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Atomic properties of amino acids: computed atom types as a guide for future force-field design.

The quantum chemical topology (QCT) is able to propose atom types by direct computation rather than by chemical intuition. In previous work, molecular electron densities of 20 amino acids and smaller derived molecules were partitioned into a set of 760 topological atoms. Each atom was characterised by seven atomic properties and subjected to cluster analysis element by element, that is, C, H, O, N, and S. From the respective dendrograms, 21 carbon atom types were distinguished, 7 hydrogen, 2 nitrogen, 6 oxygen, and 6 sulfur atom types. Herein, we contrast the QCT atom types with those of the assisted model building with energy refinement (AMBER) force field. We conclude that in spite of fair agreement between QCT and AMBER atom types, the latter are sometimes underdifferentiated and sometimes overdifferentiated. In summary, we suggest that QCT is a useful guide in designing new force fields or improving existing ones. The computational origin of QCT atom types makes their determination unbiased compared to atom type determination by chemical intuition and a priori assumptions. We provide a list of specific recommendations.

Algorithms↗

Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions.

Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a large amount of computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. This work presents major progress toward the evaluation of ab initio QM/MM free-energy surfaces and activation free energies of reactions in enzymes and in solutions. This is done by exploiting our previous idea of using the empirical valence bond (EVB) method as a reference potential and then using the linear response approximation (LRA) approach to evaluate the free energies of transfer from the EVB to the QM/MM surfaces in the reactant and product state. However, the new crucial step involves the use of a constraint at the transition state that fixes the system at a given value of the reaction coordinate and allows us to use the LRA at the transition state. The advance offered by the present approach is particularly significant because it evaluates the free energy associated with both the substrate and the solvent motions. This evaluation appeared to be a relatively simple task once one uses a classical reference potential. The main problem has been using the reference potential for the evaluation of the free-energy contributions associated with the solute motions where the difference between the reference EVB potential and the QM/MM potential can be large. The present refinement finally allows us to overcome the problems with the solute fluctuations and therefore to obtain, for the first time, a free-energy barrier that reflects the solute entropy properly. Thus, we present a way to evaluate the complete QM/MM activation free energy with an equal footing treatment of the solute and the solvent. This provides a general consistent and effective strategy for evaluating the QM/MM activation free energies in proteins and in solution. Our advance allows one to explore consistently various mechanistic and catalytic proposals while using ab initio (ai) QM/MM approaches.

Computer Simulation↗

Comparative investigation on non-IPR C68 and IPR C78 fullerenes encaging Sc3N molecules.

A computational study on the experimentally detected Sc(3)N@C(68) cluster is reported, involving quantum chemical analysis at the B3LYP/6-31G level. Extensive computations were carried out on the pure C(68) cage which does not conform with the isolated pentagon rule (IPR). The two maximally stable C(68) isomers were selected as initial Sc(3)N@C(68) cage structures. Full geometry optimization leads to a confirmation of an earlier assessment of the Sc(3)N@C(68) equilibrium geometry (Nature 2000, 408, 427), namely an eclipsed arrangement of Sc(3)N in the C(68) 6140 frame, where each Sc atom interacts with one pentagon pair. From a variety of theoretical procedures, a D(3h) structure is proposed for the free Sc(3)N molecule. Encapsulated into the C(68) enclosure, this unit is strongly stabilized with respect to rotation within the cage. The complexation energy of Sc(3)N@C(68) cage is found to be in the order of that determined for Sc(3)N@C(80) and exceeding the complexation energy of Sc(3)N@C(78). The cage-core interaction is investigated in terms of electron transfer from the encapsulated trimetallic cluster to the fullerene as well as hybridization between these two subsystems. The stabilization mechanism of Sc(3)N@C(68) is seen to be analogous to that operative in Sc(3)N@C(78). For both cages, C(68) and C(78), inclusion of Sc(3)N induces aromaticity of the cluster as a whole.

Fullerenes↗

A quantum chemical approach to the free energy calculations in condensed systems: the QM/MM method combined with the theory of energy representation.

A methodology has been proposed to compute the solvation free energy of a molecule described quantum chemically by means of quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER). The present approximate approach is quite simple to implement and requires much less computational cost as compared with the free energy perturbation or thermodynamic integration. Furthermore, the electron distribution can be treated faithfully as a quantum chemical object, and it is no longer needed to employ the artificial interaction site model, a reduced form of the realistic electron distribution, which is commonly used in the conventional solution theory. The point of the present approach is to employ the QM solute with electron density fixed at its average distribution in order to make the solute-solvent interaction pairwise. Then, the solvation free energy can be computed within the standard framework of the energy representation. The remaining minor contribution originating from the many-body effect inherent in the quantum mechanical description can be evaluated separately within a similar framework if necessary. As a test calculation, the method has been applied to a QM water solute solvated by MM water solvent in ambient and supercritical states. The results of the QM/MM-ER simulations have been in excellent agreement with the experimental values.

Journal Article↗

Quantum dissipation in unbounded systems.

In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie--Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this paper, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.

Journal Article↗

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

Journal Article↗

Anderson transition in a multiply-twisted helix.

We investigated the Anderson transition in a multiply-twisted helix in which a helical chain of components, i.e., atoms or nanoclusters, is twisted to produce a doubly-twisted helix, which itself can be twisted to produce a triply-twisted helix, and so on, in which there are couplings between adjacent rounds of helices. As the strength of the on-site random potentials increases, an Anderson transition occurs, suggesting that the number of dimensions is 3 for electrons running along the multiply-twisted helix when the couplings between adjacent rounds are strong enough. If the couplings are weakened, the dimensionality becomes less, resulting in localization of electrons. The effect of random connections between adjacent rounds of helices and random magnetic fields that thread the structure is analyzed using the spectral statistics of a quantum particle.

Computer Simulation↗

On possible pitfalls in ab initio quantum mechanics/molecular mechanics minimization approaches for studies of enzymatic reactions.

Reliable studies of enzymatic reactions by combined quantum mechanics/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a very large computer time for the evaluation of the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. A seemingly reasonable alternative is to perform energy minimization studies of the type used in gas-phase ab initio studies. However, it is hard to see why such an approach should give reliable results in protein active sites. To examine the problems with energy minimization QM/MM approaches, we chose the hypothetical reaction of a metaphosphate ion with water in the Ras.GAP complex. This hypothetical reaction served as a simple benchmark reaction. The possible problems with the QM/MM minimization were explored by generating several protein configurations from long MD simulations and using energy minimization and scanning of the reaction coordinates to evaluate the corresponding potential energy surfaces of the reaction for each of these different protein configurations. Comparing these potential energy surfaces, we found major variations of the corresponding minima. Furthermore, the reaction energies and activation energies also varied significantly even for similar protein configurations. The specific coordination of a magnesium ion, present in the active center of the protein complex, turned out to influence the energetics of the reaction in a major way, where a direct coordination to the reactant leads to an increase of the activation energy by 17 kcal/mol. Apparently, using energy minimization to generate potential surfaces for an enzymatic reaction, while starting from a single protein structure, could lead to major errors in calculations of activation free energies and binding free energies. Thus we believe that extensive samplings of the configurational space of the protein are essential for meaningful determination of the energetics of enzymatic reactions. The possible relevance of our conclusion with regard to a recent study of the RasGAP reaction is discussed.

Computational Biology↗

Interplay of stereoelectronic and enviromental effects in tuning the structural and magnetic properties of a prototypical spin probe: further insights from a first principle dynamical approach.

The nitrogen isotropic hyperfine coupling constant (hcc) and the g tensor of a prototypical spin probe (di-tert-butyl nitroxide, DTBN) in aqueous solution have been investigated by means of an integrated computational approach including Car-Parrinello molecular dynamics and quantum mechanical calculations involving a discrete-continuum embedding. The quantitative agreement between computed and experimental parameters fully validates our integrated approach. Decoupling of the structural, dynamical, and environmental contributions acting onto the spectral observables allows an unbiased judgment of the role played by different effects in determining the overall experimental observables and highlights the importance of finite-temperature vibrational averaging. Together with their intrinsic interest, our results pave the route toward more reliable interpretations of EPR parameters of complex systems of biological and technological relevance.

Journal Article↗

Assigning powders to crystal structures by high-resolution (1)H-(1)H double quantum and (1)H-(13)C J-INEPT solid-state NMR spectroscopy and first principles computation. A case study of penicillin G.

We show how powder samples at natural isotopic abundance can be assigned to crystal structures by using high-resolution proton and carbon-13 solid-state NMR spectra in combination with first principles calculations. Homonuclear proton double-quantum spectra in combination with through-bond proton-carbon HSQC spectra are used to assign the NMR spectra. We then show that the proton chemical shifts can be included in the process of assigning the spectra to a crystal structure using first principles calculations. The method is demonstrated on the K salt of penicillin G.

Algorithms↗

Quantum theory of dissociative chemisorption on metal surfaces.

Recent theoretical progress in gas-surface reaction dynamics, a field relevant to heterogeneous catalysis, is described. One of the most fundamental reactions, the dissociative chemisorption of H2 on metal surfaces, can now be treated accurately using quantum mechanics. Density functional theory is used to compute the molecule-surface interaction, and the motion of the hydrogen atoms is simulated using quantum dynamics, modeling all six molecular degrees of freedom. Theory is in good quantitative agreement with molecular beam experiments, offering useful interpretations, and allowing reliable predictions. The success of the approach calls for extensions to larger systems, such as dissociative chemisorption of polyatomic molecules.

Journal Article↗

Interplay of intrinsic and environmental effects on the magnetic properties of free radicals issuing from H-atom addition to cytosine.

Possible radical reaction products issuing from H-atom addition to cytosine have been characterized and analyzed by means of a comprehensive quantum mechanical approach including density functional computations (B3LYP), together with simulation of the solvent by the polarizable continuum model (PCM), and averaging of spectroscopic properties over the most important vibrational motions. The hyperfine couplings of the semirigid 5,6-dihydrocytos-6yl radical computed at the optimized geometry are in good agreement with their experimental counterparts. On the other hand, vibrational averaging is mandatory for obtaining an effectively planar structure for the 5,6-dihydrocytos-5yl radical with the consequent equivalence of beta-hydrogens. Finally, only proper consideration of environmental effects restores the agreement between computed and experimental couplings for the base anion protonated at N3.

Cytosine↗

Performance characteristics of a Kodak computed radiography system.

The performance characteristics of a photostimulable phosphor based computed radiographic (CR) system were studied. The modulation transfer function (MTF), noise power spectra (NPS), and detective quantum efficiency (DQE) of the Kodak Digital Science computed radiography (CR) system (Eastman Kodak Co.-model 400) were measured and compared to previously published results of a Fuji based CR system (Philips Medical Systems-PCR model 7000). To maximize comparability, the same measurement techniques and analysis methods were used. The DQE at four exposure levels (30, 3, 0.3, 0.03 mR) and two plate types (standard and high resolution) were calculated from the NPS and MTF measurements. The NPS was determined from two-dimensional Fourier analysis of uniformly exposed plates. The presampling MTF was determined from the Fourier transform (FT) of the system's finely sampled line spread function (LSF) as produced by a narrow slit. A comparison of the slit type ("beveled edge" versus "straight edge") and its effect on the resulting MTF measurements was also performed. The results show that both systems are comparable in resolution performance. The noise power studies indicated a higher level of noise for the Kodak images (approximately 20% at the low exposure levels and 40%-70% at higher exposure levels). Within the clinically relevant exposure range (0.3-3 mR), the resulting DQE for the Kodak plates ranged between 20%-50% lower than for the corresponding Fuji plates. Measurements of the presampling MTF with the two slit types have shown that a correction factor can be applied to compensate for transmission through the relief edges.

Evaluation Studies as Topic↗

Double-quantum biased covariance spectroscopy: application to the 2D INADEQUATE experiment.

A novel processing scheme is presented that converts a two-dimensional double-quantum NMR spectrum into a single-quantum correlation spectrum. The covariance-like spectrum is computed from the 2D Fourier transform spectrum by emphasizing contributions that fulfill the double-quantum condition resulting in a symmetric spectrum that is easier to analyze. The method is demonstrated for the 2D INADEQUATE experiment.

Carbon Isotopes↗

Effect of quantum noise on the detection of incipient proximal caries.

The effect of quantum noise on the radiographyic detectability of proximal carious lesions was studied. Bitewing radiographs obtained from patients considered to be free of caries were digitized and stored in a computer using a sampling interval comparable to screen-film systems. Lesions limited in depth to one half the thickness of the enamel were induced by means of computer simulation. Various amounts of randomly generated quantum noise were added to each radiographic image. The results from observer-performance studies show that the lesions can be detected reliably in the presence of substantial amounts of quantum noise, suggesting that comparable diagnostic performance could be obtained with significantly faster imagining systems than those currently used in dentistry.

Analog-Digital Conversion↗

Variational reduced-density-matrix theory applied to the potential energy surfaces of carbon monoxide in the presence of electric fields.

The variational optimization of the energy with respect to the two-electron reduced-density matrix (2-RDM), constrained by N-representability conditions, can determine the shape of molecular potential energy surfaces with useful accuracy. In this paper, we apply the 2-RDM method with a first-order optimization algorithm [Mazziotti, D. A. Phys. Rev. Lett. 2004, 93, 213001] to investigating the potential energy surfaces of carbon monoxide in the presence and absence of an electric field. Two beneficial characteristics of the 2-RDM method for computing potential energy surfaces include the following: (i) its ability to capture multireference effects without specifying any reference wave function or density matrix and (ii) its guarantee of a global energy minimum in the variational optimization. The 2-RDM method produces electronic ground-state energies with similar accuracy at equilibrium and nonequilibrium geometries in both the presence and the absence of the electric field. Computed dipole moments are similar in accuracy to the values from the computationally expensive configuration interaction with single, double, triple, and quadruple excitations. These surfaces have important applications in quantum molecular control theory.

Carbon Monoxide↗

A relativistic DFT study of one-bond fluorine-X indirect spin-spin coupling tensors.

The relativistic zeroth-order regular approximation (ZORA) DFT method was employed to investigate indirect spin-spin coupling tensors involving fluorine, (1)J(X, F). The relative contributions of the mechanisms contributing to (1)J(X, F) are discussed, with special attention paid to the magnitude and origin of the anisotropy in this tensor, DeltaJ. This quantum chemical study demonstrates that, for the systems investigated, the ZORA-DFT method reproduces the magnitude of (1)J(X, F)(iso) and indicates that DeltaJ(X, F) is of the same order of magnitude as (1)J(X, F)(iso). Several examples are provided that demonstrate the importance of considering contributions of DeltaJ to the experimental measurement of effective dipolar coupling constants, R(eff). Given the difficulties with determining DeltaJ experimentally and the promising computational results, we suggest that the quantum chemical calculation of (1)J(X, F) be used as a complementary tool to aid in the analysis of data from NMR experiments designed to measure dipolar coupling constants.

Journal Article↗

Charge distribution in the water molecule--a comparison of methods.

The charge distribution in the water molecule has been analyzed using a broad variety of basis sets, four different quantum mechanical methods (Hartree-Fock, Becke3LYP, MP2, and QCISD), and six population analysis methods (Mulliken, NPA, AIM, CHELPG, Merz-Kollman, and Resp). The influence of the molecular structure on the calculated atomic charges has been studied using small perturbations of the experimentally determined structure.

Chemistry, Physical↗