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Adiabatic and vertical ionization energies corresponding to the X A12, A B22, and B A22 final states of SO2+, O3+, and S3+ have been calculated with a variety of electron-propagator and coupled-cluster methods. The BD-T1 electron-propagator method for vertical ionization energies and coupled-cluster adiabatic and zero-point corrections yield agreement with experiment to within 0.1 eV in all cases but one. The remaining discrepancies for the A B22 state of SO2+ indicate a need for higher levels of theory in determining cationic minima and their accompanying vibrational frequencies. Predictions for the still unobserved A B22 and B A22 final states of S3+ are included. To account for increased biradical character in O3 and S3, highly correlated reference states are required to produce the correct order of final states. Electron correlation plays a subtle role in determining the contours of the Dyson orbitals obtained with BD-T1 and NR2 electron-propagator calculations.

Positively charged or neutral metal ammonia complexes can form molecular species called solvated electron precursors (SEPs) that accommodate peripheral electrons in approximately hydrogenic diffuse orbitals. This work expands the notion of SEPs to metal ammonia complexes wherein a second coordination shell with 12 ammonia molecules is attached to M(NH3)4 (M = Li, Be+, B2+) SEPs via hydrogen bonding. In such complexes, denoted M(NH3)4@12NH3, the 12 outer ammonia molecules displace the peripheral electrons even further away from the first shell of ammonia molecules. We have benchmarked several density functional methods against CCSD(T) results and found that CAM-B3LYP provides the best M(NH3)4@12NH3 structures. The electron attachment energies of the closed-shell cores calculated with electron-propagator methods and the corresponding Dyson orbitals reveal the Aufbau principle for the ground and excited states of M(NH3)4@12NH3 to be 1s, 1p, 1d, 1f, 2s, 2p, 1g, 2d. These orbitals are diffuse and delocalized over the periphery of the second solvation shell.

Ab initio electron propagator methods are employed to predict the vertical electron attachment energies (VEAEs) of OH

Ground and excited electronic states of V(NH3)0,±6 complexes, investigated with ab initio electronic structure theory, consist of a V(NH3)62+ core with up to three electrons distributed over its periphery. This result extends the concept of super-atomic, solvated-electron precursors from alkali and alkaline-earth complexes to a transition metal. In the approximately octahedral ground state of V(NH3)6, three unpaired electrons occupy 3dxz, 3dyz and 3dxy (t2g) orbitals of vanadium and two electrons occupy a diffuse 1s outer orbital. The lowest excitations involve promotion of diffuse 1s electrons to 1p or 1d diffuse orbitals, followed by a 3d (t2g → eg) transition. V(NH3)6+ is produced by removing a diffuse 1s electron, whereas the additional electron in V(NH3)6- populates a 1p diffuse orbital. The adiabatic ionization energy and electron affinity of V(NH3)6 equal 3.50 and 0.48 eV, respectively.

Dyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, density matrices, total energ...

A new generation of diagonal self-energy approximations in ab initio electron propagator theory for the calculation of electron removal energies of molecules and molecular ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approximately renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calculations whose accuracy approaches that of full configuration interaction. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approximately renormalized third-order quasiparticle or Q3+, (3) the renormalized third-order quasiparticle or RQ3, (4) the approximately renormalized linear third-order or L3+, and (5) the renormalized linear third-order or RL3 self-energies.

Tetra-amino lithium and sodium complexes M(NH3)0,−4 (M = Li, Na) have one or two electrons that occupy diffuse orbitals distributed chiefly outside the M(NH3)+4 core. The lowest-energy 1s, 1p, and 1d orbitals follow Aufbau principles found earlier for beryllium tetra-ammonia complexes. Two ground state M(NH3)4 complexes can bind covalently by coupling their 1s1 electrons into a σ-type molecular orbital. The lowest excited states of the [M(NH3)4]2 species are obtained by promoting one or two electrons from this σ to other bonding or anti-bonding σ and π-type molecular orbitals. The electronic structure of solvated electron precursors provides insights into chemical bonding between super-atomic species that are present in concentrated alkali-metal–ammonia solutions.

Tetra-amino beryllium complexes and ions, Be(NH3)40,±, have a tetrahedral Be(NH3)42+ core with one, two, or three outer electrons orbiting its periphery. Our calculations reveal a new class of molecular entities, solvated electron precursors, with Aufbau rules (1s, 1p, 1d, 2s, 1f, 2p, 2d) that differ from their familiar hydrogenic counterparts and resemble those of jellium or nuclear-shell models. The core’s radial electrostatic potential suffices to reproduce the chief features of the ab initio results. Wave function and electron-propagator methods combined with diffuse basis sets are employed to calculate accurate geometries, ionization energies, electron affinities, and excitation energies.

Positively charged or neutral metal ammonia complexes can form molecular species called solvated electron precursors (SEPs) that accommodate peripheral electrons in approximately hydrogenic diffuse orbitals. This work expands the notion of SEPs to metal ammonia complexes wherein a second coordination shell with 12 ammonia molecules is attached to M(NH

Cluster perturbation (CP) theory was developed in Paper I [F. Pawłowski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N 2 , and CH 2 , the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered.

We introduce a new class of perturbation models - the cluster perturbation (CP) models - where the major drawbacks of Møller-Plesset perturbation theory and coupled cluster perturbation theory have been eliminated. In CP theory, we consider a target excitation space relative to the Hartree-Fock state and partition the target excitation space into a parent and an auxiliary excitation space. The zeroth-order state is a coupled cluster (CC) state in the parent excitation space, and the target state is either a cluster linear or a CC state in the target excitation space. In CP theory, perturbation series are determined in orders of the CC parent state similarity-transformed fluctuation potential for the energy and for a molecular property, where the zeroth-order term in the series is the energy or a molecular property for the CC parent state and where the series formally converge to the energy or a molecular property for the target state. In CP theory, we use a generalized order concept, where the zeroth-order component of the extended parent-state Jacobian contains a fluctuation potential contribution, and use this new generalized order to treat internal relaxation in the parent excitation space at zeroth order and hence remove it from the perturbation calculation. Even more importantly, using this new generalized order concept, CP series can be determined for molecular properties of ground and excited states and for transition properties between these states, including excitation energies and energies of the excited states. The applicability of CP theory to both the energy and molecular properties and numerical results for the CP energy and molecular property series demonstrate the superiority of CP theory compared to previous perturbation models. Low-order corrections in the CP perturbation series can be expected soon to become state-of-the-art electronic structure models for the determination of energies and molecular properties of target-state quality for single-configuration dominated molecular systems.

Ab initio electron propagator methods are employed to predict the vertical electron attachment energies (VEAEs) of OH3+(H2O)n clusters. The VEAEs decrease with increasing n, and the corresponding Dyson orbitals are diffused over exterior, non-hydrogen bonded protons. Clusters formed from OH3− double Rydberg anions (DRAs) and stabilized by hydrogen bonding or electrostatic interactions between ions and polar molecules are studied through calculations on OH3−(H2O)n complexes and are compared with more stable H−(H2O)n+1 isomers. Remarkable changes in the geometry of the anionic hydronium–water clusters with respect to their cationic counterparts occur. Rydberg electrons in the uncharged and anionic clusters are held near the exterior protons of the water network. For all values of n, the anion–water complex H−(H2O)n+1 is always the most stable, with large vertical electron detachment energies (VEDEs). OH3−(H2O)n DRA isomers have well separated VEDEs and may be visible in anion photoelectron spectra. Corresponding Dyson orbitals occupy regions beyond the peripheral O–H bonds and differ significantly from those obtained for the VEAEs of the cations.

In cluster perturbation (CP) theory, we consider a target excitation space relative to a Hartree-Fock state and partition the target excitation space into a parent excitation space and an auxiliary excitation space. The zeroth-order state is in CP theory a coupled cluster (CC) state in the parent excitation space, and the target state is a CC state in the target excitation space. In this paper, we derive CP series for excitation energies in orders of the CC parent-state similarity-transformed fluctuation potential where the zeroth-order term in the series is an excitation energy for the CC parent state response eigenvalue equation and where the series formally converge to an excitation energy for the CC target state response eigenvalue equation. We give explicit expressions for the lowest-order excitation energy corrections. We also report calculations for CP excitation energy series for various parent and target excitation spaces and examine how well the lower-order corrections can reproduce the total excitation energies. Considering the fast local convergence we have observed for the CP excitation energy series, it becomes computationally attractive to use low-order corrections in CP series to obtain excitation energies of CC target state quality. For the CPS(D-n) series, the first-order correction vanishes, the second-order correction becomes the CIS(D) model, and for the CPS(D-3) model, our calculations suggest that excitation energies of CCSD quality are obtained. The numerical results also suggest that a similar behavior can be seen for the low-order excitation energy corrections for CP series where the parent state contains more than a singles excitation space, e.g., for the CPSD(T) model. We therefore expect the low-order excitation energy corrections in CP series soon to become state-of-the-art models for determining excitation energies of CC target state quality.

The theoretical foundation has been developed for establishing whether cluster perturbation (CP) series for the energy, molecular properties, and excitation energies are convergent or divergent and for using a two-state model to describe the convergence rate and convergence patterns of the higher-order terms in the CP series. To establish whether the perturbation series are convergent or divergent, a fictitious system is introduced, for which the perturbation is multiplied by a complex scaling parameter z. The requirement for convergent perturbation series becomes that the energy or molecular property, including an excitation energy, for the fictitious system is an analytic, algebraic function of z that has no singularities when the norm |z| is smaller than one. Examples of CP series for the energy and molecular properties, including excitation energies, are also presented, and the two-state model is used for the interpretation of the convergence rate and the convergence patterns of the higher-order terms in these series. The calculations show that the perturbation series effectively become a two-state model at higher orders.

Tetra-amino beryllium complexes and ions, Be(NH

The P3+ (renormalized partial third–order) self–energy approximation has been highly successful in interpretation and prediction of photoelectron spectra of atoms, molecules and ions. This method i...

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, MOller-Plesset, confi ...

Static and dynamic electric dipole polarisabilities and first hyperpolarisabilities of test molecules are evaluated within the CCSD response approach using medium-size basis sets: the large polarised LPol-n (n = ds, dl, fs, fl) sets, the aug-pc-n (n = 1, 2) basis sets of Jensen, and the SVPD and TZVPD basis sets of Rappoport and Furche. Results are compared to reference values obtained using the x-aug-cc-pVXZ (x= -, d, t; X = D, T, Q, 5) basis sets of Dunning. The aug-pc-2 basis set of Jensen proves to be an attractive choice in the case of polarisability calculations, and among the smaller sets, the LPol-ds and the TZVPD basis sets can be recommended. For the first hyperpolarisability calculations, we recommend in particular the use of the LPol-ds basis set. Other attractive choices here are the LPol-dl, the LPol-fs and the aug-pc-2 sets.

We present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide–Expand–Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the “resolution of the identity second-order Moller–Plesset perturbation theory” (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

The potential energy surface of the (1)Bu and (1)A' states of all-trans-polyenes and the corresponding protonated Schiff bases have been studied at density functional theory and coupled cluster levels. Linear polyenes and protonated Schiff bases with 4 to 12 heavy atoms have been investigated. The calculations show remarkable differences in the excited state potential energy surfaces of the polyenes and the protonated Schiff bases. The excited states of the polyenes exhibit high torsion barriers for single-bond twists and low torsion barriers for double-bond twists. The protonated Schiff bases, on the other hand, are very flexible molecules in the first excited state with low or vanishing torsion barriers for both single and double bonds. Calculations at density functional theory and coupled cluster levels yield qualitatively similar potential energy surfaces. However, significant differences are found for some single-bond torsions in longer protonated Schiff bases, which indicate a flaw of the employed time-dependent density functional theory methods. The close agreement between the approximate second and third order coupled cluster levels indicates that for these systems calculations at second order coupled cluster level are useful in the validation of results based on time-dependent density functional theory.

Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster–configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions—from which the EOM-CC expressions are derived—are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.

The ground state spectrum of the formaldehyde D 2 13 CO molecule in the range from 25 to 360 cm −1 has been recorded by a Fourier transform infrared spectrometer. The quantum number limits of the assigned transitions are J = 6–54 and K a = 0–16. The data was fitted into Watson’s A- and S-reduced Hamiltonians in I r -representation up to eighth order. The determinable constants calculated from both reductions are compared. The standard deviation of the far infrared data is 3.0 MHz. The spectroscopic constants are also calculated to high accuracy at the CCSD(T)/cc-pVQZ level of ab initio theory and agree well with the experimental ones.

The static and frequency-dependent hyperpolarizabilities of the N2 molecule have been calculated using the coupled cluster approximate triples model CC3. The CC3 basis-set limit of the hyperpolarizability has been estimated. Considering the zero-point vibrational correction and neglecting the relativistic contributions (which are found to be small) the best estimate of the static hyperpolarizability is 912.9 ± 4.3 a.u. (the uncertainty of 4.3 a.u. does not account for correlation effects beyond CC3). The effect of triples is important and increases with frequency. The hyperpolarizabilities calculated at the CC3 level agree well with experiment, the discrepancies being of 0.1–2.2%. The largest CC3 calculations employed 326 basis functions.

The static and frequency-dependent hyperpolarizability of Ne is calculated using the coupled cluster approximate triples model CC3 and a large correlation-consistent basis set. Relativisitic contributions are taken into account through first-order. Analyzing in details the one- and N -electron errors, the uncertainty of the results is estimated to be about one atomic unit, an accuracy which for the first time is obtained for a many electron system in ab initio calculations of frequency-dependent second hyperpolarizabilities. For the static hyperpolarizability of Ne we obtain a best theoretical estimate of 107.6 ± 1.0 a.u. The frequency-dependent hyperpolarizability of Ne is also calculated at the lower levels of the coupled cluster hierarchy – CCS, CC2, and CCSD – and compared to CC3 to illustrate the importance of the inclusion of the triple excitations in coupled cluster wavefunctions for an accurate determination of hyperpolarizabilities. The results at the CC3 level agree well with the latest experimental results.

The gauge invariance of the oscillator strength is examined for the lowest dipole transitions in Ne, N2 and H2O using the coupled cluster model hierarchy, CCS, CC2, CCSD, and CC3, and a variety of correlation consistent basis sets. The deviations between the oscillator strengths in the different gauges decrease from CCSD to CC3 (where connected triples are included) by about the same factor as they decrease from CCS to CC2 (where connected doubles are included). The deviations are very similar in CC2 and CCSD. The quality of the oscillator strengths is improved significantly at each level in coupled cluster hierarchy, also from CC2 to CCSD, where the equivalence between the oscillator strengths in the different gauges is very similar.

CC3 is a member of the coupled-cluster model hierarchy CCS, CC2, CCSD, CC3, and CCSDT which is especially designed to describe frequency-dependent properties. CCS is the coupled-cluster singles model, in CCSD doubles are added and in CC2 the doubles of the CCSD model are approximated using the same strategy as for triples when CCSDT is approximated to give CC3. Excitation energies have been calculated successfully using this hierarchy. The error in the excitation energies is reduced by about a factor 3 at each level for the models CCS, CC2, CCSD, and CC3, and the CC3 excitation energies closely approximate the ones of the CCSDT model. 14 Calculation of frequency-dependent polarizabilities and hyperpolarizabilities have shown similar systematic improvements to the excitation energies. 15‐17

A total of six high-resolution FT-IR spectra for trans-glyoxal-d2, trans-glyoxal-d1 and trans-glyoxal-13C2 were recorded with a resolution ranging from 0.003 to 0.004 cm−1. By means of a simultaneous ground state combination difference analysis for each of these isotopologues using the Watson Hamiltonian in A-reduction and Ir-representation the ground state rotational constants are obtained. An empirical equilibrium structure is determined for trans-glyoxal using these experimental ground state rotational constants and vibration–rotation interaction constants calculated at the CCSD(T)/cc-pVTZ level of theory. The least-squares fit yields the following structural parameters for trans-glyoxal: re(C–C) = 1.51453(38) A, re(C–H) = 1.10071(26) A, re(CO) = 1.20450(27) A, αe(CCH) = 115.251(24)°, and αe(HCO) = 123.472(19)° in excellent agreement with theoretical predictions at the CCSD(T)/cc-pVQZ level of theory.

Kβ-to-Kα X-ray intensity ratios of Ti, Cr, Fe and Co in pure metals and in Cr0.26Fe0.74, Cr0.80Co0.20 and Ti0.80Cr0.20 alloys have been measured following excitation by 59.54 keV γ-rays from a 7400 MBq (200 mCi) 241 Am point-source. The valence electronic structure of Ti, Cr, Fe and Co in the samples have been evaluated by the comparison of the measured Kβ-to-Kα intensity ratios with the results of multiconfiguration Dirac–Fock calculations performed for various electronic configurations of these metals. The 3d-electron populations obtained for pure metallic Ti, Cr, Fe and Co agree well with the results of band structure calculations of Papaconstantopoulos (Handbook of band structure of elemental solids, Plenum Press, New York, 1986). Our analysis indicates significant increase of 3d-electron population of Ti, Cr and Fe in the alloys with respect to the pure metals, except for Cr in Cr0.26Fe0.74 where the absolute 3d-electron population of Cr is found to be slightly less as compared to that of pure Cr. It has been found that to reliably explain the observed changes in the valence electronic structure of Ti, Cr, Fe and Co in their alloys it is necessary to take into account the rearrangement of electrons between 3d and (4s,4p) states of individual metal atoms, while the transfer of 3d electrons from one element to the other element can be neglected.

Kβ-to-Kα X-ray intensity ratios of Fe and Ni in pure metals and in FexNi1−x alloys (x=0.20, 0.50, 0.58) exhibiting similar crystalline structure have been measured following excitation by 59.54 keV γ-rays from a 241Am point source, to understand as to why the properties of permalloy Fe0.2Ni0.8 is distinct from other alloy compositions. It is observed that the valence electronic structure of Fe0.2Ni0.8 alloy is totally different from other alloys which may be attributed to its special magnetic properties.

A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B(0) and sums of ab initio vibration-rotation interaction constants alpha(r)(B). The vibration-rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration-rotation interaction constants are those calculated at the CCSD(T)/cc-pVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%-0.06%, surpassing the accuracy obtainable either by purely experimental techniques (except for the smallest systems such as diatomics) or by ab initio methods. (C) 2002 American Institute of Physics.

Kβ-to-Kα X-ray intensity ratios of Fe and Ni in pure metals and in FexNi1−x alloys for different compositions x (x=0.20, 0.50, 0.58) have been measured following excitation by 59.54 keV γ-rays from a 200 mCi 241Am point-source. For certain alloy compositions the Kβ-to-Kα intensity ratios of Fe and Ni differ considerably from those obtained for the pure metals. The 3d electron populations of Fe and Ni have been estimated by comparing the measured Kβ-to-Kα ratios with the results of multi-configuration Dirac–Fock (MCDF) calculations. Our results for the 3d electron populations of solid iron and nickel agree reasonably well with the earlier results of band structure calculations. In the case of alloys significant changes in the 3d electron population of Fe and Ni are observed for certain alloy compositions. These changes can be explained by assuming rearrangement of electrons between 3d and (4s,4p) valence band states of the individual metal atoms. For the alloy composition x=0.2 the change in the 3d electron population of Ni is the largest and has the opposite direction than in the case of other two alloy compositions. The totally different valence electronic structure of Fe0.2Ni0.8 alloy seems to explain the special magnetic properties of this alloy.

Kβ-to-Kα X-ray intensity ratios of Ti, V, Cr, and Co in pure metals and their disilicide compounds have been measured following excitation by 59.54 keV γ-rays from a 200 mCi 241Am point-source. The Kβ-to-Kα intensity ratios of all these metals in the disilicide compounds are found to be less than the corresponding ratios for pure metals. Comparison of the measured Kβ-to-Kα intensity ratios for the disilicides and pure metals with the multiconfiguration Dirac–Fock calculations indicates increase of the 3d electron populations of Ti, V, Cr, and Co in the disilicides from their pure metal values suggesting the rearrangement of electrons between 3d and 4s states of the individual metal atom. This rearrangement is found to be opposite to that observed in our previously reported work on NiSi2 and CuSi2.

Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium-sized π-conjugated organic molecules using recently developed LPol-n basis set family to assess their performance. Dunning's correlation-consistent basis sets of triple-ζ quality combined with MP2 method and supported by CCSD(T)/aug-cc-pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange-correlation functionals, particularly those asymptotically corrected. © 2012 Wiley Periodicals, Inc.

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A(1)Σ(u)(+), c(3)Π(u), and a(3)Σ(u)(+) manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X(1)Σ(g)(+) to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0(u)(+) state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knöckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A(1)Σ(u)(+)←X(1)Σ(g (+) transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the (1)S(0) + (3)P(1) dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.

State-of-the-art ab initio techniques have been applied to compute the potential energy curves of the (BaRb){sup +} molecular ion in the Born-Oppenheimer approximation for the singlet and triplet states dissociating into the ground-state {sup 1}S Rb{sup +} ion and the Ba atom in the ground {sup 1}S state or the lowest singlet or triplet d excited states, and for the singlet and triplet states dissociating into the ground-state {sup 2}S Rb atom and the ground-state {sup 2}S Ba{sup +} ion. The ground-state potential energy was obtained with the coupled-cluster method restricted to single, double, and nonperturbative triple excitations. The first triplet states in the {Sigma}, {Pi}, and {Delta} symmetries were computed with the restricted open-shell coupled-cluster method restricted to single, double, and nonperturbative triple excitations. All other excited-state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles, doubles, and linear triples framework. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the x {sup 1{Sigma}{yields}1{Sigma}},{sup 1{Pi}} transitions have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and doublemore » excitations. Nonadiabatic radial and angular coupling matrix elements as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration-interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit-coupled (relativistic) potential energy curves for the 0{sup +} and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single-channel scattering calculations of the collisional cross sections between the Ba{sup +} ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba{sup +} ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba{sup +} ion by collisions with ultracold Rb atoms should be possible.« less

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

An efficient, linear-scaling implementation of Kohn–Sham density-functional theory for the calculation of molecular forces for systems containing hundreds of atoms is presented. The density-fitted Coulomb force contribution is calculated in linear time by combining atomic integral screening with the continuous fast multipole method. For higher efficiency and greater simplicity, the near-field Coulomb force contribution is calculated by expanding the solid-harmonic Gaussian basis functions in Hermite rather than Cartesian Gaussians. The efficiency and linear complexity of the molecular-force evaluation is demonstrated by sample calculations and applied to the geometry optimization of a few selected large systems.

Gauge origin independent calculations of nuclear magnetic shielding tensors are carried out inside the formalism of the continuous transformation of the origin of the current density leading to formal annihilation of its diamagnetic contribution (CTOCD-DZ). We employ the unrelaxed linear response approach with a hierarchy of different coupled cluster methods in order to assess the importance of the level of approximation in the coupled cluster expansion. The basis set dependence of the computed nuclear magnetic shielding constants is also analyzed in the series of correlation consistent basis sets, with the aim of designing optimized basis sets of relatively small size.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

The time-dependent Schrödinger equation for a time-periodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasi-energy is an eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model-the coupled cluster configuration interaction (CC-CI) model-where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.

Second harmonic generation hyperpolarizabilities and their geometric derivatives have been calculated for HF, HCl, CO, and LiF, using the coupled cluster hierarchies, CCS, CC2, CCSD, CC3, and large correlation-consistent basis sets. The full configuration interaction results have been used to test the accuracy of the coupled cluster results. The CCS and CC2 methods do not improve on the Hartree-Fock results while CCSD is robust and gives significant improvements compared to CCS and CC2. The effects of triples in CC3 are in some cases substantial. Higher order correlation effects are significant for LiF. Including core-valence correlation effects is required only if high accuracy is desired. The coupled cluster results have been used as benchmarks for the results obtained by means of density functional theory using various exchange-correlation functionals. For the hyperpolarizability B3LYP was found to perform best, i.e., to give the results closest to the CC3 ones, while for the geometric derivatives none of the considered functionals was able to give a consistent description for all the considered molecules.

We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.

During the last decade it became possible to calculate by quantum chemical ab initio methods not only static but also frequency-dependent properties with high accuracy. Today, the most important tools for such calculations are coupled cluster response methods in combination with systematic hierarchies of correlation consistent basis sets. Coupled cluster response methods combine a computationally efficient treatment of electron correlation with a qualitatively correct pole structure and frequency dispersion of the response functions. Both are improved systematically within a hierarchy of coupled cluster models. The present contribution reviews recent advances in the highly accurate calculation of frequency-dependent properties of atoms and small molecules, electronic structure methods, basis set convergence and extrapolation techniques. Reported applications include first and second hyperpolarizabilities, Faraday, Buckingham and Cotton–Mouton effects as well as Jones and magneto-electric birefringence

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.

The Cauchy moments are derived and implemented for the approximate triples model CC3 with the proper N7 scaling (where N denotes the number of basis functions). The Cauchy moments are calculated for the Ne, Ar, and Kr atoms using the hierarchy of the coupled-cluster models CCS, CC2, CCSD, CC3 and a large correlation-consistent basis sets augmented with diffuse functions. A detailed investigation of the one- and N-electron errors shows that the CC3 results have the accuracy comparable to the experimental results.