Volume 138, Issue 7, 21 February 2013
 ARTICLES

 Theoretical Methods and Algorithms

Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers
View Description Hide DescriptionA direct method (DΔMBPT(2)) to calculate secondorder ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The ΔMBPT(2) method is defined as the correlated extension of the ΔHF method. Energy differences are obtained by integrating the energy derivative with respect to occupation numbers over the appropriate parameter range. This is made possible by writing the secondorder energy as a function of the occupation numbers. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the DΔMBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the DΔMBPT(2) method for IPs and EAs to a secondorder approximation of the effective Fockspace coupledcluster Hamiltonian and a secondorder electron propagator method. We also discuss the connection between the DΔMBPT(2) method for excitation energies and the CISMP2 method. Finally, as a proof of principle, we apply our method to calculate ionization potentials and excitation energies of some small molecules. For IPs, the ΔMBPT(2) results compare well to the secondorder solution of the Dyson equation. For excitation energies, the deviation from equation of motion coupled cluster singles and doubles increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the ΔMBPT(2) values. Most importantly, relaxation beyond the HartreeFock level is significant and needs to be included in future research.

Radial correlation effects on interconfigurational excitations at the end of the lanthanide series: A restricted active space second order perturbation study of Yb^{2+} and SrCl_{2}:Yb^{2+}
View Description Hide DescriptionAt the end of the lanthanide series, 4f → 5d and other interconfigurational transitions, in which one electron is excited from a tight 4f orbital to a much more diffuse one, occur with a break of many ff pairs, which make the electron correlation effects dominant. For instance, the large energy gap of 25 000 cm^{−1} (∼29 500 cm^{−1} without spinorbit coupling) above the 4f ^{14} ground state of the SrCl_{2}:Yb^{2+} material is mostly due to electron correlation. In effect, a minimal multiconfigurational restricted active space (RASSCF) calculation that includes only the 4f ^{14} ground and 4f ^{13}5d and 4f ^{13}6s openshell excited configurations gives a very small gap (5400 cm^{−1}), whereas the correlation corrections to the 4f ^{14} → 4f ^{13}5d(e _{ g }) transition energies at the second order perturbation theory (RASPT2) level are very large: 35 599 ± 439 cm^{−1}, in average, for all excited states. These corrections are too large to be accurate at second order perturbation level. When a second fshell is also included in the active space and single and double excitations to the 5d, 6s, and 5f shells are treated variationally, the (extended) RASSCF energy gap above the ground state and the electronic transitions increase by 22 038 ± 120 cm^{−1} and the RASPT2 correlation energy corrections become small (−721 ± 571 cm^{−1}), as it is desirable for a second order perturbation. A comparative analysis of both RASPT2 results reveals that the lack of the second fshell accounts for 12 700 cm^{−1} of the 14 223 ± 80 cm^{−1} overestimation of interconfigurational transitions energies by the minimal RASPT2 calculation, which indicates an inaccurate calculation of the differential radial correlation between the 4f ^{14} and 4f ^{13}5d configurations by second order perturbation theory. In order to establish practical and accurate procedures for the calculation of 4f → 5d and other interconfigurational transitions at the end of the lanthanide series, the above and other RASSCF/RASPT2 calculations on the ionization potential of Yb^{2+} in gas phase and in SrCl_{2} have been benchmarked in this paper against coupled cluster (coupled cluster singles and doubles and triples ) calculations, and RASSCF/RASPT2 calculations on the absorption spectrum of SrCl_{2}:Yb^{2+} have been compared with experiment. The results support that variational calculation of SD 4f → 5f excitations prior to RASPT2 calculations can be a realistic, accurate, and feasible choice to model radial correlation effects at the end of the lanthanide series.

Benchmarks of improved complete basis set extrapolation schemes designed for standard CCSD(T) atomization energies
View Description Hide DescriptionSimple modifications of complete basis set extrapolation formulas chosen from the literature are examined with respect to their abilities to reproduce a diverse set of 183 reference atomization energies derived primarily from very large basis set standard, frozen core coupledcluster singles, doubles plus perturbative triples (CCSD(T)) with the augccpVnZ basis sets. This reference set was augmented with a few larger chemical systems treated with explicitly correlated CCSD(T)F12b using a quadruple zeta quality basis set followed by extrapolation to complete basis set limit. Tuning the extrapolation formula parameters for the present reference set resulted in substantial reductions in the error metrics. In the case of the best performing approach, the aVnZ extrapolated results are equivalent to or better than results obtained from raw aV(n + 3)Z basis set calculations. To the extent this behavior holds for molecules outside the reference set, it represents an improvement of at least one basis set level over the original formulations and a further significant reduction in the amount of computer time needed to accurately approximate the basis set limit.

Rigorously extensive orbitalinvariant renormalized perturbative triples corrections from quasivariational coupled cluster theory
View Description Hide DescriptionWe show that, by making use of the linked tensor objects inherent to the approach, Orbitaloptimised QuasiVariational Coupled Cluster Theory (OQVCCD) leads naturally to a computationallytrivial, rigorously extensive, and orbitalinvariant renormalization of the standard (T) correction for the perturbative inclusion of the effects of connected triple excitations. The resulting prototype method, renormalized perturbative triple OQVCCD (ROQVCCD(T)), is demonstrated to predict potential energy curves for single bondbreaking processes of significantly higher accuracy than OQVCCD with the standard perturbative tripleexcitation correction (OQVCCD(T)) itself, and to be in good numerical correspondence with the existing renormalized (RCCSD(T)) and completely renormalized (CRCCSD(T)) coupledcluster singles doubles triples methods, while continuing to provide descriptions of multiple bondbreaking processes of OQVCCD(T) quality.

Magnetohydrodynamic motion of a colloidal sphere with selfelectrochemical surface reactions in a spherical cavity
View Description Hide DescriptionAn analytical study is presented for the magneticfieldinduced motion of a colloidal sphere with spontaneous electrochemical reactions on its surface situated at the center of a spherical cavity filled with an electrolyte solution at the quasisteady state. The zeta potential associated with the particle surface may have an arbitrary distribution, whereas the electric double layers adjoining the particle and cavity surfaces are taken to be thin relative to the particle size and the spacing between the solid surfaces. The electric current and magnetic flux density distributions are solved for the particle and fluid phases of arbitrary electric conductivities and magnetic permeabilities. Applying a generalized reciprocal theorem to the Stokes equations with a Lorentz force term resulting from these density distributions for the fluid motion, we obtain explicit formulas for the translational and angular velocities of the colloidal sphere valid for all values of the particletocavity size ratio. The particle velocities decrease monotonically with an increase in this size ratio. For the limiting case of an infinitely large cavity, our result reduces to the relevant solution for an unconfined spherical particle. The boundary effect on the movement of the particle with interfacial selfelectrochemical reactions induced by the magnetohydrodynamic force is equivalent to that in sedimentation and much stronger than that in general phoretic motions.

Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuationdissipation theorem
View Description Hide DescriptionInteratomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuationdissipation (ACFD) theorem, an exact expression for the electronic exchangecorrelation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the secondorder expansion of the ACFD formula upon invoking the randomphase approximation (RPA) or the fullpotential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipoledipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFDRPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the manybody dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a shortrange screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

Molecular electrostatic potential at the atomic sites in the effective core potential approximation
View Description Hide DescriptionConsidering calculations of the molecular electrostatic potential at the atomic sites (MEP@AS) in the presence of effective core potentials (ECP), we found that the consequent use of the definition of MEP@AS based on the energy derivative with respect to nuclear charge leads to a formula that differs by one term from the result of simple application of Coulomb's law. We have developed a general method to analytically treat derivatives of ECP with respect to nuclear charge. Benchmarking calculations performed on a set of simple molecules show that our formula leads to a systematic decrease in the error connected with the introduction of ECP when compared to allelectron results. Because of a straightforward implementation and relatively low costs of the developed procedure we suggest to use it by default.

ACKS2: Atomcondensed KohnSham DFT approximated to second order
View Description Hide DescriptionA new polarizable force field (PFF), namely atomcondensed KohnSham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from KohnSham density functional theory (KSDFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the KohnSham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc.108, 4315 (Year: 1986)]10.1021/ja00275a013 in which two major EEM shortcomings are fixed: ACKS2 predicts a linear sizedependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atomsinmolecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.

Density functionals for static, dynamical, and strong correlation
View Description Hide DescriptionIn this work, our exactexchangebased static + dynamical correlation density functional[A. D. Becke, J. Chem. Phys.122, 064101 (Year: 2005)]10.1063/1.1844493 is generalized to include “strong” correlation, i.e., accurate computations on dissociating chemical systems without breaking space or spin symmetries and without using multideterminantal reference states. Also, we introduce a strongcorrelation benchmark set composed of space and spinsymmetrized openshell atoms on which the generalized functional is tested. Initial results are very promising.

Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models
View Description Hide DescriptionSensitivity analysis is a powerful tool in determining parameters to which the system output is most responsive, in assessing robustness of the system to extreme circumstances or unusual environmental conditions, in identifying rate limiting pathways as a candidate for drug delivery, and in parameter estimation for calculating the Hessian of the objective function. Anderson [SIAM J. Numer. Anal.50, 2237 (Year: 2012)]10.1137/110849079 shows the advantages of the newly developed coupled finite difference (CFD) estimator over the common reaction path (CRP) [M. Rathinam, P. W. Sheppard, and M. Khammash, J. Chem. Phys.132, 034103 (Year: 2010)]10.1063/1.3280166 estimator. In this paper, we demonstrate the superiority of the CFD estimator over the common random number (CRN) estimator in a number of scenarios not considered previously in the literature, including the sensitivity of a negative log likelihood function for parameter estimation, the sensitivity of being in a rare state, and a sensitivity with fast fluctuating species. In all examples considered, the superiority of CFD over CRN is demonstrated. We also provide an example in which the CRN method is superior to the CRP method, something not previously observed in the literature. These examples, along with Anderson's results, lead to the conclusion that CFD is currently the best estimator in the class of finite difference estimators of stochastic chemical kinetic models.

Openshell pair interaction energy decomposition analysis (PIEDA): Formulation and application to the hydrogen abstraction in tripeptides
View Description Hide DescriptionAn openshell extension of the pair interaction energy decomposition analysis (PIEDA) within the framework of the fragment molecular orbital (FMO) method is developed. The openshell PIEDA method allows the analysis of inter and intramolecular interactions in terms of electrostatic, exchangerepulsion, chargetransfer, dispersion, and optional polarization energies for molecular systems with a radical or highspin fragment. Taking into account the low computational cost and scalability of the FMO and PIEDA methods, the new scheme provides a means to characterize the stabilization of radical and openshell sites in biologically relevant species. The openshell PIEDA is applied to the characterization of intramolecular interactions in capped trialanine upon hydrogen abstraction (HA) at various sites on the peptide. Hydrogen abstraction reaction is the first step in the oxidative pathway initiated by reactive oxygen or nitrogen species, associated with oxidative stress. It is found that HA results in significant geometrical reorganization of the trialanine peptide. Depending on the HA site, terminal interactions in the radical fold conformers may become weaker or stronger compared to the parent molecule, and often change the character of the noncovalent bonding from amide stacking to hydrogen bonding.

Exploring the role of internal friction in the dynamics of unfolded proteins using simple polymer models
View Description Hide DescriptionRecent experiments showed that the reconfiguration dynamics of unfolded proteins are often adequately described by simple polymer models. In particular, the Rouse model with internal friction (RIF) captures internal friction effects as observed in singlemolecule fluorescence correlation spectroscopy (FCS) studies of a number of proteins. Here we use RIF, and its nonfree draining analog, Zimm model with internal friction, to explore the effect of internal friction on the rate with which intramolecular contacts can be formed within the unfolded chain. Unlike the reconfiguration times inferred from FCS experiments, which depend linearly on the solvent viscosity, the first passage times to form intramolecular contacts are shown to display a more complex viscosity dependence. We further describe scaling relationships obeyed by contact formation times in the limits of high and low internal friction. Our findings provide experimentally testable predictions that can serve as a framework for the analysis of future studies of contact formation in proteins.
 Atoms, Molecules, and Clusters

Total, elastic, and inelastic cross sections for positron and electron collisions with tetrahydrofuran
View Description Hide DescriptionWe present total, elastic, and inelastic cross sections for positron and electron scattering from tetrahydrofuran (THF) in the energy range between 1 and 5000 eV. Total cross sections (TCS), positronium formation cross sections, the summed inelastic integral cross sections (ICS) for electronic excitations and direct ionization, as well as elastic differential cross sections (DCS) at selected incident energies, have been measured for positron collisions with THF. The positron beam used to carry out these experiments had an energy resolution in the range 40–100 meV (fullwidth at halfmaximum). We also present TCS results for positron and electron scattering from THF computed within the independent atom model using the screening corrected additivity rule approach. In addition, we calculated positronimpact elastic DCS and the sum over all inelastic ICS (except rotations and vibrations). While our integral and differential positron cross sections are the first of their kind, we compare our TCS with previous literature values for this species. We also provide a comparison between positron and electronimpact cross sections, in order to uncover any differences or similarities in the scattering dynamics with these two different projectiles.

Experimental and theoretical cross sections for positron collisions with 3hydroxytetrahydrofuran
View Description Hide DescriptionCross section results from a joint experimental and theoretical investigation into positron scattering from 3hydroxytetrahydrofuran (3HTHF) are presented. Total and positronium (Ps) formation cross sections have been measured from 1 to 190 eV using the positron beamline at the Australian National University, which has an energy resolution between 60 and 100 meV. The total cross section (TCS) and the elastic and total inelastic integral cross sections in the energy range between 1 and 1000 eV have been computed within the Independent Atom Model using the Screening Corrected Additivity Rule approach. In addition, we have calculated elastic differential cross sections at selected incident energies. Our computations represent the first theoretical results reported for this target species, while our measured Ps formation cross sections are also novel. Comparison of the present TCS with the previous results from the University of Trento shows a good level of agreement at the lowest energies. We also provide a comparison between the present cross sections for 3HTHF and those from our earlier study on the parent molecule tetrahydrofuran.

Classical dynamics of stateresolved hyperthermal O(^{3}P) + H_{2}O(^{1}A_{1}) collisions
View Description Hide DescriptionClassical dynamics calculations are performed for O(^{3}P) + H_{2}O(^{1}A_{1}) collisions from 2 to 10 km s^{‑1} (4.1–101.3 kcal mol^{−1}), focusing on product internal energies. Several methods are used to produce rovibrationally stateresolved product cross sections and to enforce zeropoint maintenance from analysis of the classical trajectories. Two potential energy surfaces are used: (1) a recently developed set of global reactive surfaces for the three lowest triplet states which model OH formation, H elimination to make H + OOH, Oatom exchange, and collisional excitation and (2) a nonreactive surface used in past classical and quantum collision studies. Comparisons to these previous studies suggest that for H_{2}O vibrational excitation, classical dynamics which include Gaussian binning procedures and/or selected zeropoint maintenance algorithms can produce results which approximate quantum scattering cross sections fairly well. Without these procedures, the classical cross sections can be many orders of magnitude greater than the quantum cross sections for exciting the bending vibration of H_{2}O, especially near threshold. The classical cross section overestimate is due to energy borrowing from stretching modes which dip below zeropoint values. For results on the reactive surfaces, the present calculations show that at higher velocities there is an unusually large amount of product internal excitation. For OOH, where 40% of available collision energy goes into internal motion, the excited product vibrational and rotational energy distributions are relatively flat and values of the OOH rotational angular momentum exceed J = 100. Other product channel distributions show an exponential falloff with energy consistent with an energy gap law. The present detailed distributions and cross sections can serve as a guide for future hyperthermal measurements of this system.

Coherent πelectron dynamics of (P)2,2′biphenol induced by ultrashort linearly polarized UV pulses: Angular momentum and ring current
View Description Hide DescriptionThe results of a theoretical investigation of coherent πelectron dynamics for nonplanar (P)2,2′biphenol induced by ultrashort linearly polarized UV pulses are presented. Expressions for the timedependent coherent angular momentum and ring current are derived by using the density matrix method. The time dependence of these coherences is determined by the offdiagonal density matrix element, which can be obtained by solving the coupled equations of motion of the electronicstate density matrix. Dephasing effects on coherent angular momentum and ring current are taken into account within the Markov approximation. The magnitudes of the electronic angular momentum and current are expressed as the sum of expectation values of the corresponding operators in the two phenol rings (L and R rings). Here, L (R) denotes the phenol ring in the left (right)hand side of (P)2,2′biphenol. We define the bond current between the nearest neighbor carbon atoms C_{ i } and C_{ j } as an electric current through a half plane perpendicular to the C_{ i }–C_{ j } bond. The bond current can be expressed in terms of the interatomic bond current. The interatomic bond current (bond current) depends on the position of the half plane on the bond and has the maximum value at the center. The coherent ring current in each ring is defined by averaging over the bond currents. Since (P)2,2′biphenol is nonplanar, the resultant angular momentum is not onedimensional. Simulations of the timedependent coherent angular momentum and ring current of (P)2,2′biphenol excited by ultrashort linearly polarized UV pulses are carried out using the molecular parameters obtained by the timedependent density functional theory (TDDFT) method. Oscillatory behaviors in the timedependent angular momentum (ring current), which can be called angular momentum (ring current) quantum beats, are classified by the symmetry of the coherent state, symmetric or antisymmetric. The bond current of the bridge bond linking the L and R rings is zero for the symmetric coherent state, while it is nonzero for the antisymmetric coherent state. The magnitudes of ring current and ring currentinduced magnetic field are also evaluated, and their possibility as a control parameter in ultrafast switching devices is discussed. The present results give a detailed description of the theoretical treatment reported in our previous paper [H. Mineo, M. Yamaki, Y. Teranish, M. Hayashi, S. H. Lin, and Y. Fujimura, J. Am. Chem. Soc.134, 14279 (Year: 2012)10.1021/ja3047848].

Characteristic oxygen Kedge circular dichroism spectra of amino acid films by improved measurement technique
View Description Hide DescriptionCircular dichroism (CD) spectroscopy in the soft xray energy region is a new tool to study the local structure of chiral materials. In this paper, we introduce a method to measure highquality CD spectra in the oxygen Kedge energy region. Characteristic CD spectra of thin films of the amino acids Ltyrosine and Laspartic acid are reported and compared with those of films of Lalanine and Lserine. The signals from the oxygen 1s → π* transitions of COO^{−}, which is a common moiety in these amino acids, reflect the local geometry of each amino acid.

Effect of geometrical orientation on the chargetransfer energetics of supramolecular (tetraphenyl)porphyrin/C_{60} dyads
View Description Hide DescriptionThe charge transfer (CT) excited state energies of donoracceptor (D/A) pairs determine the achievable opencircuit voltage of D/Abased organic solar cell devices. Changes in the relative orientation of donoracceptor pairs at the interface influence the frontier orbital energy levels, which impacts the dissociation of bound excitons at the D/Ainterface. We examine the effect of relative orientation on CT excited state energies of porphyrinfullerene dyads. The donors studied are base and Zntetraphenyl porphyrin coupled to C_{60} as the acceptor molecule in an endon configuration. We compare the energetics of a few lowlying CT states for the endon geometry to our previously calculated CT energetics of a cofacial orientation. The calculated CT excitation energies are larger for the endon orientation in comparison to the cofacial structure by about 0.7 eV, which primarily occurs due to a decrease in exciton binding energy in going from the cofacial to the endon orientation. Furthermore, changes in relative donoracceptor orientation have a larger impact on the CT energies than changes in donoracceptor distance.

Effect of length on the position of negative differential resistance and realization of multifunction in fused oligothiophenes based molecular device
View Description Hide DescriptionThe length modulation of electron transport properties for molecular devices based on fused oligothiophenes has been investigated theoretically using a combination of nonequilibrium Green's functions and firstprinciples density functional theory. The results show that the lengths of the molecules have a distinct influence on the position of negative differential resistance (NDR) of the molecular devices. By exploring the effect on transmission properties of substituent groups, hexathieno[3,2b:2′,3′d]thiophene with –NH_{2} and –NO_{2} substituents (model L) can be regard as a good candidate of multifunctional molecular device, which shows excellent rectifying performance (the largest rectification ration is 14.3 at 1.2 V) and clear NDR behavior (at 1.4 V).

Classical calculations of radiative association in absence of electronic transitions
View Description Hide DescriptionA formula for the cross section of radiative association where no electronic transitions take place is derived and tested for diatomic molecules. The approach is based on classical mechanics and therefore it is valid for direct, i.e., nonresonant, radiative association. For the formation of carbon monoxide (CO) and the cyano radical (CN), in the X ^{1}Σ^{+} and A ^{1}Π states, respectively, the treatment reproduces the baselines of the cross sections obtained using quantum mechanical perturbation theory. The method overestimates the formation cross section of potassium sodide (NaK) by about 8%. For the lower mass diatoms hydrogen fluoride (HF) and deuterium hydride (HD), the formula overestimates the cross sections by 12% and 60%, respectively. The formula can be used alone for estimates of radiative association rate constants, or in combination with BreitWigner theory to include resonance contributions.