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This second paper in a series of two describes the chirped-pulse ice apparatus that permits the detection of buffer gas cooled molecules desorbed from an energetically processed ice using broadband mm-wave rotational spectroscopy. Here, we detail the lower ice stage developed to generate ices at 4 K, which can then undergo energetic processing via UV/VUV photons or high-energy electrons and which ultimately enter the gas phase via temperature-programmed desorption (TPD). Over the course of TPD, the lower ice stage is interfaced with a buffer gas cooling cell that allows for sensitive detection via chirped-pulse rotational spectroscopy in the 60–90 GHz regime. In addition to a detailed description of the ice component of this apparatus, we show proof-of-principle experiments demonstrating the detection of H2CO products formed through irradiation of neat methanol ices or 1:1 CO + CH4 mixed ices. [ABSTRACT FROM AUTHOR]

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the "ragged list") and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the "fixed sparsity pattern") for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising. [ABSTRACT FROM AUTHOR]

The Infrared (IR) and Raman spectra of various defects in silicon, containing both oxygen atoms (in the interstitial position, Oi) and a vacancy, are computed at the quantum mechanical level by using a periodic supercell approach based on a hybrid functional (B3LYP), an all-electron Gaussian-type basis set, and the Crystal code. The first of these defects is VO: the oxygen atom, twofold coordinated, saturates the unpaired electrons of two of the four carbon atoms on first neighbors of the vacancy. The two remaining unpaired electrons on the first neighbors of the vacancy can combine to give a triplet (Sz = 1) or a singlet (Sz = 0) state; both states are investigated for the neutral form of the defect, together with the doublet solution, the ground state of the negatively charged defect. Defects containing two, three, and four oxygen atoms, in conjunction with the vacancy V, are also investigated as reported in many experimental papers: VO2 and VOOi (two oxygen atoms inside the vacancy, or one in the vacancy and one in interstitial position between two Si atoms) and VO2Oi and VO22Oi (containing three and four oxygen atoms). This study integrates and complements a recent investigation referring to Oi defects [Gentile et al., J. Chem. Phys. 152, 054502 (2020)]. A general good agreement is observed between the simulated IR spectra and experimental observations referring to VOx (x = 1–4) defects. [ABSTRACT FROM AUTHOR]

Within the context of fewest-switch surface hopping (FSSH) dynamics, one often wishes to remove the angular component of the derivative coupling between states J and K . In a previous set of papers, Shu et al. [J. Phys. Chem. Lett. 11, 1135–1140 (2020)] posited one approach for such a removal based on direct projection, while we isolated a second approach by constructing and differentiating a rotationally invariant basis. Unfortunately, neither approach was able to demonstrate a one-electron operator O ̂ whose matrix element J O ̂ K was the angular component of the derivative coupling. Here, we show that a one-electron operator can, in fact, be constructed efficiently in a semi-local fashion. The present results yield physical insight into designing new surface hopping algorithms and are of immediate use for FSSH calculations. [ABSTRACT FROM AUTHOR]

This paper reports the energies and charge and spin distributions of the low-lying excited states in singlet and triplet N2V defects in diamond from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP, PBE0, and HSE06 functionals. They assign the observed absorption at 2.463 eV, first reported by Davies et al. [Proc. R. Soc. London 351, 245 (1976)], to the excitation of a N(sp3) lone-pair electron in the singlet and triplet states, respectively, with estimates of ∼1.1 eV for that of the unpaired electrons, C(sp3). In both cases, the excited states are predicted to be highly local and strongly excitonic with 81% of the C(sp3) and 87% of the N(sp3) excited charges localized at the three C atoms nearest neighbor (nn) to the excitation sites. Also reported are the higher excited gap states of both the N lone pair and C unpaired electron. Calculated excitation energies of the bonding sp3 hybrids of the C atoms nn to the four inner atoms are close to that of the bulk, which indicates that the N2V defect is largely a local defect. The present results are in broad agreement with those reported by Udvarhelyi et al. [Phys. Rev. B 96, 155211 (2017)] from plane wave HSE06 calculations, notably for the N lone pair excitation energy, for which both predict an energy of ∼2.7 eV but with a difference of ∼0.5 eV for the excitation of the unpaired electron. [ABSTRACT FROM AUTHOR]

The general recurrence relation (RR) of paper I [J. Chem. Phys. 95, 5198 (1991)] can be improved. This improved RR, with the use of the Head–Gordon–Pople (HGP), is able to take the contraction of Gaussian-type orbitals (GTO’s) efficiently into account for the electron-repulsion-integral (ERI) evaluation. With the use of the RR by Hamilton and Schaefer and by Lindh, Ryu, and Liu (HSLRL), this improved RR makes the evaluation more rapid. Furthermore, the calculation of the roots and weights of the Rys polynomial can be improved. As a result, an extremely rapid code can be obtained for a vector computer. For example, the measured time is 135 ns per one ERI for [HH|HH] shell block of the uncontracted GTO’s, which is 16 times faster than that of paper I. When the degree of contraction K=2 for (HH|HH) shell block of the contracted GTO’s, the measured time is 40 ns per one primitive ERI. It is confirmed that the present method is most efficient for the ERI evaluation of GTO’s higher than or equal to f. It is found that both the HGP and the HSLRL RR’s are numerically unstable in their bad cases. Several procedures to avoid their instabilities are discussed. [ABSTRACT FROM AUTHOR]

The FlexiBLE embedding method introduced in Paper I [Z. Shen and W. J. Glover, J. Chem. Phys. 155, 224112 (2021)] is applied to explore the structure and dynamics of the aqueous solvated electron at an all-electron density functional theory Quantum Mechanics/Molecular Mechanics level. Compared to a one-electron mixed quantum/classical description, we find the dynamics of the many-electron model of the hydrated electron exhibits enhanced coupling to water OH stretch modes. Natural bond orbital analysis reveals this coupling is due to significant population of water OH σ* orbitals, reaching 20%. Based on this, we develop a minimal frontier orbital picture of the hydrated electron involving a cavity orbital and important coupling to 4–5 coordinating OH σ* orbitals. Implications for the interpretation of the spectroscopy of this interesting species are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present a comparative study of the redox properties of the icosahedral [Rh12E(CO)27]n− (n = 4 when E = Ge or Sn and n = 3 when E = Sb or Bi) family of clusters through in situ infrared spectroelectrochemistry experiments and density functional theory computational studies. These clusters show shared characteristics in terms of molecular structure, being all E-centered icosahedral species, and electron counting, possessing 170 valence electrons as predicted by the electron-counting rules, based on the cluster-borane analogy, for compounds with such metal geometry. However, in some cases, clusters of similar nuclearity, and beyond, may show multivalence behavior and may be stable with a different electron counting, at least on the time scale of the electrochemical analyses. The experimental results, confirmed by theoretical calculations, showed a remarkable electron-sponge behavior for [Rh12Ge(CO)27]4− (1), [Rh12Sb(CO)27]3− (3), and [Rh12Bi(CO)27]3− (4), with a cluster charge going from −2 to −6 for 1 and 3 and from −2 to −7 for cluster 4, making them examples of molecular electron reservoirs. The [Rh12Sn(CO)27]4− (2) derivative, conversely, presents a limited ability to exist in separable reduced cluster species, at least within the experimental conditions, while in the gas phase it appears to be stable both as a penta- and hexa-anion, therefore showing a similar redox activity as its congeners. As a fallout of those studies, during the preparation of [Rh12Sb(CO)27]3−, we were able to isolate a new species, namely, [Rh11Sb(CO)26]2−, which presents a Sb-centered nido-icosahedral metal structure possessing 158 cluster valence electrons, in perfect agreement with the polyhedral skeletal electron pair theory. [ABSTRACT FROM AUTHOR]

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial generalized gradient approximation (GGA) functionals, this has culminated into the recently proposed SCAN (strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals--the GGA hybrid functionals B3LYP and PBE0 and the meta-GGA functional SCAN--from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as αVee with α varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density. [ABSTRACT FROM AUTHOR]

By using perturbations in the molecular external potential, the authors deduce the Fukui function from the change in Kohn-Sham orbital energies, avoiding the troublesome differentiation of the density with respect to electron number. Though this paper focuses on the Fukui function, the same general technique can be used to compute the functional derivative of any observable with respect to the external potential. In this paper, the method is used to compute the Fukui function for the beryllium atom and the formaldehyde molecule. The follow-up paper (part II) addresses the problem of computing condensed reactivity indicators. [ABSTRACT FROM AUTHOR]

The Fukui function is a frequently used DFT concept in the description of a system’s regioselective preferences to undergo electrophilic, nucleophilic, or radical attacks. Until now, this function has usually been evaluated using finite difference approximations. The first paper in this series proposed a method for obtaining the Fukui function by a direct calculation of the functional derivative of the chemical potential with respect to the external potential. This paper extends the method to condensed Fukui functions and applies it to an extensive testing set of molecules. Results are promising, which demonstrates the usefulness of the new formalism. [ABSTRACT FROM AUTHOR]

It has become recently clear that chemical bonding under pressure is still lacking guiding principles for understanding the way electrons reorganize when their volume is constrained. As an example, it has recently been shown that simple metals can become insulators (aka electrides) when submitted to high enough pressures. This has lead to the general believe that "a fundamental yet empirically useful understanding of how pressure alters the chemistry of the elements is lacking" [R. J. Hemley, High Pressure Res. 30, 581 (2010)]. In this paper, we are interested in studying the role that the Pauli principle plays on the localization/delocalization of confined noninteracting electrons. To this end, we have considered the simple case of a 1-dimensional (1-D) double well as a confining potential, and the Electron Localization Function (ELF) has been used to characterize the degree localization/delocalization of the systems of noninteracting electrons. Then, we have systematically studied the topology of the ELF as a function of the double well parameters (barrier eight and wells distance) and of the number of electrons. We have found that the evolution of the ELF distributions has a good correspondence with the evolution of chemical bonding of atomic solids under pressure. [ABSTRACT FROM AUTHOR]

In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N − 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators Xp(ω) and Yq(ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions. [ABSTRACT FROM AUTHOR]

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k1(1)k2(1)|g1(2)g2(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion. [ABSTRACT FROM AUTHOR]

This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic techniques for studying a dye molecule in solution. Ultrafast laser pulse excitation of an electronic transition coupled to vibrational modes induces a propagating vibrational wave packet that manifests itself in oscillating signal intensities and line shapes. For the two-dimensional electronic spectra we can attribute the observed modulations to periodic enhancement and decrement of the relative amplitudes of rephasing and nonrephasing contributions to the total response. Different metrics of the two-dimensional signals are shown to relate to the frequency-frequency correlation function which provides the connection between experimentally accessible observations and the underlying microscopic molecular dynamics. A detailed theory of the time-dependent two-dimensional spectral line shapes is presented in the accompanying paper [T. Mančal et al., J. Chem. Phys. 132, 184515 (2010)]. [ABSTRACT FROM AUTHOR]

In an earlier paper [S. Thanos and A. K. Theophilou J. Chem. Phys. 124, 204109 (2006)], we found an explicit formula for the expansion of a Slater determinant |[uppercase_phi_synonym]M> in terms of eigenstates of S2. In this paper, we use the same formula to determine the spin contamination Scon of the unrestricted single determinant approximations, i.e., Hartree-Fock, optimized effective potential, and density functional theory. We derived an expression which gives Scon in terms of the overlap of the spatial parts of the spin up and spin down “corresponding” orbitals. It was found that Scon does not depend on M, the eigenvalue of Sz, at least for the lower order approximations, i.e., when |<φi|φi′>| is large. In this case, the predominant coefficient of the expansion assumes its maximum value when S=M. However, for the class of solutions that |<φi|φi′>| is small, the spin L of the largest coefficient increases with the number of unpaired electrons. We also derived the explicit form of the expansion states. [ABSTRACT FROM AUTHOR]

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The paper describes the derivation of the Kohn-Sham equations for a nanowire with direct current. A value of the electron current enters the problem as an input via a subsidiary condition imposed by pointwise Lagrange multiplier. Using the constrained minimization of the Hohenberg-Kohn energy functional, we derive a set of self-consistent equations for current carrying orbitals of the molecular wire. [ABSTRACT FROM AUTHOR]

Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multireference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics. [ABSTRACT FROM AUTHOR]

This paper concerns the behavior of an electron thermalized in supercritical xenon. It is known that the electron can become localized (or self-trapped) in certain ranges of density and temperature. In the case of xenon, localization is enhanced by the strong polarizability. Previous investigations have employed path integral Monte Carlo methods to study the quantum states of the electron and the local properties of the fluid where the electron is treated quantum mechanically and the xenon atoms are treated classically. In this paper we present a reference-interaction-site model (RISM)–polaron calculation for the system of an excess electron in xenon at T=309 K and 248 K. The system is characterized by a Lennard-Jones fluid in which the electron interacts with xenon atoms through a soft potential: a repulsive core with an attractive long range tail. The HNC (hypernetted chain) closure is imposed on the RISM–polaron equation. Significant improvements over the primitive hard sphere model are achieved. The calculation shows that, above the critical density, the electron–solvent radial distribution function g(r) predicted by the RISM–polaron theory is in good agreement with its path integral Monte Carlo counterpart. [ABSTRACT FROM AUTHOR]

This paper is a continuation of a previous investigation of the Pauli–Breit Hamiltonian in the framework of the graphical spin-dependent unitary group approach to many electron systems. The SU(2) tensor form for the spin–spin interaction and its corresponding zero spin-shift component are determined explicitly and applied to investigate the first order energy level splitting due to the spin–spin interaction, entirely within the context of the unitary group approach. Our results are also discussed in terms of the unitary group density matrix formalism. [ABSTRACT FROM AUTHOR]

In the foregoing Comment [Sommerfeld[J. Chem. Phys.125, 024307 (2006)] suggests that the computational results presented in the above referenced paper does not support the conclusion of the paper regarding the prevalence of both surface- and interior-bound electron states for (H2O)14- clusters in experiments. Herein, the author presents the method used in the selection of clusters and provide experimental results that are consistent with the findings of the paper. [ABSTRACT FROM AUTHOR]

The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H2 and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all Ms components of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa. [ABSTRACT FROM AUTHOR]

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order M∅ler-Plesset perturbation theory method, NOCI-MP2.We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis. [ABSTRACT FROM AUTHOR]

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force-as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green's functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper. [ABSTRACT FROM AUTHOR]

In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N - 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N - 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function. [ABSTRACT FROM AUTHOR]

For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH+, and Li2 molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark. [ABSTRACT FROM AUTHOR]

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T). [ABSTRACT FROM AUTHOR]

In this paper we investigated the dynamics of an electron in the presence of a time-dependent laser field in a model potential for a two-level single-electron semiconductor quantum dot (QD) that is capable of undergoing interatomic Coulombic decay (ICD) together with an electron bound to a neighboring QD. We demonstrate that ICD can be initiated by coupling the two-level QD to either a continuous or a pulsed moderate to strong laser and we obtain the total and partial decay widths of the resonance excited state in agreement with that from the solely decay of the resonance [A. Bande, K. Gokhberg, and L. S. Cederbaum, J. Chem. Phys. 135, 144112 (2011)]. A detailed discussion of the effects of direct ionization by the laser in single- or multi-photon process as well as Rabi oscillations is furthermore presented. [ABSTRACT FROM AUTHOR]

This paper explores Fano resonances due to non-adiabatic coupling of vibrational modes and the electron continuum in dipole-bound anions. We adopt a simple one-electron model consisting of a point dipole and an auxiliary potential to represent the electron interaction with the neutral core. Nuclear motion is added by assuming that harmonic vibrations modulate the dipole moment. When the model is parameterized to simulate key features of the water tetramer anion, the resultant photodetachment lineshape closely resembles that observed experimentally and analyzed as a Fano resonance with a parameter q close to -1. Other parameterizations are explored for the model and it is found that large changes in the auxiliary potential are required to change the sign of q. This is consistent with the experimental finding that q is negative for all water cluster sizes studied. [ABSTRACT FROM AUTHOR]

The multi-configuration electron-nuclear dynamics (MCEND) method is a nonadiabatic quantum dynamics approach to the description of molecular processes. MCEND is a combination of the multi-configuration time-dependent Hartree (MCTDH) method for atoms and its antisymmetrized equivalent MCTDHF for electrons. The purpose of this method is to simultaneously describe nuclear and electronic wave packets in a quantum dynamical way, without the need to calculate potential energy surfaces and diabatic coupling functions. In this paper we present first exemplary calculations of MCEND applied to the LiH molecule, and discuss computational and numerical details of our implementation. [ABSTRACT FROM AUTHOR]

The present paper deals with the interpretation of the photoelectron spectrum of the Li3O-. After several failed attempts to attribute all of the observed peaks in the experimental spectrum to anionic species, neutral species were considered assuming a sequential two-photon absorption mechanism. We find that only two of the six observed peaks can be attributed to photodetachments and that all other observed features can be assigned to ionizations from the ground and excited states of the neutral. Nuclear distributions other than three lithium atoms surrounding the oxygen are not likely to be stable. The interpretation of the experimental peak located at about 1.2 eV remains challenging. It can either be attributed to the second electron detachment (involving the HOMO -1 orbital) energy from the anion's triplet C2v state or to higher excited states (involving HOMO +10, 11, 12... orbitals) of the neutral species. Furthermore, we have examined the influence of vibrational displacements on the location of the observed peaks. We find that this effect is smaller than 0.05 eV and, therefore, must be considered as negligible. [ABSTRACT FROM AUTHOR]

A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators (T⁁) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian H⁁=e-T⁁H⁁eT⁁ in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of H⁁, expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bond-stretching potential energy surfaces for N2, CO, and the low-lying electronic states of C2 indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations. [ABSTRACT FROM AUTHOR]

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms. [ABSTRACT FROM AUTHOR]

In this paper we first use ab initio simulations to study the strains induced by charging an armchair (5,5) carbon nanotube (CNT) segment. The observed behavior is far from a monotonic expansion that one might have expected from a classical point of view. Subsequently a new method is proposed to predict the nonelectrostatic part of the electromechanical actuation response of the nanotube based on the spatial distribution of its molecular orbitals. Locally bonding and locally antibonding molecular orbitals are defined for the CNT segment structure based on analogy with bonding and antibonding orbitals in diatomic molecules. The nonmonotonic overall actuation is explained based on the above proposition and the general alignment of the expanding and contracting bonds with respect to the axis or circumference of the CNT segment. Using the well-known concept of bond order, the actuation of this complex system of many atoms is predicted with close quantitative agreement with the ab initio simulations. [ABSTRACT FROM AUTHOR]

In this paper we evaluate the performance of density functional theory with the B3LYP functional for calculations on ceria (CeO2) and cerium sesquioxide (Ce2O3). We demonstrate that B3LYP is able to describe CeO2 and Ce2O3 reasonably well. When compared to other functionals, B3LYP performs slightly better than the hybrid functional PBE0 for the electronic properties but slightly worse for the structural properties, although neither performs as well as LDA+U(U=6 eV) or PBE+U(U=5 eV). We also make an extensive comparison of atomic basis sets suitable for periodic calculations of these cerium oxides. Here we conclude that there is currently only one type of cerium basis set available in the literature that is able to give a reasonable description of the electronic structure of both CeO2 and Ce2O3. These basis sets are based on a 28 electron effective core potential (ECP) and 30 electrons are attributed to the valence space of cerium. Basis sets based on 46 electron ECPs fail for these materials. [ABSTRACT FROM AUTHOR]

Multicomponent density functional theory has been developed to treat systems with more than one type of quantum particle, such as electrons and nuclei, in an external potential. The existence of the exact universal multicomponent density functional in terms of the one-particle densities for each type of quantum particle has been proven. In the present paper, a number of important mathematical properties of the exact universal multicomponent density functional are derived. The expression relating the electron-proton pair density to the one-particle densities leads to an inequality for the potential energy component of the electron-proton correlation functional under well-defined conditions. General inequalities for the kinetic energy correlation functionals and the total electron-proton correlation functional are also derived. The coordinate scaling analysis leads to mathematical inequalities describing the effect of scaled densities on the kinetic, potential, and total energy functionals. The adiabatic connection formula defines the exact electron-proton functional in terms of an adiabatic scaling parameter that smoothly connects the noninteracting system with the fully interacting system. The virial expression provides the relation between the exact kinetic and potential energy functionals for the ground state densities of multicomponent systems. These mathematical relationships provide insight into the fundamental properties of the exact universal multicomponent density functional and serve as a guide for the development of approximate electron-proton density functionals. [ABSTRACT FROM AUTHOR]

In a previous paper [Fromager et al., J. Chem. Phys. 126, 074111 (2007)], some of the authors proposed a recipe for choosing the optimal value of the μ parameter that controls the long-range/short-range separation of the two-electron interaction in hybrid multiconfigurational self-consistent field short-range density-functional theory (MC-srDFT) methods. For general modeling with MC-srDFT methods, it is clearly desirable that the same universal value of μ can be used for any molecule. Their calculations on neutral light element compounds all yielded μopt=0.4 a.u. In this work the authors investigate the universality of this value by considering “extreme” study cases, namely, neutral and charged isoelectronic f0 actinide compounds (ThO2, PaO2+, UO22+, UN2, CUO, and NpO23+). We find for these compounds that μopt=0.3 a.u. but show that 0.4 a.u. is still acceptable. This is a promising result in the investigation of a universal range separation. The accuracy of the currently best MC-srDFT (μ=0.3 a.u.) approach has also been tested for equilibrium geometries. Though it performs as well as wave function theory and DFT for static-correlation-free systems, it fails in describing the neptunyl (VII) ion NpO23+ where static correlation is significant; bending is preferred at the MC-srDFT (μ=0.3 a.u.) level, whereas the molecule is known to be linear. This clearly shows the need for better short-range functionals, especially for the description of the short-range exchange. It also suggests that the bending tendencies observed in DFT for NpO23+ cannot be fully explained by the bad description of static correlation effects by standard functionals. A better description of the exchange seems to be essential too. [ABSTRACT FROM AUTHOR]

Long-range-corrected hybrids, which incorporate all of the long-range exact exchange interaction, improve performance for a host of molecular properties. The long-range portion of exact exchange is both computationally and formally problematic in solids, and screened hybrids therefore eliminate it. While screened hybrids give similar results to their parent global hybrids for many molecular properties, one may worry that they perform poorly for those properties that are improved by the long-range-correction procedure. In this paper, we show that at least for the Heyd–Scuseria–Ernzerhof (HSE) screened hybrid, this is not the case; for many properties improved by long-range-correction, screened hybrids and global hybrids deliver essentially the same results. We suggest that this is because screened hybrids and global hybrids have fundamentally the same many-electron self-interaction error. We also introduce some small revisions to our computational implementation of the HSE screened hybrid, and we recommend these revisions for future applications of HSE. [ABSTRACT FROM AUTHOR]

Support vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce least-squares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LS-SVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LS-SVM approach reduces the root-mean-square deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the B3LYP/6-31G(d) calculation. Thus, the LS-SVM correction on top of B3LYP/6-31G(d) is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally. [ABSTRACT FROM AUTHOR]

We describe a new grid-based (or localized orbital-based) method for treating the effects of exchange and correlation on electronic transmission through a molecular target where there are initially other bound electrons. Our algorithm combines the approaches of (i) solid-state grid-based algorithms using self-energies and (ii) the complex Kohn method from electron-molecule scattering. For the general problem of a molecular target with n-electrons, our algorithm should ideally solve for electronic transmission with a computational cost scaling as n2, although the present implementation is limited to one-dimensional problems. In this paper, we implement our algorithm to solve three one-dimensional model problems involving two electrons: (i) Single-channel resonant transmission through a double-barrier well (DBW), where the target already contains one bound-state electron [Rejec et al., Phys. Rev. B 67, 075311 (2003)]; (ii) multichannel resonant transmission through a DBW, where the incoming electron can exchange energy with the bound electron; (iii) transmission through a triple-barrier well (TBW), where the incoming electron can knock forward the bound electron, yielding a physical model of electron-assisted electron transfer. This article offers some insight about the role and size of exchange and correlation effects in molecular conduction, where few such rigorous calculations have yet been made. Such multibody effects have already been experimentally identified in mesoscopic electron transport, giving rise to the “0.7 anomaly,” whereby electrons traveling through a narrow channel pair up as singlets and triplets. We expect the effect of electronic correlation to be even more visible for conduction through molecules, where electrons should partially localize into bonding and antibonding orbitals. [ABSTRACT FROM AUTHOR]

This paper analyzes the different contributions to the magnetic coupling in systems with more than one unpaired electron per center. While in S=1/2 spin systems the Heisenberg Hamiltonian involving only bilinear exchange interactions is reliable for the description of the magnetic states, biquadratic exchange interactions must be sometimes introduced for S=1 (or higher) spin systems to account for isotropic deviations to Heisenberg behavior. The analysis establishes that the excited atomic states, the so-called non-Hund states, are responsible for the main contribution to the deviations. The kinetic exchange contribution and the spin, hole, and particle polarizations increase the magnetic coupling but essentially maintain the Heisenberg pattern. The importance of the different contributions has been studied for a series of Ni2 compounds with a polarizable double azido bridge. The coupling between two Fe3+ ions in the molecular crystal Na3FeS3, which is known experimentally to present large deviations to Heisenberg behavior, has also been investigated. [ABSTRACT FROM AUTHOR]

The diagonal linewidth in two-dimensional infrared spectra is often narrower than the distribution of transition frequencies. The width along the antidiagonal is broader than predicted by the lifetime broadening. These effects arise from time-dependent fluctuations of the transition frequencies. They can be accounted for with a semiclassical approach. For systems with many coupled vibrational modes, this approach, however, becomes computationally too demanding to be practically applicable. A time-averaging approximation was suggested for linear infrared absorption spectra. In this paper, we demonstrate that the averaging can be optimized to fit a broader scale of frequency fluctuations by using a Gaussian weight function instead of the originally proposed box function. We further generalize the time-averaging method to allow the simulation of two-dimensional infrared spectra and demonstrate the method on a simple system. The approximation delivers a large speed-up of the calculation without losing significant accuracy. [ABSTRACT FROM AUTHOR]

In this paper we explore the effects of the electronic structure, the charge state, and the nature of energy distribution of isomers on the thermodynamic properties of sodium clusters. The focus of the work is to isolate the effects of these ingredients on thermodynamic behavior by choosing specific clusters. Toward this end we investigate Na39-, Na40, and Na41+, which are the electronic closed shell systems which differ in number of atoms and charge state. We also examine Na39, Na39+, Na40+, and Na41 clusters having different charges of these clusters. Our density functional molecular dynamics simulations show that all electronic shell-closing clusters have similar melting temperature of ≈310 K. Remarkably, it is observed that an addition of even one electron to Na39 increases the melting temperature by about 40 K and makes the specific heat curve sharper. All the cationic clusters show broadened specific heat curves. [ABSTRACT FROM AUTHOR]

In this paper, the structure and spectroscopic parameters of the C5 cluster are determined using multiconfigurational quantum chemical methods as implemented in the MOLCAS software. A number of spectroscopic properties (band center positions, l-doubling parameters, and rotational constants) have been characterized. From the new results, the assignments of previous astrophysical observations [J. Goicoechea et al., Astrophys. J. 609, 225 (2004)] are discussed. A detailed exploration of the global potential energy surface confirms that C5 has a X 1Σg+ linear isomer of prominent stability and, at least, three minimum energy structures showing singlet electronic ground states. Two of them are cyclic and one has a nonplanar geometry. Vertical and adiabatic electronic transitions and vibrational spectroscopic parameters are determined for the most stable linear isomer using multiconfigurational second order perturbation theory (CASPT2) using an active space containing 12 valence orbitals with 12 active electrons and extended ANO-type basis sets. The infrared spectrum has been analyzed from an anharmonic force field derived form the local surface, determined from the energies of a grid of 1350 geometries. The force field includes four coupling terms. The CASPT2 band center position of the ν7(πu) anharmonic fundamental has been calculated to be at 102 cm-1, which validates the assignment to C5 of the pattern of bands centered at 102 cm-1 observed with the ISO telescope. [ABSTRACT FROM AUTHOR]

Many of the (ideal) infinite conjugated hydrocarbon polymers do not present a gap at the Fermi level in tight-binding calculations. However, due to the bielectronic interaction the excitation energy from the ground state to the lowest triplet state may be nonzero for some lattices (called spin gapped), while other lattices will keep a singlet-triplet degeneracy (spin-gapless lattices). This difference results in qualitative differences in their magnetic properties. Making use of the relevance of Heisenberg Hamiltonians for the study of the lowest states of conjugated hydrocarbons, this paper presents some qualitative arguments to predict the spin-gap character of various classes of such polymers. The arguments are based on real space renormalization group procedures, which considers fragments of the polymers as effective spins. Numerical evaluations, based on a renormalized excitonic method, confirm the qualitative predictions. [ABSTRACT FROM AUTHOR]

The kinetics of electron transfer during the early stages of the photosynthetic reaction cycle has recently been shown in transient absorption experiments carried out by Wang et al. [Science 316, 747 (2007)] to be strongly influenced by fluctuations in the conformation of the surrounding protein. A model of electron transfer rates in polar solvents developed by Sumi and Marcus using a reaction-diffusion formalism [J. Chem. Phys. 84, 4894 (1986)] was found to be successful in fitting the experimental absorption curves over a roughly 200 ps time interval. The fits were achieved using an empirically determined time-dependent function that described protein conformational relaxation. In the present paper, a microscopic model of this function is suggested, and it is shown that the function can be identified with the dynamic autocorrelation function of intersegment distance fluctuations that occur in a harmonic potential of mean force under the action of fractional Gaussian noise. [ABSTRACT FROM AUTHOR]

Differing perspectives on the accuracy of three-electron reduced-density-matrix (3-RDM) reconstruction in nonminimal basis sets exist in the literature. This paper demonstrates the accuracy of cumulant-based reconstructions, developed by Valdemoro (V) [F. Colmenero et al., Phys. Rev. A 47, 971 (1993)], Nakatsuji and Yasuda (NY) [Phys. Rev. Lett. 76, 1039 (1996)], Mazziotti (M) [Phys. Rev. A 60, 3618 (1999)], and Valdemoro–Tel–Pérez–Romero (VTP) [Many-electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000)]. Computationally, we extend previous investigations to study a variety of molecules, including LiH, HF, NH3, H2O, and N2, in Slater-type, double-zeta, and polarized double-zeta basis sets at both equilibrium and nonequilibrium geometries. The reconstructed 3-RDMs, compared with 3-RDMs from full configuration interaction, demonstrate in nonminimal basis sets the accuracy of the first-order expansion (V) as well as the important role of the second-order corrections (NY, M, and VTP). Calculations at nonequilibrium geometries further show that cumulant functionals can reconstruct the 3-RDM from a multireferenced 2-RDM with reasonable accuracy, which is relevant to recent multireferenced formulations of the anti-Hermitian contracted Schrödinger equation (ACSE) and canonical diagonalization. Theoretically, we perform a detailed perturbative analysis of the M functional to identify its second-order components. With these second-order components we connect the M, NY, and VTP reconstructions for the first time by deriving both the NY and VTP functionals from the M functional. Finally, these 3-RDM reconstructions are employed within the ACSE [D. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)] to compute ground-state energies which are compared with the energies from the contracted Schrödinger equation and several wave function methods. [ABSTRACT FROM AUTHOR]

A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is created. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C==C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method. [ABSTRACT FROM AUTHOR]

The Omega intracule is a three-dimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions. [ABSTRACT FROM AUTHOR]