Volume 136, Issue 24, 28 June 2012

Though molecular simulation of proteins has made notable contributions to the study of protein folding and kinetics, disagreement between simulation and experiment still exists. One of the criticisms levied against simulation is its failure to reproduce cooperative protein folding transitions. This weakness has been attributed to many factors such as a lack of polarizability and adequate capturing of solvent effects. This work, however, investigates how increasing the number of proteins simulated simultaneously can affect the cooperativity of folding transitions — a topic that has received little attention previously. Two proteins are studied in this work: phage T4 lysozyme (Protein Data Bank (PDB) ID: 7LZM) and phage 434 repressor (PDB ID: 1R69). The results show that increasing the number of proteins molecules simulated simultaneously leads to an increase in the macroscopic cooperativity for transitions that are inherently cooperative on the molecular level but has little effect on the cooperativity of other transitions. Taken as a whole, the results identify one area of consideration to improving simulations of protein folding.
 ARTICLES

 Theoretical Methods and Algorithms

Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models
View Description Hide DescriptionUsing the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the “initiator” adaptation to full configuration interactionquantum Monte Carlo (iFCIQMC), with a view to accelerating convergence. In particular, we find that the fixedshift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an iFCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N = 14 over a range of densities 0.5 ⩽ r _{ s } ⩽ 5.0 a.u. A singlepoint extrapolation scheme is introduced to produce complete basis energies for 14, 38, and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixedshift strategy to reduce the computational cost of many iFCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

Local unitary transformation method for largescale twocomponent relativistic calculations: Case for a oneelectron Dirac Hamiltonian
View Description Hide DescriptionAn accurate and efficient scheme for twocomponent relativistic calculations at the spinfree infiniteorder DouglasKrollHess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X_{2} (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)_{ n } (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linearscaling with respect to the system size and a small prefactor.

A longrange electrostatic potential based on the Wolf method chargeneutral condition
View Description Hide DescriptionMolecular simulations rely heavily on a long range electrostatic Coulomb interaction. The Coulomb potential decays inversely with distance, indicating infinite effective range. In practice, molecular simulations do not directly take into account such an infinite interaction. Therefore, the Ewald, fast multipole, and cutoff methods are frequently used. Although cutoff methods are implemented easily and the calculations are fast, it has been pointed out that they produce serious artifacts. Wolf and coworkers recently discovered one source of the artifacts. They found that when the total charge in a cutoff sphere disappeared, the cutoff error is dramatically suppressed. The Wolf method uses the chargeneutral principle combined with a potential damping that is realized using a complementary error function. To date, many molecular simulation studies have demonstrated the accuracy and reliability of the Wolf method. We propose a novel longrange potential that is constructed only from the chargeneutral condition of the Wolf method without potential damping. We also show that three simulation systems, in which involve liquid sodiumchloride, TIP3P water, and a charged protein in explicit waters with neutralized ions using the new potential, provide accurate statistical and dielectric properties when compared with the particle mesh Ewald method.

Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: Application to the ππ*/nπ* internal conversion in thymine
View Description Hide DescriptionWe face with the general problem of defining a reduced number of effective collective coordinates to describe accurately the shorttime nonadiabaticdynamics of large semirigid systems, amenable to a description in terms of coupled harmonic potential energy surfaces. We present a numeric iterative protocol to define a hierarchical representation of the Hamiltonian taking into account both linear and quadratic intra and interstate couplings (QVC, quadratic vibronic coupling model), thus generalizing the method introduced recently in the literature [E. Gindensperger, H. Köppel, and L. S. Cederbaum, J. Chem. Phys.126, 034106 (2007)]10.1063/1.2426342 for the linear vibronic coupling (LVC) model. This improvement allows to take into account the effect of harmonic frequency changes and Duschinsky mixings among the different electronic states, providing a route to upgrade the models for nonadiabatic harmonic systems to those nowadays routinely used for the simulation of vibronic spectra of adiabatic systems (negligible nonadiabatic couplings). We apply our method to the study of ππ* → nπ* internal conversion in thymine, analysing the differences in LVC and QVC predictions both for the absorptionspectrum and the dynamics of electronic populations.

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters
View Description Hide DescriptionWe present a detailed study of the energetics of waterclusters (H_{2}O)_{ n } with n ⩽ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory(DFT) with well converged coupledcluster benchmarks. We use the manybody decomposition of the total energy to classify the errors of DMC and DFT into 1body, 2body and beyond2body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1 and 2body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond2body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.

Complete nuclear motion Hamiltonian in the irreducible normal mode tensor operator formalism for the methane molecule
View Description Hide DescriptionA rovibrational model based on the normalmode complete nuclear Hamiltonian is applied to methane using our recent potential energy surface [A. V. Nikitin, M. Rey, and Vl. G. Tyuterev, Chem. Phys. Lett.501, 179 (2011)10.1016/j.cplett.2010.11.008]. The kinetic energy operator and the potential energy function are expanded in power series to which a new truncationreduction technique is applied. The vibrationrotation Hamiltonian is transformed systematically to a full symmetrized form using irreducible tensor operators. Each term of the Hamiltonian expansion can be thus cast in the tensor form whatever the order of the development. This allows to take full advantage of the symmetry properties for doubly and triply degenerate vibrations and vibrationrotation states. We apply this model to variational computations of energy levels for ^{12}CH_{4}, ^{13}CH_{4}, and ^{12}CD_{4}.

The dispersion interaction between quantum mechanics and effective fragment potential molecules
View Description Hide DescriptionA method for calculating the dispersion energy between molecules modeled with the general effective fragment potential (EFP2) method and those modeled using a full quantum mechanics (QM) method, e.g., HartreeFock (HF) or secondorder perturbation theory, is presented. C _{6}dispersion coefficients are calculated for pairs of orbitals using dynamic polarizabilities from the EFP2 portion, and dipole integrals and orbital energies from the QM portion of the system. Dividing by the sixth power of the distance between localized molecular orbital centroids yields the first term in the commonly employed London series expansion. A C _{8} term is estimated from the C _{6} term to achieve closer agreement with symmetry adapted perturbation theory values. Two damping functions for the dispersion energy are evaluated. By using terms that are already computed during an ordinary HF or EFP2 calculation, the new method enables accurate and extremely rapid evaluation of the dispersioninteraction between EFP2 and QM molecules.

Local relativistic exact decoupling
View Description Hide DescriptionWe present a systematic hierarchy of approximations for local exact decoupling of fourcomponent quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic blockdiagonal part of the Hamiltonian. Systematically, offdiagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exactdecoupling transformation—called local approximation to the unitary decoupling transformation (DLU)—provides an excellent local approximation for any relativistic exactdecoupling approach. Its orderN ^{2} scaling can be further reduced to linear scaling by employing a neighboringatomicblocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a welldefined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic blockdiagonal entries in the Hamiltonian—denoted diagonal local approximation to the Hamiltonian (DLH) in this paper—introduces an error that is on the order of the error of secondorder Douglas–Kroll–Hess (i.e., DKH2) when compared with exactdecoupling results. Hence, the local DLH approximation would be pointless in an exactdecoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations for which ultimate accuracy is not the major concern.

Deperturbative corrections for chargestabilized double ionization potential equationofmotion coupledcluster method
View Description Hide DescriptionCharge stabilization improves the numeric performance of double ionization potential equationofmotion (EOMDIP) method when using unstable (autoionizing) dianion references. However, the stabilization potential introduces an undesirable perturbation to the target states’ energies. Here we introduce and benchmark two approaches for removing the perturbation caused by the stabilization. The benchmark calculations of excitation energies in selected diradicals illustrate that the socalled core correction based on evaluating the perturbation in a small basis set is robust and yields reliable EOMDIP values, i.e., the errors of 0.0–0.3 eV against a similarlevel coupledcluster approach.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dynamical (e,2e) studies of tetrahydrofurfuryl alcohol
View Description Hide DescriptionCross section data for electron scattering from DNA are important for modelling radiation damage in biological systems. Triply differential cross sections for the electron impact ionization of the highest occupied outer valence orbital of tetrahydrofurfuryl alcohol, which can be considered as an analogue to the deoxyribose backbone molecule in DNA, have been measured using the (e,2e) technique. The measurements have been performed with coplanar asymmetric kinematics at an incident electron energy of 250 eV, an ejected electron energy of 20 eV, and at scattered electron angles of −5°, −10°, and −15°. Experimental results are compared with corresponding theoretical calculations performed using the molecular 3body distorted wave model. Some important differences are observed between the experiment and calculations.

Prediction of the existence of the N_{2}H^{−} molecular anion
View Description Hide DescriptionWe predict the existence of the N_{2}H^{−} anion from first principle calculations. We present the threedimensional potential energy surface and the bound states of the N_{2}H^{−}/D^{−} van der Waals anion. The electronic calculations were performed using stateoftheart ab initio methods and the nuclear motions were solved using a quantum closecoupling scattering theory. A Tshaped equilibrium structure was found, with a well depth of 349.1 cm^{−1}, where 18 bound states have been located for N_{2}H^{−} and 25 for N_{2}D^{−} for total angular momentumJ = 0. We also present the absorption spectra of the N_{2}H^{−} complex. This anion could be formed after low energy collisions between N_{2} and H^{−} through radiative association. The importance of this prediction in astrophysics and the possible use of N_{2}H^{−} as a tracer of N_{2} and H^{−} in the interstellar medium is discussed.

Ab initio calculations of the lowest electronic states in the CuNO system
View Description Hide DescriptionThe lowest singlet and triplet electronic levels of the A′ and A″ symmetry species of the neutral coppernitrosyl (CuNO) system are calculated by ab initio methods at the multireference configuration interaction (MRCI) level of theory with single and double excitations, and at the coupled cluster level of theory with both perturbational (CCSD(T)) and full inclusion of triple excitations (CCSDT). Experimental data are difficult to obtain, hence the importance of carrying out calculations as accurate as possible to address the structure and dynamics of this system. This paper aims at validating a theoretical protocol to develop global potential energy surfaces for transition metal nitrosyl complexes. For the MRCI calculations, the comparison of level energies at linear structures and their values from and symmetry restricted calculations has allowed to obtain clear settings regarding atomic basis sizes, active orbital spaces and roots obtained at the multiconfigurational selfconsistent field (MCSCF) level of theory. It is shown that a complete active space involving 18 valence electrons, 11 molecular orbitals and the prior determination of 12 roots in the MCSCF calculation is needed for overall qualitatively correct results from the MRCI calculations. Atomic basis sets of the valence triplezeta type are sufficient. The present calculations yield a bound singlet A′ ground state for CuNO. The CCSD(T) calculations give a quantitatively more reliable account of electronic correlation close to equilibrium, while the MRCI energies allow to ensure the qualitative assessment needed for global potential energy surfaces. Relativistic coupled cluster calculations using the DouglasKrollHess Hamiltonian yield a dissociation energy of CuNO into Cu and NO to be (59 ± 5) kJ mol^{−1} ((4940 ± 400) hc cm^{−1}). Favorable comparison is made with some of previous theoretical results and a few known experimental data.

Binary and ternary recombination of para and ortho with electrons: State selective study at 77–200 K
View Description Hide DescriptionMeasurements in afterglow plasmas with spectroscopically determined relative abundances of ions in the paranuclear and orthonuclear spin states provide clear evidence that at low temperatures (77–200 K) para ions recombine significantly faster with electrons than ions in the ortho state, in agreement with a recent theoretical prediction. The cavity ringdown absorption spectroscopy used here provides an in situ determination of the para/ortho abundance ratio and yields additional information on the translational and rotational temperatures of the recombining ions. The results show that recombination with electrons occurs by both binary recombination and thirdbody (helium) assisted recombination, and that both the twobody and threebody rate coefficients depend on the nuclear spin states. Electronstabilized (collisionalradiative) recombination appears to make only a small contribution.

From strong van der Waals complexes to hydrogen bonding: From CO⋯H_{2}O to CS⋯H_{2}O and SiO⋯H_{2}O complexes
View Description Hide DescriptionStructures and interactionenergies of complexes valence isoelectronic to the important CO⋯H_{2}O complex, namely SiO⋯H_{2}O and CS⋯H_{2}O, have been studied for the first time using highlevel ab initio methods. Although CO, SiO, and CS are valence isoelectronic, the structures of their complexes with water differ significantly, owing partially to their widely varied dipole moments. The predicted dissociation energies D_{0} are 1.8 (CO⋯H_{2}O), 2.7 (CS⋯H_{2}O), and 4.9 (SiO⋯H_{2}O) kcal/mol. The implications of these results have been examined in light of the dipole moments of the separate moieties and current concepts of hydrogen bonding. It is hoped that the present results will spark additional interest in these complexes and in the general noncovalent paradigms they represent.

Ab initio determination of the ionization potentials of water clusters (H_{2}O)_{ n } (n = 2−6)
View Description Hide DescriptionHighlevel quantumchemical ab initiocoupledcluster and multiconfigurational perturbation methods have been used to compute the vertical and adiabatic ionization potentials of several water clusters: dimer, trimer, tetramer, pentamer, hexamer book, hexamer ring, hexamer cage, and hexamer prism. The present results establish reference values at a level not reported before for these systems, calibrating different computational strategies and helping to discard less reliable theoretical and experimental data. The systematic study with the increasing size of the water cluster allows obtaining some clues on the structure and reductive properties of liquid water.

The I_{2} dissociation mechanisms in the chemical oxygeniodine laser revisited
View Description Hide DescriptionThe recently suggested mechanism of I_{2}dissociation in the chemical oxygeniodine laser (COIL) [K. Waichman, B. D. Barmashenko, and S. Rosenwaks, J. Appl. Phys.106, 063108 (2009)10.1063/1.3213380; K. Waichman, B. D. Barmashenko, and S. Rosenwaks, J. Chem. Phys.133, 084301 (2010)]10.1063/1.3480397 was largely based on the suggestion of V. N. Azyazov, S. Yu. Pichugin, and M. C. Heaven [J. Chem. Phys.130, 104306 (2009)]10.1063/1.3081454 that the vibrational population of O_{2}(a) produced in the chemical generator is high enough to play an essential role in the dissociation. The results of model calculations based on this mechanism agreed very well with measurements of the small signal gain g, I_{2}dissociation fraction F, and temperature T in the COIL. This mechanism is here revisited, following the recent experiments of M. V. Zagidullin [Quantum Electron.40, 794 (2010)]10.1070/QE2010v040n09ABEH014357 where the observed low population of O_{2}(b, v = 1) led to the conclusion that the vibrational population of O_{2}(a) at the outlet of the generator is close to thermal equilibrium value. This value corresponds to a very small probability, ∼0.05, of O_{2}(a) energy pooling to the states O_{2}(X,a,b, v > 0). We show that the dissociation mechanism can reproduce the experimentally observed values of g, F, and T in the COIL only if most of the energy released in the processes of O_{2}(a) energy pooling and O_{2}(b) quenching by H_{2}O ends up as vibrational energy of the products, O_{2}(X,a,b), where the vibrational states v = 2 and 3 are significantly populated. We discuss possible reasons for the differences in the suggested vibrational population and explain how these differences can be reconciled.

Stark coefficients for highly excited rovibrational states of H_{2}O
View Description Hide DescriptionQuantum beatspectroscopy is combined with tripleresonance vibrational overtone excitation to measure the Stark coefficients (SCs) of the water molecule for 28 rovibrational levels lying from 27 600 to 41 000 cm^{−1}. These data provide a stringent test for assessing the accuracy of the available potential energy surfaces (PESs) and dipole momentsurfaces (DMSs) of this benchmark molecule in this energy region, which is inaccessible by direct absorption. SCs, calculated using the combination of a high accuracy, spectroscopically determined PES and a recent ab initio DMS, are within the 1% accuracy of available experimental data for levels below 25 000 cm^{−1}, and within 4.5% for coefficients associated with levels up to 35 000 cm^{−1}. However, the error in the computed coefficients is over 60% for the very high rovibrational states lying just below the lowest dissociation threshold, due, it seems, to lack of a high accuracy PES in this region. The comparative analysis suggests further steps, which may bring the theoretical predictions closer to the experimental accuracy.

Accurate theoretical study of PS^{q} (q = 0,+1,−1) in the gas phase
View Description Hide DescriptionHighly correlated ab initio methods were used in order to generate the potential energy curves and spinorbit couplings of electronic ground and excited states of PS and PS^{+}. We also computed those of the bound parts of the electronic states of the PS^{−} anion. We used standard coupled cluster CCSD(T) level with augmented correlationconsistentbasis sets, internally contacted multireference configuration interaction, and the newly developed CCSD(T)F12 methods in connection with the explicitly correlated basis sets. Corevalence correction and scalar relativistic effects were examined. Our data consist of a set of spectroscopic parameters (equilibrium geometries, harmonic vibrational frequencies, rotational constants, spinorbit, and spinspin constants), adiabatic ionization energies, and electron affinities. For the low laying electronic states, our calculations are consistent with previous works whereas the high excited states present rather different shapes. Based on these new computations, the earlier ultraviolet bands of PS and PS^{+} were reassigned. For PS^{−} and in addition to the already known anionic three bound electronic states (i.e., X^{3}Σ^{−}, ^{1}Δ, and 1^{1}Σ^{+}), our calculations show that the ^{1}Σ^{−}, ^{3}Σ^{+}, and the ^{3}Δ states are energetically below their quartet parent neutral state (a^{4}Π). The depletion of the J = 3 component of PS^{−}(^{3}Δ) will mainly occur via weak interactions with the electron continuum wave.

The microwave and millimeter spectrum of ZnCCH ( ^{2}Σ^{+}): A new zinccontaining free radical
View Description Hide DescriptionThe pure rotational spectrum of the ZnCCH ( ^{2}Σ^{+}) radical has been measured using Fourier transform microwave (FTMW) and millimeter directabsorption methods in the frequency range of 7–260 GHz. This work is the first study of ZnCCH by any type of spectroscopic technique. In the FTMW system, the radical was synthesized in a mixture of zinc vapor and 0.05% acetylene in argon, using a discharge assisted laser ablation source. In the millimeterwave spectrometer, the molecule was created from the reaction of zinc vapor, produced in a Broidatype oven, with pure acetylene in a dc discharge. Thirteen rotational transitions were recorded for the main species, ^{64}ZnCCH, and between 4 and 10 for the ^{66}ZnCCH, ^{68}ZnCCH, ^{64}ZnCCD, and ^{64}Zn^{13}C^{13}CH isotopologues. The fine structure doublets were observed in all the data, and in the FTMW spectra, hydrogen, deuterium, and carbon13 hyperfine splittings were resolved. The data have been analyzed with a ^{2}Σ Hamiltonian, and rotational, spinrotation, and H, D, and ^{13}C hyperfine parameters have been established for this radical. From the rotational constants, an r _{m} ^{(1)} structure was determined with r _{ZnC} = 1.9083 Å, r _{CC} = 1.2313 Å, and r _{CH} = 1.0508 Å. The geometry suggests that ZnCCH is primarily a covalent species with the zinc atom singly bonded to the C≡C—H moiety. This result is consistent with the hyperfine parameters, which suggest that the unpaired electron is localized on the zinc nucleus. The spinrotation constant indicates that an excited ^{2}Π state may exist ∼19 000 cm^{−1} in energy above the ground state.

Theoretical study of the spectroscopically relevant parameters for the detection of HNP^{q} and HPN^{q} (q = 0, +1, −1) in the gas phase
View Description Hide DescriptionHigh level ab initio electronic structure calculations at different levels of theory have been performed on HNP and HPN neutrals, anions, and cations. This includes standard coupled cluster CCSD(T) level with augmented correlationconsistent basis sets, internally contacted multireference configuration interaction, and the newly developed CCSD(T)F12 methods in connection with the explicitly correlated basis sets. Core–valence correction and scalar relativistic effects were examined. We present optimized equilibrium geometries, harmonic vibrational frequencies, rotational constants, adiabatic ionization energies, electron affinities, vertical detachment energies, and relative energies. In addition, the threedimensional potential energy surfaces of HNP^{−1,0,+1} and of HPN^{−1,0,+1} were generated at the (R)CCSD(T)F12b/ccpVTZF12 level. The anharmonic terms and fundamentals were derived using second order perturbation theory. For HNP, our best estimate for the adiabatic ionization energy is 7.31 eV, for the adiabatic electron affinity is 0.47 eV. The higher energy isomer, HPN, is 23.23 kcal/mol above HNP. HPN possesses a rather large adiabatic electron affinity of 1.62 eV. The intramolecular isomerization pathways were computed. Our calculations show that HNP^{−} to HPN^{−} reaction is subject to electron detachment.