected reaction barriers are between 58 and 97 kJ/mol for the six different proton jump paths. These are density functional results employing the B3LYP functional.

Improving description of hydrogen bonds at the semiempirical level: water-water interactions as test case

Hydrogen bonding is not well described by available semiempirical theories. This is an important restriction because hydrogen bonds represent a key feature in many chemical and biochemical processes, besides being responsible for the singular properties of water. In this study, we describe a possible solution to this problem. The basic idea is to replace the nonphysical gaussian correction functions (GCF) appearing in the core–core repulsion terms of most MNDO-based semiempirical methods by a simple function exhibiting the correct physical behavior in the whole range of intermolecular separation distances. The parameterized interaction function (PIF) is the sum of atom-pair contributions, each one having five adjustable parameters. In this work, the approach is used to study water–water interactions. The parameters are optimized to reproduce a reference ab initio intermolecular energy surface for the water–water dimer obtained at the MP2/aug-cc-pVQZ level. OO, OH, and HH parameters are reported for the PM3 method. The results of PM3-PIF calculations remarkably improve qualitatively and quantitatively those obtained at the standard PM3 level, both for water–dimer properties and for water clusters up to the hexamer. For example, the root-mean-square deviation of the PM3-PIF interaction energies, with respect to ab initio values obtained using 700 points of the water dimer surface, is only 0.47 kcal/mol. This value is much smaller than that obtained using the standard PM3 method (4.2 kcal/mol). The PM3-PIF water dimer energy minimum (−5.0 kcal/mol) is also much closer to ab initio data (−5.0±0.01 kcal/mol) than PM3 (−3.50 kcal/mol). The method is therefore promising for the development of new semiempirical approaches as well as for application of combined quantum mechanics and molecular mechanics techniques to investigate chemical processes in water. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 572–581, 2000

Stereoselectivity and Chiral Recognition in Copper(I) Olefin Complexes with a Chiral Diamine

Trigonal copper(I) complexes of the chiral bidentate ligand (1S,2S)-N,N′-Bis-(mesitylmethyl)-1,2-diphenyl-1,2-ethanediamine ((S,S)-1) have been prepared with hydrocarbon olefins, as well as with allylic alcohols and ethers. The stereochemistry of the complexes has been investigated by 1H NMR spectroscopy and by combined quantum mechanics and molecular mechanics (QM/MM) computational methods. The coordinated chiral nitrogen atoms can display equal (R, R) or opposite (R, S) configuration, the latter being disfavored if steric hindrance is present above and below the coordination plane. Although the complexes exist as rapidly equilibrated mixtures of stereoisomers, one of these is often dominant, and prochiral olefins are coordinated with high enantioface selection. In addition, the [(S,S)-1]-Cu+ fragment selectively recognizes the R enantiomer of secondary allylic alcohols and ethers, as confirmed by the X-ray crystal structure analysis of the adduct with (R)-1-buten-3-ol. The reasons for the observed selectivities have been elucidated, and lead to some implications which are consistent with the enantioselection observed in catalytic cyclopropanation reactions promoted by copper complexes of the same ligand.

Stereoselectivity and chiral recognition in copper(I) olefin complexes with a chiral diamine

Trigonal copper(I) complexes of the chiral bidentate ligand (1S,2S)-N,N'-Bis-(mesitylmethyl)-1,2-diphenyl-1,2-ethanediamine ((S,S)-1) have been prepared with hydrocarbon olefins, as well as with allylic alcohols and ethers. The stereochemistry of the complexes has been investigated by 1H NMR spectroscopy and by combined quantum mechanics and molecular mechanics (QM/MM) computational methods. The coordinated chiral nitrogen atoms can display equal (R, R) or opposite (R, S) configuration, the latter being disfavored if steric hindrance is present above and below the coordination plane. Although the complexes exist as rapidly equilibrated mixtures of stereoisomers, one of these is often dominant, and prochiral olefins are coordinated with high enantioface selection. In addition, the [(S,S)-1]-Cu+ fragment selectively recognizes the R enantiomer of secondary allylic alcohols and ethers, as confirmed by the X-ray crystal structure analysis of the adduct with (R)-1-buten-3-ol. The reasons for the observed selectivities have been elucidated, and lead to some implications which are consistent with the enantioselection observed in catalytic cyclopropanation reactions promoted by copper complexes of the same ligand.

QM/MM and SCRF studies of the ionization state of 8-methylpterin substrate bound to dihydrofolate reductase: existence of a low-barrier hydrogen bond

Using combined semiempirical quantum mechanics and molecular mechanics (QM/MM) and ab initio self-consistent reaction field (SCRF) calculations, we determined that a low-barrier hydrogen bond (LBHB) is formed when the mechanism-based substrate 8-methylpterin binds to dihydrofolate reductase (DHFR). The substrate initially was assumed bound either in the ion-pair form corresponding to N3-protonated substrate hydrogen (H) bonded to the unprotonated (carboxylate) of the conserved Glu30 residue in the active site, or in the neutral-pair form corresponding to unprotonated substrate H bonded to the neutral (carboxylic acid) form of Glu30. The free energy of interaction of these H-bonded systems with the protein/solvent surroundings was computed using a coordinate-coupled free energy perturbation (FEP) method implemented within the molecular dynamics (MD) simulation scheme and using a semiempirical (PM3) QM/MM force field. The free energy obtained from the QM/MM force-field simulations corresponds most closely with the corresponding free energy component obtained from HF/6-31G∗ SCRF calculations using a value of 2 for the dielectric constant (ϵ) for the solvated protein. Calculations were performed at levels ranging from HF/6-31G to MP2/6-31G∗ to B3LYP/6-31+G∗∗, with varying dielectric constants. The energy-minimized path for motion of the proton in the H bond along a one-dimensional reaction coordinate was calculated at HF/6-31G, HF/6-31G∗ (ϵ = 1) and B3LYP/6-31G∗ (ϵ = 2) levels. These calculations identified a second neutral-pair complex, involving the 2-amino group of substrate, which also interacts with Glu30, which is lower in energy than the ion-pair form. A harmonic vibrational analysis shows that the first vibrational state appears to lie near or above the TS connecting potential energy minima corresponding to the two neutral-pair configurations, thus indicating an LBHB. Consequently, the H-bonded system will have a significant probability of being found in the ion-pair form, in agreement with experimental spectral studies indicating an enzyme-bound cation and suggesting that the LBHB would activate substrate towards hydride-ion transfer from NADPH.

Combining quantum mechanics and interatomic potential functions inab initio studies of extended systems

The errors made when large chemical systems are replaced by small models are discussed: interrupted charge transfer, missing structure constraints, neglected long-range interactions. A combined quantum mechanics (QM)–interatomic potential function (Pot) approach is described. Characteristic features of the QM-Pot approach include: (1) periodic boundary conditions, (2) consistent definition of forces in the presence of link atoms that terminate the QM cluster, (3) interatomic potential functions parametrized on ab initio data and accounting for polarization effects, (4) use of reaction force fields (EVB potentials) in combination with QM methods for efficient localization of transition structures in large systems, (5) implementation as a loose coupling of existing QM and Pot engines. Comparison is made with some other hybrid QM/MM methods. Applications of the combined QM-Pot method for ab initio modeling of the structure and reactivity of zeolite catalysts are reviewed with both protons and transition metal cations as active species. Potential functions of the ion-pair shell-model type available for such studies are compiled. The reliability of the method is checked by comparison with periodic ab initio studies and by examining the convergence of the results with increasing size of the QM cluster. The problems tackled are: different types of Cu+ sites in the CuZSM-5 catalyst and their properties, acidity differences between active sites in different zeolite framework structures (energies of deprotonation, NH3 adsorption energies), and proton mobility in acidic zeolites. The combined QM-Pot approach made possible a full ab initio prediction of reaction rates for an elementary process on the surface of solid catalysts and of how these rates differ between different catalysts with the same active site. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1470–1493, 2000

QM and STR: The Combining of Quantum Mechanics and Relativity Theory

Combining quantum mechanics with special relativity requires (i) that a spacetime representation of quantum states be found; (ii) that such states, represented as extended along equal-time hyperplanes, be invariant when transformed from one frame to another; and (iii) that collapses of states be instantaneous in every frame. These requirements are met using branching spacetime, in which probabilities of outcomes are represented by the numerical proportions of branches on which the outcomes occur. Quantum states of systems are then identified with the probability values, built into spacetime along spacelike hypersurfaces, of all possible outcomes of all possible tests to which the systems can be subjected.

Geometry, stochastic calculus, and quantum fields in a noncommutative space–time

The algebras of nonrelativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the noncommutativity of the space–time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space–time, on quantum stochastic calculus, and on the construction of quantum fields. Some of these effects are studied in this paper.

Solvent effects on the 1(n,π∗) transition of formaldehyde in liquid water. A QM/MM study using the mean field approximation

Abstract In this Letter we propose a new method for the study of solvent effects on electron spectra that combines quantum mechanics (QM) in the description of the solute molecule and molecular mechanics (MM) in the description of the solvent. Unlike other QM/MM methods, the solvent perturbation is introduced into the solute molecular Hamiltonian in an averaged way, i.e., we use a mean field approximation. The method is implemented at the multiconfigurational self-consistent field and configuration interaction levels. Numerical results for the solvent shift of formaldehyde in liquid water are presented.

A combined quantum mechanics and molecular dynamics study of small Jahn–Teller distorted hydrocarbons: Another difficult test for density-functional theory

Temperature, vibrational, and matrix effects on the geometry and hyperfine coupling constants of the methane and ethane radical cations are investigated with a combined quantum mechanics and molecular dynamics technique. Density-functional theory (the B3LYP functional) is implemented as the quantum mechanical method. Results obtained for the methane cation are discouraging. The hyperfine coupling constants (HFCCs) obtained from the simulations are in poor agreement with experimental results. These deficiencies are ascribed to the inadequacy of density-functional theory to describe the potential energy surface in this radical. Results obtained for the ethane radical cation with the identical method are more promising. The HFCCs obtained from the simulations are in better agreement with experimental results obtained at 4 K than those obtained from static, gas-phase calculations, indicating vibrational effects are important for this radical even at low temperatures. Temperature effects on the HFCCs in the ethane radical cation observed experimentally are also well reproduced by the simulations.