Quantum Mechanical Potential Energy Surface Research Articles

A trajectory surface hopping study of the vibration-induced autodetachment dynamics of the 1-nitropropane anion

In this study, we investigate the autodetachment dynamics of the 1-nitropropane anion after vibrational excitation of the energetically lowest C–H stretching mode using our recently developed extended quantum classical surface hopping approach including the detachment continuum. Therein the detachment from an electronic bound anion state is treated as a nonadiabatic transition into discretized detachment continuum states for an ensemble of classical nuclear trajectories propagated on quantum mechanical potential energy surfaces. The initial ensemble is obtained by sampling a phase space distribution accounting for the vibrational excitation of the C–H stretching mode of the molecule to match the experimental conditions. The simulated kinetic energy distribution of the ejected electrons reproduces characteristic features of the available experimental data. Analysis of the nuclear dynamics points out that the approach to neutral-like geometries with decreased pyramidalization angle of the NO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} group and reduced the N–O bond lengths are the crucial factors enhancing the ultrafast autodetachment process in vibrationally excited 1-nitropropane. This is facilitated when the dipole-bound first excited state of the anion is populated, which is structurally similar to the neutral system. Although only a small transient population of this state is observed, it acts as an efficient doorway to the detachment continuum and is responsible for a significant amount of the ejected electrons.

Quantum-classical dynamics of vibration-induced autoionization in molecules.

We present a novel method for the simulation of the vibration-induced autoionization dynamics in molecular anions in the framework of the quantum-classical surface hopping approach. Classical trajectories starting from quantum initial conditions are propagated on a quantum-mechanical potential energy surface while allowing for autoionization through transitions into discretized continuum states. These transitions are induced by the couplings between the electronic states of the bound anionic system and the electron-detached system composed of the neutral molecule and the free electron. A discretization scheme for the detached system is introduced, and a set of formulas is derived that enable the approximate calculation of couplings between the bound and free-electron states. We demonstrate our method on the example of the anion of vinylidene, a high-energy isomer of acetylene, for which detailed experimental data are available. Our results provide information on the time scale of the autoionization process and give insight into the energetic and angular distribution of the ejected electrons, as well as the associated changes in the molecular geometry. We identify the formation of structures with reduced C-C bond lengths and T-like conformations through bending of the CH2 group with respect to the C-C axis and point out the role of autoionization as a driving process for the isomerization to acetylene.

Development of a Many-Body Force Field for Aqueous Alkali Metal and Halogen Ions: An Energy Decomposition Analysis Guided Approach.

Aqueous solutions of alkyl/alkaline metal and halide ions play a crucial functional role in biological systems such as proteins, membranes, and nucleic acids and for interfacial chemistry in geomedia and in the atmosphere. We present the MB-UCB many-body force field for monovalent and divalent ions that includes polarization, charge penetration to describe the short-range permanent electrostatics accurately, as well as a model for charge transfer to better describe the quantum mechanical potential energy surface and its components obtained from the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA). We find that the MB-UCB force field is in very good agreement with a validation suite of ion-ion and ion-water cluster data, exhibiting overall better cancellation of errors among energy components, unlike the case for other many-body potentials that do not utilize an EDA scheme. However, limitations in the functional form for the classical many-body energy components do limit the best achievable accuracy through complete cancellation of error and warrant further study.

Combining EXAFS and Computer Simulations to Refine the Structural Description of Actinyls in Water.

EXAFS spectroscopy is one of the most used techniques to solve the structure of actinoid solutions. In this work a systematic analysis of the EXAFS spectra of four actinyl cations, [UO2]2+, [NpO2]2+, [NpO2]+ and [PuO2]2+ has been carried out by comparing experimental results with theoretical spectra. These were obtained by averaging individual contributions from snapshots taken from classical Molecular Dynamics simulations which employed a recently developed [AnO2]2+/+ –H2O force field based on the hydrated ion model using a quantum-mechanical (B3LYP) potential energy surface. Analysis of the complex EXAFS signal shows that both An-O and An-O single scattering paths as well as multiple scattering ones involving [AnO2]+/2+ molecular cation and first-shell water molecules are mixed up all together to produce a very complex signal. Simulated EXAFS from the B3LYP force field are in reasonable agreement for some of the cases studied, although the k= 6–8 Å region is hard to be reproduced theoretically. Except uranyl, all studied actinyls are open-shell electron configurations, therefore it has been investigated how simulated EXAFS spectra are affected by minute changes of An-O bond distances produced by the inclusion of static and dynamic electron correlation in the quantum mechanical calculations. A [NpO2]+−H2O force field based on a NEVPT2 potential energy surface has been developed. The small structural changes incorporated by the electron correlation on the actinyl aqua ion geometry, typically smaller than 0.07 Å, leads to improve the simulated spectrum with respect to that obtained from the B3LYP force field. For the other open-shell actinyls, [NpO2]2+ and [PuO2]2+, a simplified strategy has been adopted to improve the simulated EXAFS spectrum. It is computed taking as reference structure the NEVPT2 optimized geometry and including the DW factors of their corresponding MD simulations employing the B3LYP force field. A better agreement between the experimental and the simulated EXAFS spectra is found, confirming the a priori guess that the inclusion of dynamic and static correlation refine the structural description of the open-shell actinyl aqua ions.

A machine learning based intramolecular potential for a flexible organic molecule.

Quantum mechanical predictive modelling in chemistry and biology is often hindered by the long time scales and large system sizes required of the computational model. Here, we employ the kernel regression machine learning technique to construct an analytical potential, using the Gaussian Approximation Potential software and framework, that reproduces the quantum mechanical potential energy surface of a small, flexible, drug-like molecule, 3-(benzyloxy)pyridin-2-amine. Challenges linked to the high dimensionality of the configurational space of the molecule are overcome by developing an iterative training protocol and employing a representation that separates short and long range interactions. The analytical model is connected to the MCPRO simulation software, which allows us to perform Monte Carlo simulations of the small molecule bound to two proteins, p38 MAP kinase and leukotriene A4 hydrolase, as well as in water. We demonstrate that our machine learning based intramolecular model is transferable to the condensed phase, and demonstrate that the use of a faithful representation of the quantum mechanical potential energy surface can result in corrections to absolute protein-ligand binding free energies of up to 2 kcal mol-1 in the example studied here.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Improving the Force Field Description of Tyrosine-Choline Cation-π Interactions: QM Investigation of Phenol-N(Me)4+ Interactions.

Cation-π interactions between tyrosine amino acids and compounds containing N,N,N-trimethylethanolammonium (N(CH3)3) are involved in the recognition of histone tails by chromodomains and in the recognition of phosphatidylcholine (PC) phospholipids by membrane-binding proteins. Yet, the lack of explicit polarization or charge transfer effects in molecular mechanics force fields raises questions about the reliability of the representation of these interactions in biomolecular simulations. Here, we investigate the nature of phenol-tetramethylammonium (TMA) interactions using quantum mechanical (QM) calculations, which we also use to evaluate the accuracy of the additive CHARMM36 and Drude polarizable force fields in modeling tyrosine-choline interactions. We show that the potential energy surface (PES) obtained using SAPT2+/aug-cc-pVDZ compares well with the large basis-set CCSD(T) PES when TMA approaches the phenol ring perpendicularly. Furthermore, the SAPT energy decomposition reveals comparable contributions from electrostatics and dispersion in phenol-TMA interactions. We then compared the SAPT2+/aug-cc-pVDZ PES obtained along various approach directions to the corresponding PES obtained with CHARMM, and we show that the force field accurately reproduces the minimum distances while the interaction energies are underestimated. The use of the Drude polarizable force field significantly improves the interaction energies but decreases the agreement on distances at energy minima. The best agreement between force field and QM PES is obtained by modifying the Lennard-Jones terms for atom pairs involved in the phenol-TMA cation-π interactions. This is further shown to improve the correlation between the occupancy of tyrosine-choline cation-π interactions obtained from molecular dynamics simulations of a bilayer-bound bacterial phospholipase and experimental affinity data of the wild-type protein and selected mutants.

MERGED-BEAMS REACTION STUDIES OF O +

ABSTRACT We have measured the reaction of O + H 3 + ?> forming OH+ and H 2 O + . ?> This is believed to be one of the key gas-phase astrochemical processes initiating the formation of water molecules in dense molecular clouds. For this work, we have used a novel merged fast-beams apparatus that overlaps a beam of H 3 + ?> onto a beam of ground-term neutral O. Here, we present cross-section data for forming OH+ and H 2 O + ?> at relative energies from ≈3.5 meV to ≈15.5 and 0.13 eV, respectively. Measurements were performed for statistically populated O ( 3 P J ) ?> in the ground term reacting with hot H 3 + ?> (with an internal temperature of ∼2500–3000 K). From these data, we have derived rate coefficients for translational temperatures from ≈27 K to ∼105 K for the formation of OH+ and ∼103 K for the formation of H2O+. In order to convert these results to a thermal rate coefficient suitable for astrochemistry, we have added the results together for both exit channels and scaled the summed data on statistically populated oxygen to thermally populated oxygen. For this we have used theory as a guide, thereby accounting for the temperature dependence of the O fine-structure levels. Our results are in good agreement with two independent flowing afterglow measurements at a temperature of ≈300 K, and with a corresponding level of H 3 + ?> internal excitation. This good agreement suggests that the internal excitation of the H 3 + ?> does not play a significant role in this reaction. The Langevin rate coefficient is in reasonable agreement with the experimental results at 10 K but a factor of ∼2 larger at 300 K. The two published classical trajectory studies using quantum-mechanical potential energy surfaces lie a factor of ∼1.5 above our experimental results over this 10–300 K range.

Towards a Polarizable Force Field for RNA based on the Classical Drude Oscillator

RNA plays many important roles in the cell, including information transfer, gene regulation, protein synthesis, and catalysis. This diversity in function arises in part from the adoption of complex tertiary structures and interconversion between multiple conformational states in response to bound metabolites or changes in other cellular conditions. Modeling RNA with atomistic resolution using molecular dynamics (MD) simulations requires a high-quality empirical force field that can adequately describe the properties of both canonical and non-canonical structures and is sensitive to environmental conditions. To this end, we are developing a force field for RNA that includes the explicit treatment of electronic polarization using the classical Drude Oscillator model. Optimization is focused on the RNA 2′-hydroxyl group and the phosphodiester backbone targeting 2-D quantum mechanical (QM) potential energy and dipole moment surfaces in combination with condensed phase MD simulations of both canonical and non-canonical RNA structures. Parameter validation involves conducting MD simulations of various RNAs not included in the training set.

Fitting of dihedral terms in classical force fields as an analytic linear least-squares problem.

The derivation and optimization of most energy terms in modern force fields are aided by automated computational tools. It is therefore important to have algorithms to rapidly and precisely train large numbers of interconnected parameters to allow investigators to make better decisions about the content of molecular models. In particular, the traditional approach to deriving dihedral parameters has been a least-squares fit to target conformational energies through variational optimization strategies. We present a computational approach for simultaneously fitting force field dihedral amplitudes and phase constants which is analytic within the scope of the data set. This approach completes the optimal molecular mechanics representation of a quantum mechanical potential energy surface in a single linear least-squares fit by recasting the dihedral potential into a linear function in the parameters. We compare the resulting method to a genetic algorithm in terms of computational time and quality of fit for two simple molecules. As suggested in previous studies, arbitrary dihedral phases are only necessary when modeling chiral molecules, which include more than half of drugs currently in use, so we also examined a dihedral parametrization case for the drug amoxicillin and one of its stereoisomers where the target dihedral includes a chiral center. Asymmetric dihedral phases are needed in these types of cases to properly represent the quantum mechanical energy surface and to differentiate between stereoisomers about the chiral center.

Intrinsic energy landscapes of amino acid side-chains.

Amino acid side-chain conformational properties influence the overall structural and dynamic properties of proteins and, therefore, their biological functions. In this study, quantum mechanical (QM) potential energy surfaces for the rotation of side-chain χ(1) and χ(2) torsions in dipeptides in the alphaR, beta, and alphaL backbone conformations were calculated. The QM energy surfaces provide a broad view of the intrinsic conformational properties of each amino acid side-chain. The extent to which intrinsic energetics dictates side-chain orientation was studied through comparisons of the QM energy surfaces with χ(1) and χ(2) free energy surfaces from probability distributions obtained from a survey of high resolution crystal structures. In general, the survey probability maxima are centered in minima of the QM surfaces as expected for sp(3) (or sp(2) for χ(2) of Asn, Phe, Trp, and Tyr) atom centers with strong variations between amino acids occurring in the energies of the minima indicating intrinsic differences in rotamer preferences. High correlations between the QM and survey data were found for hydrophobic side-chains except Met, suggesting minimal influence of the protein and solution environments on their conformational distributions. Conversely, low correlations for polar or charged side-chains indicate a dominant role of the environment in stabilizing conformations that are not intrinsically favored. Data also link the presence of off-rotamers in His and Trp to favorable interactions with the backbone. Results also suggest that the intrinsic energetics of the side-chains of Phe and Tyr may play important roles in protein folding and stability. Analyses on whether intrinsic side-chain energetics can influence backbone preference identified a strong correlation for residues in the alphaL backbone conformation. It is suggested that this correlation reflects the intrinsic instability of the alphaL backbone such that assumption of this backbone conformation is facilitated by intrinsically favorable side-chain conformations. Together our results offer a broad overview of the conformational properties of amino acid side-chains and the QM data may be used as target data for force field optimization.

Reactive force field simulation of proton diffusion inBaZrO3 using an empirical valence bond approach

A new reactive force field to describe proton diffusion within the solid oxide fuel cell materialBaZrO3 has been derived. Using a quantum mechanical potential energy surface, the parameters of aninteratomic potential model to describe hydroxyl groups within both pure and yttrium-dopedBaZrO3 have been determined. Reactivity is then incorporated through the use of the empiricalvalence bond model. Molecular dynamics simulations (EVB-MD) have been performed toexplore the diffusion of hydrogen using a stochastic thermostat and barostatwhose equations are extended to the isostress–isothermal ensemble. In the lowconcentration limit, the presence of yttrium is found not to significantly influence thediffusivity of hydrogen, despite the proton having a longer residence time at oxygenadjacent to the dopant. This lack of influence is due to the fact that trappingoccurs infrequently, even when the proton diffuses through octahedra adjacent tothe dopant. The activation energy for diffusion is found to be 0.42 eV, in goodagreement with experimental values, though the prefactor is slightly underestimated.

On the Solvation of the Zn2+ Ion in Methanol: A Combined Quantum Mechanics, Molecular Dynamics, and EXAFS Approach

The solvation properties of the Zn(2+) ion in methanol solution have been investigated using a combined approach based on molecular dynamics (MD) simulations and extended X-ray absorption fine structure (EXAFS) experimental results. The quantum mechanical potential energy surface for the interaction of the Zn(2+) ion with a methanol molecule has been calculated taking into account the effect of bulk solvent by the polarizable continuum model (PCM). The effective Zn-methanol interactions have been fitted by suitable analytical potentials, and have been utilized in the MD simulation to obtain the structural properties of the solution. The reliability of the whole procedure has been assessed by comparing the theoretical structural results with the EXAFS experimental data. The structural parameters of the first solvation shells issuing from the MD simulations provide an effective complement to the EXAFS experiments.

ForceFit: A code to fit classical force fields to quantum mechanical potential energy surfaces

The ForceFit program package has been developed for fitting classical force field parameters based upon a force matching algorithm to quantum mechanical gradients of configurations that span the potential energy surface of the system. The program, which runs under UNIX and is written in C++, is an easy-to-use, nonproprietary platform that enables gradient fitting of a wide variety of functional force field forms to quantum mechanical information obtained from an array of common electronic structure codes. All aspects of the fitting process are run from a graphical user interface, from the parsing of quantum mechanical data, assembling of a potential energy surface database, setting the force field, and variables to be optimized, choosing a molecular mechanics code for comparison to the reference data, and finally, the initiation of a least squares minimization algorithm. Furthermore, the code is based on a modular templated code design that enables the facile addition of new functionality to the program.

Models of S/π interactions in protein structures: Comparison of the H2S–benzene complex with PDB data

S/pi interactions are prevalent in biochemistry and play an important role in protein folding and stabilization. Geometries of cysteine/aromatic interactions found in crystal structures from the Brookhaven Protein Data Bank (PDB) are analyzed and compared with the equilibrium configurations predicted by high-level quantum mechanical results for the H(2)S-benzene complex. A correlation is observed between the energetically favorable configurations on the quantum mechanical potential energy surface of the H(2)S-benzene model and the cysteine/aromatic configurations most frequently found in crystal structures of the PDB. In contrast to some previous PDB analyses, configurations with the sulfur over the aromatic ring are found to be the most important. Our results suggest that accurate quantum computations on models of noncovalent interactions may be helpful in understanding the structures of proteins and other complex systems.

SASS: A symmetry adapted stochastic search algorithm exploiting site symmetry

A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.

Monte Carlo Simulation of Cisplatin Molecule in Aqueous Solution

The Lennard-Jones (12-6) parameters were obtained for all atoms of cisplatin molecule using the ab initio quantum mechanical potential energy surface for the water-cisplatin interaction as reference data. The parameters found were (epsilon/kcal.mol(-1) and sigma/angstroms) 1.0550, 3.6590 (Pt); 0.0381, 4.6272 (Cl); 0.0455, 3.3783 (N); and 0.0185, 0.0936 (H) and provided very good results for the description of the aqueous solution of cisplatin through Monte Carlo simulation. From statistical analysis of solute-solvent interactions, we observed that the NH3 groups are involved in 53% of the calculated hydrogen bonds with a significant contribution from chlorides (41%) and only 6% involving the Pt center. This is in agreement with the expected behavior for such molecules. Two hydration shells with 22 and 81 water molecules, respectively, centered around 4.6 and 7.3 angstroms were found from the center of mass pair correlation function analysis. The cisplatin atomic Lennard-Jones parameters are reported for the first time, and they might be useful for studying the structure, properties, and processes of cisplatin-like molecules in aqueous solution, including explicitly the solvent effect.

Growing multiconfigurational potential energy surfaces with applications to X+H2 (X=C,N,O) reactions

A previously developed method, based on a Shepard interpolation procedure to automatically construct a quantum mechanical potential energy surface (PES), is extended to the construction of multiple potential energy surfaces using multiconfigurational wave functions. These calculations are accomplished with the interface of the PES-building program, GROW, and the GAMESS suite of electronic structure programs. The efficient computation of multiconfigurational self-consistent field surfaces is illustrated with the C + H2, N + H2, and O + H2 reactions.

New force field for calcium binding sites in annexin–membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.

On the halide hydration study: Development of first-principles halide ion-water interaction potential based on a polarizable model

The development of first-principles halide-water interaction potentials for fluoride and iodide anions is presented. The model adopted is the mobile charge densities in harmonic oscillator that allows for a flexible and polarizable character of the interacting particles. The set of points of the quantum mechanical potential energy surfaces are calculated up to the MP2 level. The nonadditive many-body contributions were included explicitly at the three-body terms. Structural and energetic properties of the [X(H2O)n]− clusters (n=1–6) are studied with the new interaction potentials developed. Halide aqueous solutions are also studied by means of Monte Carlo simulations. The agreement between experimental and our predicted estimations shows the good behavior of the proposed potentials. The developed potentials are able to properly describe both the microsolvation of clusters in gas phase and their hydration in aqueous solutions. The different nature of the interactions among F−, Br−, I− and water appears in the set of studied properties, thus giving a gradual change in the behavior along the group.