Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

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.     

Closed-shell coupled-cluster theory with spin-orbit coupling

A two-component closed-shell coupled-cluster (CC) approach using relativistic effective core potentials with spin-orbit coupling included in the post-Hartree-Fock treatment is proposed and implemented at the CC singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations [CCSD(T)]. The latter invokes as an additional approximation the neglect of the occupied-occupied and virtual-virtual blocks of the spin-orbit coupling matrix in order to avoid the iterative N(7) steps in the treatment of triple excitations. The computational effort of the implemented two-component CC methods is about 10-15 times that of its corresponding nonrelativistic counterpart, which needs to be compared to the by a factor of 32 higher cost for fully relativistic schemes and schemes with spin-orbit coupling included already at the Hartree-Fock self-consistent field (HF-SCF) level. This substantial computational saving is due to the use of real molecular orbitals and real two-electron integrals. Results on 5p-, 6p-, and 7p-block element compounds show that the bond lengths and harmonic frequencies obtained with the present two-component CCSD method agree well with those computed with the CCSD approach including spin-orbit coupling at the HF-SCF level even for the 7p-block element compounds. As for the CCSD(T) approach, high accuracy for 5p- and 6p-block element compounds is retained. However, the difference in bond lengths and harmonic frequencies becomes somewhat more pronounced for the 7p-block element compounds.     

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a "global analysis" (that is to say that all non-negligible interactions are explicitly included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are r(CC) = 120.2958(7) pm and r(CH) = 106.164(1) pm.     

Perturbative treatment of scalar-relativistic effects in coupled-cluster calculations of equilibrium geometries and harmonic vibrational frequencies using analytic second-derivative techniques

An analytic scheme for the computation of scalar-relativistic corrections to nuclear forces is presented. Relativistic corrections are included via a perturbative treatment involving the mass-velocity and the one-electron and two-electron Darwin terms. Such a scheme requires mixed second derivatives of the nonrelativistic energy with respect to the relativistic perturbation and the nuclear coordinates and can be implemented using available second-derivative techniques. Our implementation for Hartree-Fock self-consistent field, second-order Moller-Plesset perturbation theory, as well as the coupled-cluster level is used to investigate the relativistic effects on the geometrical parameters and harmonic vibrational frequencies for a set of molecules containing light elements (HX, X=F, Cl, Br; H2X, X=O, S; HXY, X=O, S and Y=F, Cl, Br). The focus of our calculations is the basis-set dependence of the corresponding relativistic effects, additivity of electron correlation and relativistic effects, and the importance of core correlation on relativistic effects.     

Automated generation of coupled-cluster diagrams: implementation in the multireference state-specific coupled-cluster approach with the complete-active-space reference

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specific multireference coupled-cluster theory (SSMRCC) based on the concept of a "formal reference state." The algorithm was tested in SSMRCC calculations describing dissociation of a single bond and in calculations describing simultaneous dissociation of two single bonds--the problem requiring up to six-particle excitations in the CC operator.     

Theoretical predictions of nuclear magnetic resonance parameters in a novel organo-xenon species: chemical shifts and nuclear quadrupole couplings in HXeCCH

We calibrate the methodology for the calculation of nuclear magnetic resonance (NMR) properties in novel organo-xenon compounds. The available state-of-the-art quantum-chemical approaches are combined and applied to the HXeCCH molecule as the model system. The studied properties are (129)Xe, (1)H, and (13)C chemical shifts and shielding anisotropies, as well as (131)Xe and (2)H nuclear quadrupole coupling constants. The aim is to obtain, as accurately as currently possible, converged results with respect to the basis set, electron correlation, and relativistic effects, including the coupling of relativity and correlation. This is done, on one hand, by nonrelativistic correlated ab initio calculations up to the CCSD(T) level and, on the other hand, for chemical shifts and shielding anisotropies by the leading-order relativistic Breit-Pauli perturbation theory (BPPT) with correlated ab initio and density-functional theory (DFT) reference states. BPPT at the uncorrelated Hartree-Fock level as well as the corresponding fully relativistic Dirac-Hartree-Fock method are found to be inapplicable due to a dramatic overestimation of relativistic effects, implying the influence of triplet instability in this multiply bonded system. In contrast, the fully relativistic second-order Moller-Plesset perturbation theory method can be applied for the quadrupole coupling, which is a ground-state electric property. The performance of DFT with various exchange-correlation functionals is found to be inadequate for the nonrelativistic shifts and shielding anisotropies as compared to the CCSD(T) results. The relativistic BPPT corrections to these quantities can, however, be reasonably predicted by DFT, due to the improved triplet excitation spectrum as compared to the Hartree-Fock method, as well as error cancellation within the five main BPPT contributions. We establish three computationally feasible models with characteristic error margins for future calculations of larger organo-xenon compounds to guide forthcoming experimental NMR efforts. The predicted (129)Xe chemical shift in HXeCCH is in a novel range for this nucleus, between weakly bonded or solvated atomic xenon and xenon in the hitherto characterized molecules.     

An overview of coupled cluster theory and its applications in physics

Summary What has since become known as the normal coupled cluster method (NCCM) was invented about thirty years ago to calculate ground-state energies of closed-shell atomic nuclei. Coupled cluster (CC) techniques have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within the NCCM. Further extensions deal both with systems at nonzero temperature and with general dynamical behaviour. More recently, a new version of CC theory, the so-called extended coupled cluster method (ECCM) has been introduced. It has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. CC techniques are now widely recognized as providing one of the most universally applicable, most powerful, and most accurate of all microscopicab initio methods in quantum many-body theory. The number of successful applications within physics is now impressively large. In most such cases the numerical results are either the best or among the best available. A typical case is the electron gas, where the CC results for the correlation energy agree over the entire metallic density range to within less than 1 millihartree (or <1%) with the essentially exact Green's function Monte Carlo results. The role of CC theory within modern quantum many-body theory is first surveyed, by a comparison with other techniques. Its full range of applications in physics is then reviewed. These include problems in nuclear physics, both for finite nuclei and infinite nuclear matter; the electron gas; various integrable and nonintegrable models; various relativistic quantum field theories; and quantum spin chain and lattice models. Particular applications of the ECCM include the quantum hydrodynamics of a zero-temperature, strongly-interacting condensed Bose fluid; a charged impurity in a polarizable medium (e.g., positron annihilation in metals); and various anharmonic oscillator and spin systems.     

Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings.

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.     

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, H(2)O, NH(3), and CH(4)) as well as the more challenging molecules CO, N(2), and O(3) [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational g tensors.     

Theoretical study on the low-lying electronic states of NiH and NiAt

The low-lying electronic states of NiH and NiAt are investigated by using multireference second-order perturbation theory with relativistic effects taken into account. The potential energy curves as well as the corresponding spectroscopic constants are reported. The results are grossly in good agreement with the available experimental data and should thus be very useful for guiding future experimental measurements. A cross comparison with other nickel monohalides NiX (X = F, Cl, Br, and I) reveals that the change in the spin-orbit splittings when going from lighter to heavier ligands results more from the state interaction than from the relativistic effects of the ligands.     

On the ground and some low-lying excited states of ScB: a multiconfigurational study

The electronic structure of a series of low-lying excited triplet and quintet states of scandium boride (ScB) was examined using multireference configuration interaction (including Davidson's correction for quadruple excitations) and single-reference coupled cluster (CC) methods with averaged natural orbital (ANO) basis sets. The CC approach was used only for the lowest quintet state. The authors have analyzed eight low-lying triplets 3Sigma-(2), 3Sigma+, 3Pi(3), and 3Delta(2) dissociating to Sc(2D)/B(2P) atoms and eight low-lying quintet states 5Sigma-, 5Sigma+, 5Pi(2), 5Phi, and 5Delta(3) dissociating to Sc(4F)/B(2P) atoms. They report the potential energy curves and spectroscopic parameters of ScB obtained with the multireference configuration interaction (MRCI) technique including all singly and doubly excited configurations obtained with the ANO-S basis set. For the two lowest states they obtained also improved ANO-L spectroscopic constants, dipole and quadrupole moments as well as scalar relativistic effects based on the Douglas-Kroll-Hess Hamiltonian. They provide the analysis of the bonding based on Mulliken populations and occupation numbers. Since the two lowest states, 3Sigma- and 5Sigma-, lie energetically very close, their principal goal was to resolve the nature of the ground state of ScB. Their nonrelativistic MRCI(Q) (including Davidson correction) results indicate that the quintet is more stable than the triplet by about 800 cm(-1). Inclusion of scalar relativistic effects reduces this difference to about 240 cm(-1). The dissociation energies for 5Sigma- ScB range from 3.20 to 3.30 eV while those for the 3Sigma- range from 1.70 to 1.80 eV.     

Rotational spectra of 1-chloro-2-fluoroethylene. II. Equilibrium structures of the cis and trans isomer

Equilibrium structures for the cis and trans isomer of 1-chloro-2-fluoroethylene are reported. The structures are obtained within a least-squares fit procedure using the available experimental ground-state rotational constants for various isotopic species of both forms. Vibrational effects were eliminated before the analysis using vibration-rotation interaction constants derived from computed quadratic and cubic force fields with the required quantum chemical calculations carried out using second-order Moller-Plesset perturbation as well as coupled-cluster (CC) theory. The semiexperimental or empirical equilibrium geometries obtained in this way agree well with the corresponding theoretical predictions obtained from CC calculations [at the CCSD(T) level] after extrapolation to the complete basis-set limit and inclusion of core-valence correlation corrections. The present results allow a detailed analysis of the geometrical differences between the two forms of 1-chloro-2-fluoroethylene. They are also compared to the structural data available for other halogenated ethylenes.     

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.     

Rotational spectra of rare isotopic species of bromofluoromethane: determination of the equilibrium structure from ab initio calculations and microwave spectroscopy

Guided by theoretical predictions, the rotational spectra of the mono- and bideuterated species of bromofluoromethane, CDH(79)BrF, CDH(81)BrF, CD(2) (79)BrF, and CD(2) (81)BrF, have been recorded for the first time. Assignment of a few hundred rotational transitions led to the accurate determination of the ground-state rotational constants, all of the quartic and most of the sextic centrifugal distortion constants, as well as the full bromine quadrupole-coupling tensor for both (79)Br and (81)Br, in good agreement with corresponding theoretical predictions based on high-level coupled-cluster calculations. The rotational spectra of the (13)C containing species (13)CH(2) (79)BrF and (13)CH(2) (81)BrF have been observed in natural abundance and have been assigned, thus allowing the determination of the rotational and centrifugal distortion constants as well as the bromine quadrupole-coupling tensor. Furthermore, empirical equilibrium structures have been obtained within a least-squares fit procedure using the available experimental ground-state rotational constants for various isotopic species. Vibrational effects have been accounted for in the analysis using vibration-rotation interaction constants derived from anharmonic force fields computed at the second-order Moller-Plesset perturbation theory as well as coupled-cluster (CC) levels. The empirical equilibrium geometries obtained in this way agree well with the corresponding theoretical predictions obtained from CC calculations [at the CCSD(T) level] after extrapolation to the complete basis set limit and inclusion of core-valence correlation corrections and relativistic effects.     

Fully relativistic coupled cluster and DFT study of electric field gradients at Hg in 199Hg compounds

We investigate the magnitude and interplay of relativistic and electron correlation effects on the electric field gradient (EFG) at the position of Hg in linear and bent HgL(2) (L = CH(3), Cl, Br, I) and trigonal planar [HgCl(3)](-) compounds using four-component relativistic Dirac-Coulomb (DC) and non-relativistic (NR) calculations at the Hartree-Fock (HF), DFT, MP2 and coupled cluster (CC) levels. The relativistic and electron correlation contributions to EFG have opposite signs and are not additive, demonstrating the importance of taking into account relativistic and electron correlation contributions on an equal footing. DC-MP2 overestimates the electron correlation correction by 0.48-0.56 a.u. for Hg-halides and by 0.8 a.u. for Hg(CH(3))(2), respectively, while DC-CCSD underestimates the correlation correction by 0.57-0.66 a.u. compared to the reference DC-CCSD-T data. EFGs obtained at the DC-DFT level vary considerably with the functional; DC-CAMB3LYP and DC-BH&H reproduce DC-CCSD-T results within 0.08-0.24 a.u. (1%-3%) for Hg(CH(3))(2) and Hg-halides, respectively. An updated value of the nuclear quadrupole moment of the I = 5/2 excited state of (199)Hg, Q((199)Hg) = 0.675(12) b is derived from the literature. This value compares well with that derived from our calculated EFG at the DC-CCSD-T level and the experimental data for Hg(CH(3))(2); Q((199)Hg) = 0.650 b.     

A direct relativistic four-component multiconfiguration self-consistent-field method for molecules

A new direct relativistic four-component Kramers-restricted multiconfiguration self-consistent-field (KR-MCSCF) code for molecules has been implemented. The program is based upon Kramers-paired spinors and a full implementation of the binary double groups (D(2h)(*) and subgroups). The underlying quaternion algebra for one-electron operators was extended to treat two-electron integrals and density matrices in an efficient and nonredundant way. The iterative procedure is direct with respect to both configurational and spinor variational parameters; this permits the use of large configuration expansions and many basis functions. The relativistic minimum-maximum principle is implemented in a second-order restricted-step optimization algorithm, which provides sharp and well-controlled convergence. This paper focuses on the necessary modifications of nonrelativistic MCSCF methodology to obtain a fully variational KR-MCSCF implementation. The general implementation also allows for the use of molecular integrals from a two-component relativistic Hamiltonian as, for example, the Douglas-Kroll-Hess variants. Several sample applications concern the determination of spectroscopic properties of heavy-element atoms and molecules, demonstrating the influence of spin-orbit coupling in MCSCF approaches to such systems and showing the potential of the new method.     

On the performance of two-component energy-consistent pseudopotentials in atomic Fock-space coupled cluster calculations

The four-component atomic intermediate-Hamiltonian Fock-space coupled cluster (IHFSCC) code of Landau et al. [J. Chem. Phys. 115, 6862 (2001)] has been adapted to two-component calculations with relativistic pseudopotentials of the energy-consistent variety. Recently adjusted energy-consistent pseudopotentials for group 11 and 12 transition elements as well as group 13 and 14 post-d main group elements, which were fitted to atomic valence spectra from four-component multiconfiguration Dirac-Hartree-Fock calculations, are tested in IHFSCC calculations for ionization potentials, electron affinities, and excitation energies of a variety of atoms and ions. Where comparison is possible, the deviations from experimental data are in good agreement with those found in previously published IHFSCC all-electron calculations: experimental data are usually reproduced within a few hundred wavenumbers.     

Electron–positron pair production and bremsstrahlung at intermediate energies in the field of heavy atoms

The Coulomb corrections (CC) to the processes of bremsstrahlung and pair production are investigated. The next-to-leading term in the high-energy asymptotics is found. This term becomes very essential in the region of intermediate energies. The influence of screening for CC is small for differential cross section, spectrum, and the total cross section of pair production. The same is true for the spectrum of bremsstrahlung, but not for the differential cross section, where the influence of screening can be very large. The corresponding screening corrections as well as the modification of the differential cross section of bremsstrahlung are found. A comparison of our results for the total cross section of pair production with the experimental data available is performed. This comparison has justified our analytical results and allowed to elaborate a simple ansatz for the next-to-leading correction. The influence of the electron beam shape on CC for bremsstrahlung is investigated. It turns out that the differential cross section is very sensitive to this shape.     

Comparative study of relativistic density functional methods applied to actinide species AcO(2)(2+) and AcF(6) for Ac = U,Np

A two-component relativistic density functional method based on the Douglas-Kroll-Hess transformation has been applied to the actinyls and hexafluorides of U and Np. All-electron scalar relativistic calculations as well as calculations including spin-orbit interaction have been compared to results obtained with a pseudopotential approach. In addition, several exchange-correlation potentials have been applied to examine their performance for the bond lengths and vibrational frequencies of the title compounds. The calculations confirm the well-known accuracy of the LDA approach for geometries and frequencies, which is corroborated for the hexafluorides where gas phase experimental data are available. Comparison with results of accurate wave function based methods provides further confirmation of this finding. Gradient-corrected functionals tend to overestimate bond lengths and underestimate frequencies also for actinide compounds. The results obtained with Stoll-Preuss (small core) effective core potentials agree very well with those of all-electron calculations, while calculations with Hay-Martin large core pseudopotentials are somewhat less accurate. For all molecules and properties considered, spin-orbit effects have been found negligible concomitant with the closed-shell electronic structure of the U(VI) compounds and the open-shell situation of the Np(VI) compounds with a single valence f electron.