Volume 137, Issue 16, 28 October 2012

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normalmode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and offdiagonal dipoledipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the active site of the protein.
 COMMUNICATIONS


Communication: A vibrational study of propargyl cation using the vacuum ultraviolet laser velocitymap imaging photoelectron method
View Description Hide DescriptionBy employing the vacuum ultraviolet (VUV) laser velocitymap imaging photoelectron (VUVVMIPE) method, we have obtained a vibrationally resolved photoelectron spectrum of gaseous propargyl radical [C_{3}H_{3}(X ^{2}B_{1})] in the energy range of 04600 cm^{−1} above its ionization energy. The cold C_{3}H_{3} radicals were produced from a supersonically cooled radical beam source based on 193 nm ArF photodissociation of C_{3}H_{3}Cl. The VUVVMIPE spectrum of C_{3}H_{3} thus obtained reveals a FranckCondon factor (FCF) pattern with a highly dominant origin band along with weak vibrational progressions associated with excitations of the C–C ν _{5} ^{+}(a_{1}) and C≡C ν _{3} ^{+}(a_{1}) symmetric stretching modes and the CCH ν _{7} ^{+}(b_{1}) outofplane bending mode of C_{3}H_{3} ^{+}(X ^{1}A_{1}). The ν _{5} ^{+}(a_{1}) vibrational frequency of 1120 cm^{−1} determined in the present study is lower than the value deduced from the recent Artagged infrared photodissociation study by 102 cm^{−1}, confirming the highly accurate vibrational frequency predictions obtained by the most recent stateoftheart ab initioquantum calculations. The observation of the FCF disallowed ν _{7} ^{+}(b_{1}) mode is indicative of vibronic interactions. The discrepancy observed between the FCF pattern determined in the present study and that predicted by a recent highlevel quantum theoretical investigation can be taken as evidence that the potential energy surfaces used in the latter theoretical study are in need of improvement in order to provide a reliable FCF prediction for the C_{3}H_{3}/C_{3}H_{3} ^{+}photoionization system.
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 ARTICLES

 Theoretical Methods and Algorithms

Stochastic mapping of first order reaction networks: A systematic comparison of the stochastic and deterministic kinetic approaches
View Description Hide DescriptionStochastic maps are developed and used for first order reaction networks to decide whether the deterministic kinetic approach is appropriate for a certain evaluation problem or the use of the computationally more demanding stochastic approach is inevitable. On these maps, the decision between the two approaches is based on the standard deviation of the expectation of detected variables: when the relative standard deviation is larger than 1%, the use of the stochastic method is necessary. Four different systems are considered as examples: the irreversible first order reaction, the reversible first order reaction, two consecutive irreversible first order reactions, and the unidirectional triangle reaction. Experimental examples are used to illustrate the practical use of the theoretical results. It is shown that the maps do not only depend on particle numbers, but the influence of parameters such as time, rate constants, and the identity of the detected target variable is also an important factor.

The embedded manybody expansion for energetics of molecular crystals
View Description Hide DescriptionReliable prediction of molecular crystal energetics is a vital goal for computational chemistry. Here we show that accurate results can be obtained from a monomerbased manybody expansion truncated at the twobody level, with the monomer and dimer calculations suitably embedded in a model of the crystalline environment. By including the two dominant effects—electrostatics and exchangerepulsion—we are able to capture the important nonadditive terms in the energy, and approach very closely results from full periodic secondorder MøllerPlesset calculations. The advantage of the current scheme is that extension to coupledcluster and explicitly correlated F12 methods is completely straightforward. We demonstrate the approach through calculations on carbon dioxide, hydrogen fluoride, and ice XIh and XIc. In accord with previous studies, we find these two icepolymorphs to be very close in energy, with our periodic coupledcluster single double tripleF12 calculation giving the hexagonal structure more stable by around 0.3 kJ mol^{−1}.

Arbitrary order El'yashevich–Wilson B tensor formulas for the most frequently used internal coordinates in molecular vibrational analyses
View Description Hide DescriptionIn recent years, internal coordinates have become the preferred means of expressing potential energy surfaces. The ability to transform quantities from chemically significant internal coordinates to primitive Cartesian coordinates and spectroscopically relevant normal coordinates is thus critical to the further development of computational chemistry. In the present work, general nth order formulas are presented for the Cartesian derivatives of the five most commonly used internal coordinates—bond stretching, bond angle, torsion, outofplane angle, and linear bending. To compose such formulas in a reasonably understandable fashion, a new notation is developed that is a generalization of that which has been used previously for similar purposes. The notation developed leads to easily programmable and reasonably understandable arbitrary order formulas, yet it is powerful enough to express the arbitrary order Btensor of a general, Npoint internal coordinate, as is done herein. The techniques employed in the derivation of such formulas are relatively straightforward, and could presumably be applied to a number of other internal coordinates as needed.

Symmetryadapted perturbation theory based on unrestricted KohnSham orbitals for highspin openshell van der Waals complexes
View Description Hide DescriptionTwo openshell formulations of the symmetryadapted perturbation theory are presented. They are based on the spinunrestricted KohnSham (SAPT(UKS)) and unrestricted HartreeFock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory(DFT) compared to the previous formulation of openshell SAPT based on spinrestricted KohnSham method of Żuchowski et al. [J. Chem. Phys.129, 084101 (2008)10.1063/1.2968556]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following openshell van der Waals complexes: He⋯NH, H_{2}O⋯HO_{2}, He⋯OH, Ar⋯OH, Ar⋯NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Πstate radicals (He⋯OH, Ar⋯OH, Ar⋯NO). In the interactions of transition metal dimers ()Au_{2} and ()Cr_{2} we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.

Harnessing the metageneralized gradient approximation for timedependent density functional theory
View Description Hide DescriptionDensity functionals within the metageneralized gradient approximation (MGGA) are widely used for groundstate electronic structure calculations. However, the gauge variance of the kinetic energy density τ confounds applications of MGGAs to timedependent systems, excited states, magnetic properties, and states with strong spinorbit coupling. Becke and Tao used the paramagneticcurrent density to construct a gauge invariant generalized kinetic energy density . We show that , where τ_{ W } is the von Weizsäcker kinetic energy density of a oneelectron system. Thus, replacing τ by leads to currentdependent MGGAs (cMGGAs) that are not only gauge invariant but also restore the accuracy of MGGAs in isoorbital regions for timedependent and currentcarrying states. The current dependence of cMGGAs produces a vector exchangecorrelation (XC) potential in the timedependent adiabatic KohnSham (KS) equations. While MGGA response properties of currentfree ground states become manifestly gaugevariant to second order, linear response properties are affected by a new XC kernel appearing in the cMGGA magnetic orbital rotation Hessian. This kernel reflects the firstorder coupling of KS orbitals due to changes in the paramagneticcurrent density and has apparently been ignored in previous MGGA response implementations. Inclusion of the current dependence increases total computation times by less than 50%. Benchmark applications to 109 adiabatic excitation energies using the TaoPerdewStaroverovScuseria (TPSS) MGGA and its hybrid version TPSSh show that cMGGA excitation energies are slightly lower than the MGGA ones on average, but exhibit fewer outliers. Similarly, the optical rotations of 13 small organic molecules show a small but systematic improvement upon inclusion of the magnetic XC kernel. We conclude that cMGGAs should replace MGGAs in all applications involving timedependent or currentcarrying states.

A test of systematic coarsegraining of molecular dynamics simulations: Thermodynamic properties
View Description Hide DescriptionCoarsegraining (CG) techniques have recently attracted great interest for providing descriptions at a mesoscopic level of resolution that preserve fluid thermodynamic and transport behaviors with a reduced number of degrees of freedom and hence less computational effort. One fundamental question arises: how well and to what extent can a “bottomup” developed mesoscale model recover the physical properties of a molecular scale system? To answer this question, we explore systematically the properties of a CG model that is developed to represent an intermediate mesoscale model between the atomistic and continuum scales. This CG model aims to reduce the computational cost relative to a full atomistic simulation, and we assess to what extent it is possible to preserve both the thermodynamic and transport properties of an underlying reference allatom LennardJones (LJ) system. In this paper, only the thermodynamic properties are considered in detail. The transport properties will be examined in subsequent work. To coarsegrain, we first use the iterative Boltzmann inversion (IBI) to determine a CG potential for a (1ϕ)N mesoscale particle system, where ϕ is the degree of coarsegraining, so as to reproduce the radial distribution function (RDF) of an N atomic particle system. Even though the uniqueness theorem guarantees a one to one relationship between the RDF and an effective pairwise potential, we find that RDFs are insensitive to the longrange part of the IBIdetermined potentials, which provides some significant flexibility in further matching other properties. We then propose a reformulation of IBI as a robust minimization procedure that enables simultaneous matching of the RDF and the fluid pressure. We find that this new method mainly changes the attractive tail region of the CG potentials, and it improves the isothermal compressibility relative to pure IBI. We also find that there are optimal interaction cutoff lengths for the CG system, as a function of ϕ, that are required to attain an adequate potential while maintaining computational speedup. To demonstrate the universality of the method, we test a range of state points for the LJ liquid as well as several LJ chain fluids.

A oneparameter quantum cluster equilibrium approach
View Description Hide DescriptionThe established quantum cluster equilibrium approach is further developed in this work. The equations are reformulated to result in a oneparameter expression, i.e., with one of two empirical parameters eliminated. Instead of a parametrized constant mean field interaction we present two further approaches using temperature dependent mean field functions. The suggested functions are assessed by means of two test systems, namely hydrogen fluoride and water which are investigated concerning their liquid phase properties as well as the phenomenon of evaporation. The obtained thermodynamic data are compared with each other for the different mean field functions including the conventional approach as well as to experimental data.

Brownian dynamics simulations with hardbody interactions: Spherical particles
View Description Hide DescriptionA novel approach to account for hardbody interactions in (overdamped) Brownian dynamics simulations is proposed for systems with nonvanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a onedimensional halfline. The motion of a Brownian particle is decomposed into a component that is affected by hardbody interactions and into components that are unaffected. The hardbody interactions are incorporated by replacing the “affected” component of motion by the evolution on a halfline. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with spacefixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heuristic algorithms is carried out.

Adiabatic and nonadiabatic contributions to the energy of a system subject to a timedependent perturbation: Complete separation and physical interpretation
View Description Hide DescriptionWhen a timedependent perturbation acts on a quantum system that is initially in the nondegenerate ground state 0⟩ of an unperturbed Hamiltonian H_{0}, the wave function acquires excitedstate components k⟩ with coefficients c_{k}(t) exp(−iE_{k}t/ℏ), where E_{k} denotes the energy of the unperturbed state k⟩. It is well known that each coefficient c_{k}(t) separates into an adiabatic term a_{k}(t) that reflects the adjustment of the ground state to the perturbation – without actual transitions – and a nonadiabatic term b_{k}(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the timedependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the crossterms between the adiabatic and nonadiabatic parts of c_{k}(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH′(t). The nonadiabatic term is a sum over excited states k⟩ of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates k′(t)⟩ of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state k′(t)⟩ is given by λ^{2} b_{k}(t)^{2}. At third order, the transition probability depends on a secondorder transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule.

Restricted active space spinflip configuration interaction: Theory and examples for multiple spin flips with odd numbers of electrons
View Description Hide DescriptionThe restricted active space spin flip (RASSF) method is extended to allow ground and excited states of molecular radicals to be described at low cost (for small numbers of spin flips). RASSF allows for any number of spin flips and a flexible active space while maintaining pure spin eigenfunctions for all states by maintaining a spin complete set of determinants and using spinrestricted orbitals. The implementation supports both even and odd numbers of electrons, while use of resolution of the identity integrals and a shared memory parallel implementation allow for fast computation. Examples of multiplebond dissociation,excited states in triradicals, spin conversions in organic multiradicals, and mixedvalence metal coordination complexes demonstrate the broad usefulness of RASSF.

Mixing atoms and coarsegrained beads in modelling polymer melts
View Description Hide DescriptionWe present a simple hybrid model for macromolecules where the single molecules are modelled with both atoms and coarsegrained beads. We apply our approach to two different polymer melts, polystyrene and polyethylene, for which the coarsegrained potential has been developed using the iterative Boltzmann inversion procedure. Our results show that it is possible to couple the two potentials without modifying them and that the mixed model preserves the local and the global structure of the melts in each of the case presented. The degree of resolution present in each single molecule seems to not affect the robustness of the model. The mixed potential does not show any bias and no cluster of particles of different resolution has been observed.

An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo
View Description Hide DescriptionBy performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the approach of Valeev et al. The required one and twoparticle density matrices are computed onthefly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMCF12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the oneelectron basis by two cardinal numbers.

Determination of Kohn–Sham effective potentials from electron densities using the differential virial theorem
View Description Hide DescriptionWe present an accurate method for constructing the Kohn–Sham effective potential corresponding to a given electron density in onedimensional and spherically symmetric systems. The method is based on the differential virial theorem—an exact relation between the effective potential, the electron density, and the kinetic energy density. A distinctive feature of the proposed technique is that it employs a sizeconsistent bosonic reference potential to ensure the correct asymptotic behavior of the resulting Kohn–Sham potential. We describe a practical implementation of our method and use it to obtain highquality exchangecorrelation and correlation potentials of the neon and argon atoms from ab initio densities generated in large Slater and Gaussiantype basis sets.
 Advanced Experimental Techniques

Constant time tensor correlation experiments by nongammaencoded recoupling pulse sequences
View Description Hide DescriptionConstanttime tensor correlation under magicangle spinning conditions is an important technique in solidstate nuclear magnetic resonance spectroscopy for the measurements of backbone or sidechain torsion angles of polypeptides and proteins. We introduce a general method for the design of constanttime tensor correlation experiments under magicangle spinning. Our method requires that the amplitude of the average Hamiltonian must depend on all the three Euler angles bringing the principal axis system to the rotorfixed frame, which is commonly referred to as nongamma encoding. We abbreviate this novel approach as COrrelation of NonGammaEncoded Experiment (CONGEE), which exploits the orientationdependence of nongammaencoded sequences with respect to the magicangle rotation axis. By manipulating the relative orientation of the average Hamiltonians created by two nongammaencoded sequences, one can obtain a modulation of the detected signal, from which the structural information can be extracted when the tensor orientations relative to the molecular frame are known. CONGEE has a prominent feature that the number of rf pulses and the total pulse sequence duration can be maintained to be constant so that for torsion angle determination the effects of systematic errors owing to the experimental imperfections and/or T 2 effects could be minimized. As a proof of concept, we illustrate the utility of CONGEE in the correlation between the C^{′} chemical shift tensor and the C^{ α }–H^{ α } dipolar tensor for the backbone psi angle determination. In addition to a detailed theoretical analysis, numerical simulations and experiments measured for [U^{13}C, ^{15}N]Lalanine and Nacetyl[U^{13}C, ^{15}N]D,Lvaline are used to validate our approach at a spinning frequency of 20 kHz.

Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics
View Description Hide DescriptionWe report on the simultaneous detection of the fluorescence lifetime, spectrum, and threedimensional dipole orientation determination of single perylene diimide molecules deposited on a silica surface as a model system for studying fluorophore internal and orientational dynamics. We employ a multiparameter detection scheme to demonstrate how jumps in the orientation of the molecule can be disentangled from spectral jumps, both leading to changes of the detected total fluorescence intensity. The fluorescence lifetime determined simultaneously from the same photons is also sensitive to the orientation of the dipole with respect to the interface between media with different refractive indices. The correlated changes of the lifetime and orientation we observe are in good agreement with theory.
 Atoms, Molecules, and Clusters

Spectroscopy of 3, 4, 9, 10perylenetetracarboxylic dianhydride (PTCDA) attached to rare gas samples: Clusters vs. bulk matrices. I. Absorption spectroscopy
View Description Hide DescriptionThe interaction between 3, 4, 9, 10perylenetetracarboxylic dianhydride (PTCDA) and rare gas or parahydrogen samples is studied by means of laserinduced fluorescence excitation spectroscopy. The comparison between spectra of PTCDA embedded in a neon matrix and spectra attached to large neon clusters shows that these large organic molecules reside on the surface of the clusters when doped by the pickup technique. PTCDA molecules can adopt different conformations when attached to argon, neon, and parahydrogen clusters which implies that the surface of such clusters has a welldefined structure without liquid or fluxional properties. Moreover, a precise analysis of the doping process of these clusters reveals that the mobility of large molecules on the clustersurface is quenched, preventing agglomeration and complex formation.

Spectroscopy of 3, 4, 9, 10perylenetetracarboxylic dianhydride (PTCDA) attached to rare gas samples: Clusters vs. bulk matrices. II. Fluorescence emission spectroscopy
View Description Hide DescriptionThe interaction between 3, 4, 9, 10perylenetetracarboxylic dianhydride (PTCDA) molecules and solid rare gas samples is studied by means of fluorescenceemission spectroscopy. Laserexcited PTCDAdoped large argon, neon, and parahydrogen clusters along with PTCDA embedded in helium nanodroplets are spectroscopically characterized with respect to line broadening and shifting. A fast nonradiative relaxation is observed before a radiative decay in the electronic ground state takes place. In comparison, fluorescence emission studies of PTCDA embedded in bulk neon and argon matrices result in much more complex spectral signatures characterized by a splitting of the different emission lines. These can be assigned to the appearance of site isomers of the surrounding matrix lattice structure.

Nonlocal electronphonon coupling in the pentacene crystal: Beyond the Γpoint approximation
View Description Hide DescriptionThere is currently increasing interest in understanding the impact of the nonlocal (Peierlstype) electronphonon mechanism on charge transport in organic molecular semiconductors. Most estimates of the nonlocal coupling constants reported in the literature are based on the Γpoint phonon modes. Here, the influence of phonon modes spanning the entire Brillouin zone (phonon dispersion) on the nonlocal electronphonon couplings is investigated for the pentacene crystal. The phonon modes are obtained by using a supercell approach. The results underline that the overall nonlocal couplings are substantially underestimated by calculations taking sole account of the phonons at the Γ point of the unit cell. The variance of the transfer integrals based on Γpoint normalmode calculations at room temperature is underestimated in some cases by 40% for herringbonetype dimers and by over 80% for cofacial dimers. Our calculations show that the overall coupling is somewhat larger for holes than for electrons. The results also suggest that the interactions of charge carriers (both electrons and holes) with acoustic and optical phonons are comparable. Therefore, an adequate description of the chargetransport properties in pentacene and similar systems requires that these two electronphonon coupling mechanisms be treated on the same footing.

Probing the structural and electronic properties of small vanadium dioxide clusters by density functional theory and comparison with experimental photoelectron spectroscopy
View Description Hide DescriptionThe structural evolution and bonding of a series of early transitionmetal dioxide clusters, (n = 3–9, q = 0, −1), have been investigated using density functional theory (DFT) calculations and the results are compared with experimental literature data. For each vanadium dioxide cluster, many lowlying isomers are generated using the Saunders “Kick” global minimum stochastic search method. Theoretical electron detachment energies (both vertical and adiabatic) were compared with the experimental measurements to verify the ground states of the vanadium dioxide clusters obtained from the DFT calculations. Five kinds of dissociative adsorption configurations of groundstate structure of are identified. The dissociative adsorption of O_{2} on V_{n} ^{−1, 0} is more favorable than O_{2} molecular adsorption. Furthermore, the adsorption energy of O_{2} is higher than that of a single atom on the bare V_{n} ^{−1, 0} clusters, but less than twice the adsorption energy for an atom, indicating that O_{2} being adsorbed on vanadium clusters are more difficult than single O atom adsorbed on vanadium clusters.