A new expression for the direct quantum mechanical evaluation of the thermal rate constant

Based on the formalism of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889(1983)], we derive a new expression for the thermal rate constant for a chemical reaction. The expression involves an unperturbed, i.e., reactant or product channel Boltzmann operator for the imaginary time propagation, making it possible to compute efficiently the rate constant for a range of temperatures. We illustrate numerical aspects with an extensive study of the one-dimensional Eckart barrier problem, as well as a study of the three-dimensional (J = 0) D + H2 problem.     

Ground-state properties of the retinal molecule: from quantum mechanical to classical mechanical computations of retinal proteins

Retinal proteins are excellent systems for understanding essential physiological processes such as signal transduction and ion pumping. Although the conjugated polyene system of the retinal chromophore is best described with quantum mechanics, simulations of the long-timescale dynamics of a retinal protein in its physiological, flexible, lipid-membrane environment can only be performed at the classical mechanical level. Torsional energy barriers are a critical ingredient of the classical force-field parameters. Here we review briefly current retinal force fields and discuss new quantum mechanical computations to assess how the retinal Schiff base model and the approach used to derive the force-field parameters may influence the torsional potentials.     

Scaled quantum mechanical force field for glycine in basic solution

We obtain scale factors for three glycinate-nH₂O ab initio force fields, using the 4–31G basis set, that can be used in building a scaled quantum mechanical force field for alanine and, subsequently, for peptides in aqueous solutions. Force constants from the fully optimized glycinate-nH₂O supermolecules were scaled by using experimentally determined vibrational frequencies of glycine in water at pH 13. Similar calculations were performed for methylamine and acetate. Scale factors for the stretching modes of acetate are within 2% of the related scale factors for glycinate. The scale factor for the NH₂ scissor mode in methylamine is also in agreement with that of glycinate. Changes in the scale factors as a function of the number of hydrating water molecules were also similar between glycinate and acetate. Amine groups showed relatively small changes. Scale factors for glycinate with no hydrating molecules were extrapolated from the supermolecule results, since the optimized structure of isolated glycinate obtained with the 4–31G basis set yielded one imaginary frequency. Good agreements between calculated and experimental frequencies for glycinate, acetate, and methyl amine were obtained for each set of scale factors. Scaling appears to compensate for the systematic effects of hydration on force constants, making it possible to obtain reliable frequency predictions for amino acids in water without resorting to expensive super-molecule calculations.     

Interpretation of the vibrational spectra of matrix-isolated uracil from scaled ab initio quantum mechanical force fields

The vibrational spectrum of uracil trapped in an argon matrix has been interpreted based on ab initio Hartree–Fock SCF calculations with a split-valence 4?21 basis set. The directly computed theoretical general valence force field was scaled with empirical scale factors in order to correct for the systematic errors originating in the limitation of the theoretical model. Scale factors transferred from related molecules provided a priori prediction of fundamental frequencies and intensities, permitting several corrections to be proposed for earlier assignments. Using the observed spectrum with the few altered assignments, a new set of scale factors was optimized to give the best force field available from combined consideration of the experimental and the theoretical data. For unknown reasons, the out-of-plane force field predicted a spectrum agreeing slightly less well with experiment than did the in-plane force field. However, the overall agreement between theory and experiment provided additional support for the assumptions involved in the method. The computed force fields were compared with others available from previous work. The comparison demonstrated the importance of expanding the energy surface around the true energy minimum and of using a proper scaling procedure. Previous scaled CNDO /2 calculations were found to be surprisingly good despite the large corrections required and the fact that they were made at an incorrect geometry.     

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.     

Extension of the density functional derived scaled quantum mechanical force field procedure

The density functional derived scaled quantum mechanical (SQM) force field method of Rauhut and Pulay [J. Phys. Chem. 99 (1995) 3093] has been extended. The original procedure (employing B3-LYP/6-31G* computations and 11 transferable scale factors for the different kinds of internal coordinates) was capable to reproduce the vibrational fundamentals of 31 simple organic (H, C, N, O) molecules with a total mean deviation of about 13 cm(-1). The present Density Functional Theory based SQM force field method is an extension of the original one: with the help of 20 transferable scale factors can reproduce the fundamentals of 20 inorganic, organic and organosilicon molecules containing nonmetallic first and second-row atoms with a total mean deviation of 10.8 cm(-1). The transferability and reliability of the new set of scale factors are demonstrated on the examples of the a priori SQM vibrational spectra of cis and gauche-cyclopropylchlorosilane.     

The effect of a mechanical force on quantum reaction rate: quantum Bell formula

The purpose of this note is to derive a quantum-mechanical analog of Bell's formula, which describes the sensitivity of a chemical reaction to a mechanical pulling force. According to this formula, the reaction rate depends exponentially on the force f, i.e., k(f) ~ exp(f/f(c)), where the force scale f(c) is estimated as the thermal energy k(B)T divided by a distance a between the reactant and transition states along the pulling coordinate. Here I use instanton theory to show that, at low temperatures where quantum tunneling is dominant, this force scale becomes f(c) ~ ?ω/a (in the limit where frictional damping is absent) or f(c) ~ ?τ(-1)/a (in the strong damping limit). Here ω is a characteristic vibration frequency along the pulling coordinate and τ is a characteristic relaxation time in the reactant state. That is, unlike the classical case where f(c) is unaffected by dissipation, this force scale becomes friction dependent in the quantum limit. I further derive higher-order corrections in the force dependence of the rate, describe generalizations to many degrees of freedom, and discuss connection to other quantum rate theories.     

Ab initio protein structure prediction with force field parameters derived from water-phase quantum chemical calculation

Molecular dynamics (MD) simulations are extensively used in the study of the structures and functions of proteins. Ab initio protein structure prediction is one of the most important subjects in computational biology, and many trials have been performed using MD simulation so far. Since the results of MD simulations largely depend on the force field, reliable force field parameters are indispensable for the success of MD simulation. In this work, we have modified atom charges in a standard force field on the basis of water-phase quantum chemical calculations. The modified force field turned out appropriate for ab initio protein structure prediction by the MD simulation with the generalized Born method. Detailed analysis was performed in terms of the conformational stability of amino acid residues, the stability of secondary structure of proteins, and the accuracy for prediction of protein tertiary structure, comparing the modified force field with a standard one. The energy balance between alpha-helix and beta-sheet structures was significantly improved by the modification of charge parameters.     

Scaled quantum mechanical (SQM) force field and theoretical vibrational spectrum for benzonitrile

The complete harmonic force field of benzonitrile has been determined by ab initio Hartree—Fock calculations using a 4–21 Gaussian basis set. As force constants are systematically over-estimated at this level, the directly calculated force field was scaled by empirical factors previously optimized for benzene and HCN. Frequencies calculated from this scaled quantum mechanical (SQM) force field confirm the published experimental assignments for benzonitrile, benzonitrile-p-d and benzonitrile-d₅. Aside from the CH (and CD) stretching frequencies, which are strongly affected by anharmonicity, the mean deviation between the observed and calculated frequencies is below 9 cm⁻¹ for each isotopomer. Theoretical i.r. intensities reproduce the main features of the spectra semiquantitatively.     

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. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001     

A new exact quantum mechanical rovibrational kinetic energy operator for penta-atomic systems in internal coordinates

The concrete molecule-fixed (MF) kinetic energy operator for penta-atomic molecules is expressed in terms of the parameterδ, the matrix element G_(?), and angular momentum operator (?). The applications of the operator are also discussed. Finally, a general compact form of kinetic energy operator suitable for calculating the rovibrational spectra of polyatomie molecules is presented.     

Non self-consistent field theory — A new approach in quantum mechanical calculations

An R ^o-independent electronic repulsion matrix is constructed, replacing the R ^o-dependent Hamiltonian matrix (R ^o is the density matrix). A non-SCF theory is developed to solve the eigenequation without using an iterative procedure. Three methods are proposed to solve for the eigenvectors and eigenvalues. Illustrative calculations are reported comparing the non-SCF and SCF theories. The calculated results are as expected: the ground state energies are nearly unchanged while the orbital energies are nearer to the experimental results. Other physical properties and spectral quantities are also compared. It is found that the ZDO assumption is applicable in the non-SCF theory if it is applicable in SCF theory.

---

Zusammenfassung Eine R ^o-unabhängige Elektronenabstoßungsmatrix wird eingeführt, die die R ^o-abhängige Hamiltonmatrix ersetzt (R ^o ist die Dichtematrix). Zur Lösung der Eigenwertgleichung ohne iterative Prozeduren wird eine sog. Nicht-SCF-Theorie aufgestellt. An Beispielen werden die Ergebnisse von SCF- und Nicht-SCF-Rechnungen verglichen; dabei erweisen sich die Energien des Grundzustandes als nahezu unverändert, während die Energien der Orbitale näher bei den experimentellen Werten liegen. Die zero-differential-overlap-Näherung ist immer dann in der neuen Theorie anwendbar, wenn sie in der SCF-Theorie anwendbar ist.

---

Résumé Une matrice de répulsion électronique indépendante de R ^o est construite, remplaçant la matrice hamiltonienne dépendant de R ^o (R ^o matrice de densité). Une théorie non SCF est développée afin de résoudre l'équation aux valeurs propres sans itérations. Trois méthodes de résolution du problème aux valeurs propres sont proposées. Des calculs illustrent la comparaison entre les théories SCF et non SCF. Les résultats des calculs sont comme prévus: l'énergie de l'état fondamental varie peu alors que les énergies orbitales sont plus proches des résultats expérimentaux. D'autres propriétés physiques ainsi que des grandeurs spectrales sont comparées. On trouve que l'approximation du recouvrement différentiel nul est applicable dans la théorie non SCF si elle est applicable dans la théorie SCF.

     

A new evaluation technique for analyzing the thermoluminescence glow curve and calculating the trap parameters

A step-fitting simulation technique was developed for the thermoluminescence (TL) glow-curve analysis and the kinetic trap parameters determination. These parameters include the order of kinetics b, the activation energy E (eV) and the pre-exponential factor S″ (s⁻¹). A general equation was developed to estimate the order of kinetics b. The characteristics point of this equation is that any set of three data points in a TL glow curve can yield the kinetics order. Using this characteristic, an improved procedure was suggested to separate a composite glow curve, which includes several overlapping peaks, into its individual components and to obtain the trap parameters of the glow peaks. The program was used to analyze the TL glow curve of the UV dosimetric material pure zirconium oxide (ZrO₂).     

A transferable active-learning strategy for reactive molecular force fields

Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels–Alder reaction in the gas phase and non-equilibrium dynamics (a model S_N2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems.

An efficient strategy for training Gaussian Approximation Potential (GAP) models to study chemical reactions using hierarchical and active learning.     

Theoretical prediction of vibrational spectra. Scaled quantum mechanical (SQM) force field for fluorobenzene

The complete harmonic force field of fluorobenzene has been determined from ab initio Hartree-Fock calculations using the 4–21 Gaussian basis set. As force constants are systematically overestimated at this level of theory, the directly calculated force field was scaled by empirical factors taken over from benzene and methylfluoride. Except for a slight overestimation of the CF stretching frequency, the scaled quantum mechanical (SQM) force field obtained in this way reproduces the experimental fundamental frequencies of the parent molecule and two deuterated isotopomers within 20 cm⁻¹ (with mean deviations below 12 cm⁻¹), and experimental assignments are analyzed on this basis. Theoretical i.r. intensities reproduce the main features of the spectra fairly well.