Volume 133, Issue 18, 14 November 2010
Index of content:
Protein dynamics evolves in a high-dimensional space, comprising aharmonic, strongly correlated motional modes. Such correlation often plays an important role in analyzing protein function. In order to identify significantly correlated collective motions, here we employ independent subspace analysis based on the subspace joint approximate diagonalization of eigenmatrices algorithm for the analysis of molecular dynamics (MD) simulation trajectories. From the 100 ns MD simulation of T4 lysozyme, we extract several independent subspaces in each of which collective modes are significantly correlated, and identify the other modes as independent. This method successfully detects the modes along which long-tailed non-Gaussian probability distributions are obtained. Based on the time cross-correlation analysis, we identified a series of events among domain motions and more localized motions in the protein, indicating the connection between the functionally relevant phenomena which have been independently revealed by experiments.
- Theoretical Methods and Algorithms
Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms133(2010); http://dx.doi.org/10.1063/1.3493677View Description Hide Description
Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul.7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schrödinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wave functions, and use of Slater-type orbitals (STOs). The required Coulomb integrals for STOs are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to transition metal atoms are in good agreement with experimental data. In particular, we reproduce the anomalous magnetic moment and orbital filling of chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.
133(2010); http://dx.doi.org/10.1063/1.3491809View Description Hide Description
Explicitly correlated CCSD(T)-F12a/b methods combined with basis sets specifically designed for this technique have been tested for their ability to reproduce standard CCSD(T) benchmark data covering 16 small molecules composed of hydrogen and carbon. The standard method calibration set was obtained with very large one-particle basis sets, including some aug-cc-pV7Z and aug-cc-pV8Z results. Whenever possible, the molecular properties (atomization energies, structures, and harmonic frequencies) were extrapolated to the complete basis set limit in order to facilitate a direct comparison of the standard and explicitly correlated approaches without ambiguities arising from the use of different basis sets. With basis sets of triple- quality or better, the F12a variant was found to overshoot the presumed basis set limit, while the F12b method converged rapidly and uniformly. Extrapolation of F12b energies to the basis set limit was found to be very effective at reproducing the best standard method atomization energies. Even extrapolations based on the small cc-pVDZ-F12/cc-pVTZ-F12 combination proved capable of a mean absolute deviation of 0.20 kcal/mol. The accuracy and simultaneous cost savings of the F12b approach are such that it should enable high quality property calculations to be performed on chemical systems that are too large for standard CCSD(T).
Application of second-order Møller–Plesset perturbation theory with resolution-of-identity approximation to periodic systems133(2010); http://dx.doi.org/10.1063/1.3503153View Description Hide Description
Efficient periodic boundary condition (PBC) calculations by the second-order Møller–Plesset perturbation (MP2) method based on crystal orbital formalism are developed by introducing the resolution-of-identity (RI) approximation of four-center two-electron repulsion integrals (ERIs). The formulation and implementation of the PBC RI-MP2 method are presented. In this method, the mixed auxiliary basis functions of the combination of Poisson and Gaussian type functions are used to circumvent the slow convergence of the lattice sum of the long-range ERIs. Test calculations of one-dimensional periodic trans-polyacetylene show that the PBC RI-MP2 method greatly reduces the computational times as well as memory and disk sizes, without the loss of accuracy, compared to the conventional PBC MP2 method.
Quantum theory of molecular collisions in a magnetic field: Efficient calculations based on the total angular momentum representation133(2010); http://dx.doi.org/10.1063/1.3503500View Description Hide Description
An efficient method is presented for rigorous quantum calculations of atom-molecule and molecule-molecule collisions in a magnetic field. The method is based on the expansion of the wave function of the collision complex in basis functions with well-defined total angular momentum in the body-fixed coordinate frame. We outline the general theory of the method for collisions of diatomic molecules in the and electronic states with structureless atoms and with unlike and molecules. The cross sections for elastic scattering and Zeeman relaxation in low-temperature collisions of and molecules with atoms converge quickly with respect to the number of total angular momentum states included in the basis set, leading to a dramatic enhancement in computational efficiency compared to the previously used methods [A. Volpi and J. L. Bohn, Phys. Rev. A65, 052712 (2002); R. V. Krems and A. Dalgarno, J. Chem. Phys.120, 2296 (2004)]. Our approach is thus well suited for theoretical studies of strongly anisotropic molecular collisions in the presence of external electromagnetic fields.
Quantum wavepacket ab initio molecular dynamics: Generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure133(2010); http://dx.doi.org/10.1063/1.3504167View Description Hide Description
We present a generalization to our previously developed quantum wavepacket ab initiomolecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.
Multireference general-model-space state-universal and state-specific coupled-cluster approaches to excited states133(2010); http://dx.doi.org/10.1063/1.3494538View Description Hide Description
The concept of C-conditions, originally introduced in the framework of the multireference (MR), general-model-space (GMS), state-universal (SU),coupled-cluster (CC) approach with singles and doubles (GMS-SU-CCSD) to account for the internal amplitudes that vanish in the case of a complete model space, is applied to a state-selective or state-specific Mukherjee MR-CC method (MkCCSD). In contrast to the existing applications, the emphasis is on the description of excited states, particularly those belonging to the same symmetry species. The applicability of the C-conditions in all MR-SU-CC approaches is emphasized. Convergence problems encountered in the MkCCSD method when handling higher-lying states are pointed out. The performance of the GMS-SU-CCSD and MkCCSD methods is illustrated by considering low-lying vertical excitation energies of the ethylene molecule and para-benzyne diradical. A comparison with the equation-of-motion CCSD results, as well as with the available experimental data and recent multireference configuration interaction theoretical results, is also provided.
133(2010); http://dx.doi.org/10.1063/1.3491264View Description Hide Description
Highly correlated ab initio methods are used to predict the equilibrium structures and spectroscopic parameters of the anion. The total energies and physical properties are reported using CASSCF/MRCI, RCCSD(T), and RCCSD(T)-F12 approaches and extended basis sets. The search of stable geometries leads to a total of 12 isomers (4 linear and 8 cyclic), for which electronic ground states have close-shell configurations. The stability of the linear form, , is prominent. For the most stable linear isomer, the equilibrium rotational constant has been calculated with RCCSD(T) and a complete basis set. Core-correlation and vibrational effects have been taken into account to predict a of 2621.68 MHz for and 2460.48 MHz for . The dipole moment of was found to be 2.9707 D with CASSCF/aug-cc-pV5Z and the electron affinity to be 2.7 eV with RCCSD(T)-F12A/aug-cc-pVTZ. Anharmonic spectroscopic parameters are derived from a quadratic, cubic, and quartic RCCSD(T)-F12A force field and second order perturbation theory. CASSCF/MRCI vertical excitations supply three metastable electronic states, and . Electron affinities calculated for a series of chains type and allow us to discuss the anion formation probabilities.
Iterative linearized density matrix propagation for modeling coherent excitation energy transfer in photosynthetic light harvesting133(2010); http://dx.doi.org/10.1063/1.3498901View Description Hide Description
Rather than incoherent hopping between chromophores, experimental evidence suggests that the excitation energy transfer in some biological light harvesting systems initially occurs coherently, and involves coherent superposition states in which excitation spreads over multiple chromophores separated by several nanometers. Treating such delocalized coherent superposition states in the presence of decoherence and dissipation arising from coupling to an environment is a significant challenge for conventional theoretical tools that either use a perturbative approach or make the Markovian approximation. In this paper, we extend the recently developed iterative linearized density matrix (ILDM) propagation scheme [E. R. Dunkel et al., J. Chem. Phys.129, 114106 (2008)] to study coherent excitation energy transfer in a model of the Fenna–Matthews–Olsen light harvesting complex from green sulfur bacteria. This approach is nonperturbative and uses a discrete path integral description employing a short time approximation to the density matrix propagator that accounts for interference between forward and backward paths of the quantum excitonic system while linearizing the phase in the difference between the forward and backward paths of the environmental degrees of freedom resulting in a classical-like treatment of these variables. The approach avoids making the Markovian approximation and we demonstrate that it successfully describes the coherent beating of the site populations on different chromophores and gives good agreement with other methods that have been developed recently for going beyond the usual approximations, thus providing a new reliable theoretical tool to study coherent exciton transfer in light harvesting systems. We conclude with a discussion of decoherence in independent bilinearly coupled harmonic chromophore baths. The ILDM propagation approach in principle can be applied to more general descriptions of the environment.
133(2010); http://dx.doi.org/10.1063/1.3494113View Description Hide Description
The primary characteristics of single reference coupled-cluster (CC) theory are size-extensivity and size-consistency, invariance under orbital rotations of the occupied or virtual space, the exactness of CC theory for electron systems when the cluster operator is truncated to -tuple excitations, and the relative insensitivity of CC theory to the choice of the reference determinant. In this work, we propose a continuous class of methods which display the desirable features of the coupled-cluster approach with single and double excitations (CCSD). These methods are closely related to the CCSD method itself and are inspired by the coupled electron pair approximation (CEPA). It is demonstrated that one can systematically improve upon CCSD and obtain geometries, harmonic vibrational frequencies, and total energies from a parameterized version of CCSD or by selecting a specific member from this continuous family of approaches. In particular, one finds that one such approach, the pCCSD(−1,1) method, is a significant improvement over CCSD for the calculation of equilibrium structures and harmonic frequencies. Moreover, this method behaves surprisingly well in the calculation of potential energy surfaces for single bond dissociation. It appears that this methodology has significant promise for chemical applications and may be particularly useful in applications to larger molecules within the framework of a high accuracy local correlation approach.
133(2010); http://dx.doi.org/10.1063/1.3499812View Description Hide Description
The use of discrete variable representation (DVR) basis sets within ab initiomolecular dynamics calculations allows the latter to be performed with converged energies and, more importantly, converged forces. In this paper, we show how to carry out ab initiomolecular dynamics calculations in the isothermal-isobaric ensemble with fully flexible simulation boxes within the DVR basis set framework. In particular, we derive the appropriate DVR based expression for the pressure tensor when the electronic structure is represented using Kohn–Sham density functional theory, and we examine the convergence of this expression as a function of the basis set size. An illustrative example using 64 silicon atoms in a fully flexible box using a combination of the Martyna–Tobias–Klein [Martyna et al., J. Chem. Phys.101, 4177 (1994)] and Car–Parrinello [Car and Parinello, Phys. Rev. Lett.55, 2471 (1985)] algorithms is presented to demonstrate the efficacy of the approach.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
Toward spectroscopic accuracy for open-shell systems: Molecular structure and hyperfine coupling constants of , , , and as test cases133(2010); http://dx.doi.org/10.1063/1.3503763View Description Hide Description
In the present paper, we investigate the molecular structure and hyperfine couplings of a series of radicals containing first- and second-row atoms for which accurate gas-phase microwave results are available. The presence of - and, especially, -hydrogen atoms makes the evaluation of magnetic properties of these radicals particularly challenging. Geometrical parameters have been computed by the coupled-cluster ansatz in conjunction with hierarchical series of basis sets, thus accounting for extrapolation to the complete basis-set limit. Core correlation as well as higher excitations in the electronic-correlation treatment have also been taken into account. An analogous approach has been employed for evaluating hyperfine coupling constants with particular emphasis given to basis-set, correlation, and geometrical effects. The corresponding vibrational corrections, required for a meaningful comparison to experimental data, have also been investigated. The remarkable agreement with experiment confirms the reliability of the present computational approach, already validated for radicals, thus establishing the way for setting up a benchmark database for magnetic properties.
133(2010); http://dx.doi.org/10.1063/1.3494539View Description Hide Description
The interaction-induceddipole momentsurface of the van der Waals complex has been calculated for a broad range of intermolecular separations and configurations in the approximation of the rigid interacting molecules at the MP2 and CCSD(T) levels of theory using the correlation-consistent aug-cc-pVTZ basis set with the basis set superposition error correction. The simple model to account for the exchange effects in the range of small overlap of the electron shells of interacting molecules and the induction and dispersioninteractions for large has been suggested. This model allows describing the dipole moment of van der Waals complexes in analytical form both for large , where induction and dispersion have the key role, and for smaller including whole ranges of their potential wells, where the exchange effects are important. The proposed model was tested on a number of configurations of the complex and was applied for the analytical description of the dipole momentsurface for the family of the most stable configurations of the complex.
133(2010); http://dx.doi.org/10.1063/1.3495765View Description Hide Description
A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to monitor time-resolved infrared absorption of transient species produced upon irradiation at 248 nm of a flowing mixture of and at 260 K. Two transient bands observed with origins at and are tentatively assigned to the antisymmetric -deformation and stretching modes of , respectively; the observed band contour indicates that the less stable conformer likely contributes to these absorption bands. A band with an origin at , observed at a slightly later period, is assigned to the stretching mode of , likely produced via secondary reactions of . These bands fit satisfactorily with vibrational wavenumbers and rotational contours simulated based on rotational parameters of , , and predicted with density-functional theories B3LYP/aug-cc-pVTZ and B3P86/aug-cc-pVTZ. Two additional bands near 1170 and observed at a later period are tentatively assigned to and , respectively; both species are likely produced from self-reaction of . The production of via secondary reactions was also observed and possible reaction mechanism is discussed.
133(2010); http://dx.doi.org/10.1063/1.3502493View Description Hide Description
Transition states and reaction paths for a hydrogen molecule dissociating on small aluminum clusters have been calculated using density functional theory. The two lowest spin states have been taken into account for all the clusters considered, with . The aluminum dimer, which shows a electronic ground state, has also been studied at the coupled cluster and configuration interaction level for comparison and to check the accuracy of single determinant calculations in this special case, where two degenerate configurations should be taken into account. The calculated reaction barriers give an explanation of the experimentally observed reactivity of hydrogen on Al clusters of different size [Cox et al. , J. Chem. Phys.84, 4651 (1986)] and reproduce the high observed reactivity of the cluster. The electronic structure of the systems was also systematically investigated in order to determine the role played by interactions of specific molecular orbitals for different nuclear arrangements. Singlet clusters (with even) exhibit the lowest barriers to dissociation because their highest doubly occupied molecular orbitals allow for a more favorable interaction with the antibonding molecular orbital of .
A ground state morphed intermolecular potential for the hydrogen bonded and van der Waals isomers in OC:HI and a prediction of an anomalous deuterium isotope effect133(2010); http://dx.doi.org/10.1063/1.3505145View Description Hide Description
An extended analysis of the noncovalent interaction OC:HI is reported using microwave and infrared supersonic jet spectroscopic techniques. All available spectroscopic data then provide the basis for generating an accurately determined vibrationally complete semiempirical intermolecular potential function using a four-dimensional potential coordinate morphing methodology. These results are consistent with the existence of four bound isomers: OC–HI, OC–IH, CO–HI, and CO–IH. Analysis also leads to unequivocal characterization of the common isotopic ground state as having the OC–HI structure and with the first excited state having the OC–IH structure with an energy of above the ground state. The potential is consistent with the following barriers between the pairs of isomers: (OC–IH/OC–HI), (CO–IH/CO–HI), (OC–IH/CO–IH), and (OC–HI/CO–HI) defined with respect to each lower minimum. The potential is also determined to have a linear OC–IH van der Waals global equilibrium minimum structure having , , and . This is differentiated from its OC–HI ground state hydrogen bound structure having , , and where the distances are defined between the centers of mass of the monomers and and as for and 2. A fundamentally new molecular phenomenon - ground state isotopic isomerization is proposed based on the generated semiempirical potential. The protonated ground state hydrogen-bonded OC–HI structure is predicted to be converted on deuteration to the corresponding ground state van der Waals OC–ID isomeric structure. This results in a large anomalous isotope effect in which the center of mass distance between monomeric components changes from 4.895(1) to 4.286(1) Å. Such a proposed isotopic effect is demonstrated to be a consequence of differential zero point energy factors resulting from the shallower nature of hydrogen bonding at a local potential minimum (greater quartic character of the potential) relative to the corresponding van der Waals global minimum. Further consequences of this anomalous deuterium isotope effect are also discussed.
133(2010); http://dx.doi.org/10.1063/1.3490480View Description Hide Description
Electronic structure calculations at the CASSCF and UB3LYP levels of theory with the aug-cc-pVDZ basis set were used to characterize structures, vibrational frequencies, and energies for stationary points on the ground state triplet and singlet potential energy surfaces (PESs). Spin-orbit couplings between the PESs were calculated using state averaged CASSCF wave functions. More accurate energies were obtained for the CASSCF structures with the MRMP2/aug-cc-pVDZ method. An important and necessary aspect of the calculations was the need to use different CASSCF active spaces for the different reaction paths on the investigated PESs. The CASSCF calculations focused on addition to form the biradical on the triplet and singlet surfaces, and isomerization reaction paths ensuing from this biradical. The triplet and singlet biradicals are very similar in structure, primarily differing in their dihedral angles. The MRMP2 values for the barrier to form the biradical are 33.8 and 6.1 kcal/mol, respectively, for the triplet and singlet surfaces. On the singlet surface, isomerizes to dioxetane and ethane-peroxide with MRMP2 barriers of 7.8 and 21.3 kcal/mol. A more exhaustive search of reaction paths was made for the singlet surface using the UB3LYP/aug-cc-pVDZ theory. The triplet and singlet surfaces cross between the structures for the addition transition states and the biradical intermediates. Trapping in the triplet biradical intermediate, following addition, is expected to enhance intersystem crossing.
133(2010); http://dx.doi.org/10.1063/1.3493336View Description Hide Description
We present here the first experimental and theoretical study of the microwave spectrum of 5-methyltropolone, which can be visualized as a seven-membered “aromatic” carbon ring with a five-membered hydrogen-bonded cyclic structure at the top and a methyl group at the bottom. The molecule is known from earlier studies in the literature to exhibit two large-amplitude motions, an intramolecular hydrogen transfer and a methyl torsion. The former motion is particularly interesting because transfer of the hydrogen atom from the hydroxyl to the carbonyl group induces a tautomerization in the molecule, which then triggers a 60° internal rotation of the methyl group. Measurements were carried out by Fourier-transform microwave spectroscopy in the 8–24 GHz frequency range. Theoretical analysis was carried out using a tunneling-rotational Hamiltonian based on a extended-group-theory formalism. Our global fit of 1015 transitions to 20 molecular parameters gave a root-mean-square deviation of 1.5 kHz. The tunneling splitting of the two levels arising from a hypothetical pure hydrogen-transfer motion is calculated to be 1310 MHz. The tunneling splitting of the two levels arising from a hypothetical pure methyl top internal-rotation motion is calculated to be 885 MHz. We have also carried out ab initio calculations, which support the structural parameters determined from our spectroscopicanalysis and give estimates of the barriers to the two large-amplitude motions.
Growth of polyaromatic molecules via ion-molecule reactions: An experimental and theoretical mechanistic study133(2010); http://dx.doi.org/10.1063/1.3505553View Description Hide Description
The reactivity of naphthyl cations with benzene is investigated in a joint experimental and theoretical approach. Experiments are performed by using guided ion beam tandem mass spectrometers equipped with electron impact or atmospheric pressure chemical ion sources to generate with different amounts of internal excitation. Under single collision conditions, C–C coupling reactions leading to hydrocarbon growth are observed. The most abundant ionic products are , (with ), and . From pressure-dependent measurements, absolute cross sections of and (at a collision energy of about 0.2 eV in the center of mass frame) are derived for channels leading to the formation of and ions, respectively. From cross section values a phenomenological total rate constant at an average collision energy of about 0.27 eV can be estimated for the process products. The energy behavior of the reactive cross sections, as well as further experiments performed using partial isotopic labeling of reagents, support the idea that the reaction proceeds via a long lived association product, presumably the covalently bound protonated phenylnaphthalene, from which lighter species are generated by elimination of neutral fragments (H, , ). A major signal relevant to the fragmentation of the initial adduct belongs to . Since it is not obvious how loss from can take place to form the radical cation, a theoretical investigation focuses on possible unimolecular transformations apt to produce it. Naphthylium can act as an electrophile and add to the system of benzene, leading to a barrierless formation of the ionic adduct with an exothermicity of about . From this structure, an intramolecular electrophilic addition followed by H shifts and ring opening steps leads to an overall exothermic loss ( with respect to reagents) of the methyl radical from that part of the system which comes from benzene. Methyl loss can take place also from the “naphthyl” part, though via an endoergic route. Experimental and theoretical results show that an ionic route is viable for the growth of polycyclic aromatic species by association of smaller building blocks (naphthyl and phenyl rings) and this may be of particular relevance for understanding the formation of large molecules in ionized gases.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
Energy-transfer and charge-separation pathways in the reaction center of photosystem II revealed by coherent two-dimensional optical spectroscopy133(2010); http://dx.doi.org/10.1063/1.3493580View Description Hide Description
The excited state dynamics and relaxation of electrons and holes in the photosynthetic reaction center of photosystem II are simulated using a two-band tight-binding model. The dissipative exciton and charge carrier motions are calculated using a transport theory, which includes a strong coupling to a harmonic bath with experimentally determined spectral density, and reduces to the Redfield, the Förster, and the Marcus expressions in the proper parameter regimes. The simulated third order two-dimensional signals, generated in the directions , , and , clearly reveal the exciton migration and the charge-separation processes.
- Polymers and Complex Systems
Spherical polymer brushes under good solvent conditions: Molecular dynamics results compared to density functional theory133(2010); http://dx.doi.org/10.1063/1.3494902View Description Hide Description
A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.