Volume 140, Issue 1, 07 January 2014

Transitions in atoms and molecules provide an ideal test ground for constraining or detecting a possible variation of the fundamental constants of nature. In this perspective, we review molecular species that are of specific interest in the search for a drifting protontoelectron mass ratio μ. In particular, we outline the procedures that are used to calculate the sensitivity coefficients for transitions in these molecules and discuss current searches. These methods have led to a rate of change in μ bounded to 6 × 10^{−14}/yr from a laboratory experiment performed in the present epoch. On a cosmological time scale, the variation is limited to Δμ/μ < 10^{−5} for lookback times of 10–12× 10^{9} years and to Δμ/μ < 10^{−7} for lookback times of 7× 10^{9} years. The last result, obtained from highredshift observation of methanol, translates into /yr if a linear rate of change is assumed.
 PERSPECTIVES


Perspective: Tipping the scales: Search for drifting constants from molecular spectra
View Description Hide DescriptionTransitions in atoms and molecules provide an ideal test ground for constraining or detecting a possible variation of the fundamental constants of nature. In this perspective, we review molecular species that are of specific interest in the search for a drifting protontoelectron mass ratio μ. In particular, we outline the procedures that are used to calculate the sensitivity coefficients for transitions in these molecules and discuss current searches. These methods have led to a rate of change in μ bounded to 6 × 10^{−14}/yr from a laboratory experiment performed in the present epoch. On a cosmological time scale, the variation is limited to Δμ/μ < 10^{−5} for lookback times of 10–12× 10^{9} years and to Δμ/μ < 10^{−7} for lookback times of 7× 10^{9} years. The last result, obtained from highredshift observation of methanol, translates into /yr if a linear rate of change is assumed.
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 COMMUNICATIONS


Communication: Spectroscopic characterization of an alkyl substituted Criegee intermediate synCH_{3}CHOO through pure rotational transitions
View Description Hide DescriptionAn alkylsubstituted Criegee intermediate synCH3CHOO was detected in the gas phase through Fouriertransform microwave spectroscopy. Observed pure rotational transitions show a small splitting corresponding to the A/E components due to the threefold methyl internal rotation. The rotational constants and the barrier height of the hindered methyl rotation were determined to be A = 17 586.5295(15) MHz, B = 7133.4799(41) MHz, C = 5229.1704(40) MHz, and V 3 = 837.1(17) cm^{−1}. Highlevel ab initio calculations which reproduce the experimentally determined values well indicate that the inplane C–H bond in the methyl moiety is trans to the C–O bond, and other two protons are directed to the terminal oxygen atom for the most stable structure of synCH3CHOO. The torsional barrier of the methyl top is fairly large in synCH3CHOO, implying a significant interaction between the terminal oxygen and the protons of the methyl moiety, which may be responsible for the high production yields of the OH radical from energized alkylsubstituted Criegee intermediates.

Communication: The origin of rotational enhancement effect for the reaction of H_{2}O^{+} + H_{2} (D_{2})
View Description Hide DescriptionWe have measured the absolute integral cross sections (σ’s) for H3O^{+} formed by the reaction of rovibrationally selected H2O^{+}(X ^{2} B 1; v 1 ^{+} v 2 ^{+} v 3 ^{+} = 000; N ^{+} K a ^{+} K c ^{+} = 000, 111, and 211) ion with H2 at the centerofmass collision energy (E cm) range of 0.03–10.00 eV. The σ(000), σ(111), and σ(211) values thus obtained reveal rotational enhancements at low E cm < 0.50 eV, in agreement with the observation of the previous study of the H2O^{+}(X ^{2} B 1) + D2 reaction. This Communication presents important progress concerning the highlevel ab initio quantum calculation of the potential energy surface for the H2O^{+}(X ^{2} B 1) + H2 (D2) reactions, which has provided valuable insight into the origin of the rotational enhancement effect. Governed by the charge and dipoleinducedmultipole interactions, the calculation shows that H2 (D2) approaches the H end of H2O^{+}(X ^{2} B 1) in the long range, whereas chemical force in the short range favors the orientation of H2 (D2) toward the O side of H2O^{+}. The reorientation of H2O^{+} reactant ion facilitated by rotational excitation thus promotes the H2O^{+} + H2 (D2) reaction along the minimum energy pathway, rendering the observed rotational enhancement effects. The occurrence of this effect at low E cm indicates that the long range charge and dipoleinducedmultipole interactions of the colliding pair play a significant role in the dynamics of the exothermic H2O^{+} + H2 (D2) reactions.

Communication: Permanent dipoles contribute to electric polarization in chiral NMR spectra
View Description Hide DescriptionNuclear magnetic resonance spectroscopy is blind to chirality because the spectra of a molecule and its mirror image are identical unless the environment is chiral. However, precessing nuclear magnetic moments in chiral molecules in a strong magnetic field induce an electric polarization through the nuclear magnetic shielding polarizability. This effect is equal and opposite for a molecule and its mirror image but is small and has not yet been observed. It is shown that the permanent electric dipole moment of a chiral molecule is partially oriented through the antisymmetric part of the nuclear magnetic shielding tensor, causing the electric dipole to precess with the nuclear magnetic moment and producing a much larger temperaturedependent electric polarization with better prospects of detection.
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 ARTICLES

 Theoretical Methods and Algorithms

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches
View Description Hide DescriptionPerformance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a timedependent linear response APSG method (TDAPSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li2, BH, H2O, and CH2O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TDAPSG perform better in describing double excitations than ERPA due to inclusion of the socalled diagonal double elements. Analysis of the potential energy curves of Li2, BH, and H2O reveals that ERPA2 and TDAPSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSGbased methods approaches that of the timedependent HartreeFock method with the increase of the system size. A possibility of improving the accuracy of the TDAPSG method for single excitations by splitting the electronelectron interaction operator into the long and shortrange terms and employing density functionals to treat the latter is presented.

Canonical form of the HartreeFock orbitals in openshell systems
View Description Hide DescriptionThis work compares different approaches to deriving HartreeFock (HF) orbitals and orbital energies for openshell systems. We compare the basic HF equations underlying both the classic openshell HF methods, which are the restricted openshell HF (ROHF) and unrestricted HF (UHF) methods, and a number of the novel (amended) versions of these methods. The main attention is paid to a treatment of the validity of Brillouin's and Koopmans’ theorems in the amended versions. We show that these two theorems are fully obeyed only in the special (canonical) form of the ROHF method developed by Plakhutin et al. [J. Chem. Phys.125, 204110 (2006)] and by Davidson and Plakhutin [J. Chem. Phys.132, 184110 (2010)], while each of the amended UHF methods suffers from some deficiencies inherent to original UHF and ROHF methods. To compare the HF orbitals derived by different methods in two different forms – DODS (different orbitals for different spins) and SODS (the same orbitals for different spins), we develop the new ROHFDODS method which combines the use of DODS underlying amended UHF methods and the main advantage of the canonical ROHF method which is a fulfillment of the rigorous Koopmans’ conditions. The main result of this work is that the orbitals and orbital energies derived with the new ROHFDODS method appear identical to those derived with the canonical ROHF method based on the use of SODS. A discussion is presented of some related problems arising in openshell HF methods such as a violation of the Aufbau principle.

Infinite swapping in curved spaces
View Description Hide DescriptionWe develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys.135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.

Quantum Markovian master equation for scattering from surfaces
View Description Hide DescriptionWe propose a semiphenomenological Markovian Master equation for describing the quantum dynamics of atomsurface scattering. It embodies the Lindbladlike structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multiconfigurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.

Structural, vibrational, and quasiparticle band structure of 1,1diamino2,2dinitroethelene from ab initio calculations
View Description Hide DescriptionThe effects of pressure on the structural and vibrational properties of the layered molecular crystal 1,1diamino2,2dinitroethelene (FOX7) are explored by first principles calculations. We observe significant changes in the calculated structural properties with different corrections for treating van der Waals interactions to Density Functional Theory (DFT), as compared with standard DFT functionals. In particular, the calculated ground state lattice parameters, volume and bulk modulus obtained with Grimme's scheme, are found to agree well with experiments. The calculated vibrational frequencies demonstrate the dependence of the intra and intermolecular interactions on FOX7 under pressure. In addition, we also found a significant increment in the N–H...O hydrogen bond strength under compression. This is explained by the change in bond lengths between nitrogen, hydrogen, and oxygen atoms, as well as calculated IR spectra under pressure. Finally, the computed band gap is about 2.3 eV with generalized gradient approximation, and is enhanced to 5.1 eV with the GW approximation, which reveals the importance of performing quasiparticle calculations in high energy density materials.

Multilayer Potfit: An accurate potential representation for efficient highdimensional quantum dynamics
View Description Hide DescriptionThe multilayer multiconfiguration timedependent Hartree method (MLMCTDH) is a highly efficient scheme for studying the dynamics of highdimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system possesses a particular structure through which the multidimensional matrix elements can be computed efficiently. In the field of quantum molecular dynamics, the effective interaction between the atoms is often described by potential energy surfaces (PES), and it is necessary to fit such PES into the desired structure. For highdimensional systems, the current approaches for this fitting process either lead to fits that are too large to be practical, or their accuracy is difficult to predict and control. This article introduces multilayer Potfit (MLPF), a novel fitting scheme that results in a PES representation in the hierarchical tensor (HT) format. The scheme is based on the hierarchical singular value decomposition, which can yield a nearoptimal fit and give strict bounds for the obtained accuracy. Here, a recursive scheme for using the HTformat PES within MLMCTDH is derived, and theoretical estimates as well as a computational example show that the use of MLPF can reduce the numerical effort for MLMCTDH by orders of magnitude, compared to the traditionally used POTFIT representation of the PES. Moreover, it is shown that MLPF is especially beneficial for highaccuracy PES representations, and it turns out that MLPF leads to computational savings already for comparatively small systems with just four modes.

Cubicscaling algorithm and selfconsistent field for the randomphase approximation with secondorder screened exchange
View Description Hide DescriptionThe randomphase approximation with secondorder screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and it scales as operations and memory for n electrons. We derive a new algorithm that reduces its scaling to operations and memory using controlled approximations and a new selfconsistent field that approximates Brueckner coupledcluster doubles theory with RPA+SOSEX, referred to as Brueckner RPA theory. The algorithm comparably reduces the scaling of secondorder MøllerPlesset perturbation theory with smaller cost prefactors than RPA+SOSEX. Within a semiempirical model, we study H2 dissociation to test accuracy and H n rings to verify scaling.
 Advanced Experimental Techniques

Composite and shaped pulses for efficient and robust pumping of disconnected eigenstates in magnetic resonance
View Description Hide DescriptionHyperpolarization methods, which can enhance nuclear spin signals by orders of magnitude, open up important new opportunities in magnetic resonance. However, many of these applications are limited by spin lattice relaxation, which typically destroys the hyperpolarization in seconds. Significant lifetime enhancements have been found with “disconnected eigenstates” such as the singlet state between a pair of nearly equivalent spins, or the “singletsinglet” state involving two pairs of chemically equivalent spins; the challenge is to populate these states (for example, from thermal equilibrium magnetization or hyperpolarization) and to later recall the population into observable signal. Existing methods for populating these states are limited by either excess energy dissipation or high sensitivity to inhomogeneities. Here we overcome the limitations by extending recent work using continuouswave irradiation to include composite and adiabatic pulse excitations. Traditional composite and adiabatic pulses fail completely in this problem because the interactions driving the transitions are fundamentally different, but the new shapes we introduce can move population between accessible and disconnected eigenstates over a wide range of radiofrequency (RF) amplitudes and offsets while depositing insignificant amounts of power.
 Atoms, Molecules, and Clusters

Analysis of depolarization ratios of ClNO_{2} dissolved in methanol
View Description Hide DescriptionA detailed analysis of the resonance Raman depolarization ratio dispersion curve for the N–O symmetric stretch of nitryl chloride in methanol at excitation wavelengths spanning the D absorption band is presented. The depolarization ratios are modeled using the timedependent formalism for Raman scattering with contributions from two excited states (2^{1}A1 and 3^{1}B1), which are taken as linearly dissociative along the Cl–N coordinate. The analysis focuses on the interplay between different types of broadening revealing the importance of inhomogenous broadening in determining the relative contributions of the two electronic transitions. We find that the transition dipole moment (M) for 2^{1}A1 is greater than for 3^{1}B1, in agreement with gas phase calculations in the literature [A. Lesar, M. Hdoscek, M. Muhlhauser, and S. D. Peyerimhoff, Chem. Phys. Lett.383, 84 (2004)]. However, we find that the polarity of the solvent influences the excited state energetics, leading to a reversal in the ordering of these two states with 3^{1}B1 shifting to lower energies. Molecular dynamics simulations along with linear response and ab initio calculations support the evidence extracted from resonance Raman intensity analysis, providing insights on ClNO2 electronic structure, solvation effects in methanol, and the source of broadening, emphasizing the importance of a contribution from inhomogeneous linewidth.

Analysis of the nearedge Xrayabsorption finestructure of anthracene: A combined theoretical and experimental study
View Description Hide DescriptionThe nearedge fine structure of the carbon Kedge absorption spectrum of anthracene was measured and theoretically analyzed by density functional theory calculations implemented in the StoBe code. It is demonstrated that the consideration of electronic relaxation of excited states around localized core holes yields a significant improvement of the calculated excitation energies and reproduces the experimentally observed fine structure well. The detailed analysis of excitation spectra calculated for each symmetry inequivalent excitation center allows in particular to examine the influence of chemical shifts and core hole effects on the excitation energies. Moreover, the visualization of final states explains the large variations in the oscillator strength of various transitions as well as the nature of Rydbergstates that exhibit a notable density of states below the ionization potentials.

Reactions between cold methyl halide molecules and alkalimetal atoms
View Description Hide DescriptionWe investigate the potential energy surfaces and activation energies for reactions between methyl halide molecules CH3 X (X = F, Cl, Br, I) and alkalimetal atoms A (A = Li, Na, K, Rb) using highlevel ab initio calculations. We examine the anisotropy of each intermolecular potential energy surface (PES) and the mechanism and energetics of the only available exothermic reaction pathway, CH3 X + A → CH3 + AX. The region of the transition state is explored using twodimensional PES cuts and estimates of the activation energies are inferred. Nearly all combinations of methyl halide and alkalimetal atom have positive barrier heights, indicating that reactions at low temperatures will be slow.

A study of the bending motion in tetratomic molecules by the algebraic operator expansion method
View Description Hide DescriptionWe study the bending motion in the tetratomic molecules C2H2 ( ), C2H2 ( ^{1} A u ) transS 1, C2H2 ( ^{1} A 2) cisS 1, and ^{1} A 1 H2CO. We show that the algebraic operator expansion method with only linear terms comprised of the basic operators is able to describe the main features of the level energies in these molecules in terms of two (linear) or three (transbent, cisbent, and branched) parameters. By including quadratic terms, the rms deviation in comparison with experiment goes down to typically ∼10 cm^{−1} over the entire range of energy 0–6000 cm^{−1}. We determine the parameters by fitting the available data, and from these parameters we construct the algebraic potential functions. Our results are of particular interest in highenergy regions where spectra are very congested and conventional methods, forcefield expansions or Dunhamexpansions plus perturbations, are difficult to apply.
 Liquids, Glasses, and Crystals

Salting out the polar polymorph: Analysis by alchemical solvent transformation
View Description Hide DescriptionWe computationally examine how adding NaCl to an aqueous solution with α and γglycine nuclei alters the structure and interfacial energy of the nuclei. The polar γglycine nucleus in pure aqueous solution develops a melted layer of amorphous glycine around the nucleus. When NaCl is added, a double layer is formed that stabilizes the polar glycine polymorph and eliminates the surface melted layer. In contrast, the nonpolar αglycine nucleus is largely unaffected by the addition of NaCl. To quantify the stabilizing effect of NaCl on γglycine nuclei, we alchemically transform the aqueous glycine solution into a brine solution of glycine. The alchemical transformation is performed both with and without a nucleus in solution and for nuclei of αglycine and γglycine polymorphs. The calculations show that adding 80 mg/ml NaCl reduces the interfacial free energy of a γglycine nucleus by 7.7 mJ/m^{2} and increases the interfacial free energy of an αglycine nucleus by 3.1 mJ/m^{2}. Both results are consistent with experimental reports on nucleation rates which suggest: J(α, brine) < J(γ, brine) < J(α, water). For γglycine nuclei, DebyeHückel theory qualitatively, but not quantitatively, captures the effect of salt addition. Only the alchemical solvent transformation approach can predict the results for both polar and nonpolar polymorphs. The results suggest a general “salting out” strategy for obtaining polar polymorphs and also a general approach to computationally estimate the effects of solvent additives on interfacial free energies for nucleation.

Is there a third order phase transition for supercritical fluids?
View Description Hide DescriptionWe prove that according to Molecular Dynamics (MD) simulations of liquid mixtures of LennardJones (LJ) particles, there is no third order phase transition in the supercritical regime beyond Andrew's critical point. This result is in open contrast with recent theoretical studies and experiments which instead suggest not only its existence but also its universality regarding the chemical nature of the fluid. We argue that our results are solid enough to go beyond the limitations of MD and the generic character of LJ models, thus suggesting a rather smooth liquidvapor thermodynamic behavior of fluids in supercritical regime.

Designing heavy metal oxide glasses with threshold properties from network rigidity
View Description Hide DescriptionHere, we show that a new class of glasses composed of heavy metal oxides involving transition metals (V2O5–TeO2) can surprisingly be designed from very basic tools using topology and rigidity of their underlying molecular networks. When investigated as a function of composition, such glasses display abrupt changes in network packing and enthalpy of relaxation at T g , underscoring presence of flexible to rigid elastic phase transitions. We find that these elastic phases are fully consistent with polaronic nature of electronic conductivity at high V2O5 content. Such observations have new implications for designing electronic glasses which differ from the traditional amorphous electrolytes having only mobile ions as charge carriers.

Dielectric relaxation in ionic liquids: Role of ionion and iondipole interactions, and effects of heterogeneity
View Description Hide DescriptionA semimolecular theory for studying the dielectric relaxation (DR) dynamics in ionic liquids (ILs) has been developed here. The theory predicts triphasic relaxation of the generalized orientational correlation function in the collective limit. Relaxation process involves contributions from dipoledipole, iondipole, and ionion interactions. While the dipoledipole and ionion interactions dictate the predicted three relaxation time constants, the relaxation amplitudes are determined by dipoledipole, iondipole, and ionion interactions. The ionion interaction produces a time constant in the range of 51000μs which parallels with the conductivity dominated dielectric loss peak observed in broadband dielectric measurements of ILs. Analytical expressions for two time constants originating from dipolar interactions in ILs match exactly with those derived earlier for dipolar solvents. The theory explores relations among single particle rotational time, collective rotational time, and DR time for ILs. Use of molecular volume for the rotating dipolar ion of a given IL leads to a predicted DR time constant much larger than the slowest DR time constant measured in experiments. In contrast, similar consideration for dipolar liquids produces semiquantitative agreement between theory and experiments. This difference between ILs and common dipolar solvents has been understood in terms of extremely low effective rotational volume of dipolar ion, argued to arise from medium heterogeneity. Effective rotational volumes predicted by the present theory for ILs are in general agreement with estimates from experimental DR data and simulation results. Calculations at higher temperatures predict faster relaxation time constants reducing the difference between theory and experiments.