Finite-field Technique Research Articles

Two-loop helicity amplitudes for gg \u2192 ZZ with full top-quark mass effects

We calculate the two-loop QCD corrections to gg → ZZ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies.

Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

Differential equations on unitarity cut surfaces

We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. We speed up the computation using finite field techniques and rational function reconstruction.

Static electric dipole polarizabilities of An(5+/6+) and AnO2 (+/2+) (An = U, Np, and Pu) ions.

The parallel components of static electric dipole polarizabilities have been calculated for the lowest lying spin-orbit states of the penta- and hexavalent oxidation states of the actinides (An) U, Np, and Pu, in both their atomic and molecular diyl ion forms (An(5+/6+) and AnO2 (+/2+)) using the numerical finite-field technique within a four-component relativistic framework. The four-component Dirac-Hartree-Fock method formed the reference for MP2 and CCSD(T) calculations, while multireference Fock space coupled-cluster (FSCC), intermediate Hamiltonian Fock space coupled-cluster (IH-FSCC) and Kramers restricted configuration interaction (KRCI) methods were used to incorporate additional electron correlation. It is observed that electron correlation has significant (∼5 a.u.(3)) impact upon the parallel component of the polarizabilities of the diyls. To the best of our knowledge, these quantities have not been previously reported and they can serve as reference values in the determination of various electronic and response properties (for example intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications. The highest quality numbers for the parallel components (αzz) of the polarizability for the lowest Ω levels corresponding to the ground electronic states are (in a.u.(3)) 44.15 and 41.17 for UO2 (+) and UO2 (2+), respectively, 45.64 and 41.42 for NpO2 (+) and NpO2 (2+), respectively, and 47.15 for the PuO2 (+) ion.

Static Electric Dipole Polarizabilities of Tri- and Tetravalent U, Np, and Pu Ions

High-quality static electric dipole polarizabilities have been determined for the ground states of the hard-sphere cations of U, Np, and Pu in the III and IV oxidation states. The polarizabilities have been calculated using the numerical finite field technique in a four-component relativistic framework. Methods including Fock-space coupled cluster (FSCC) and Kramers-restricted configuration interaction (KRCI) have been performed in order to account for electron correlation effects. Comparisons between polarizabilities calculated using Dirac-Hartree-Fock (DHF), FSCC, and KRCI methods have been made using both triple- and quadruple-ζ basis sets for U(4+). In addition to the ground state, this study also reports the polarizability data for the first two excited states of U(3+/4+), Np(3+/4+), and Pu(3+/4+) ions at different levels of theory. The values reported in this work are the most accurate to date calculations for the dipole polarizabilities of the hard-sphere tri- and tetravalent actinide ions and may serve as reference values, aiding in the calculation of various electronic and response properties (for example, intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications.

Electric dipole (hyper)polarizabilities of spatially confined LiH molecule

In this study we report on the electronic contributions to the linear and nonlinear static electronic electric dipole properties, namely the dipole moment (μ), the polarizability (α), and the first-hyperpolarizability (β), of spatially confined LiH molecule in its ground X (1)Σ(+) state. The finite-field technique is applied to estimate the corresponding energy and dipole moment derivatives with respect to external electric field. Various forms of confining potential, of either spherical or cylindrical symmetry, are included in the Hamiltonian in the form of one-electron operator. The computations are performed at several levels of approximation including the coupled-cluster methods as well as multi-configurational (full configuration interaction) and explicitly correlated Gaussian wavefunctions. The performance of Kohn-Sham density functional theory for the selected exchange-correlation functionals is also discussed. In general, the orbital compression effects lead to a substantial reduction in all the studied properties regardless of the symmetry of confining potential, however, the rate of this reduction varies depending on the type of applied potential. Only in the case of dipole moment under a cylindrical confinement a gradual increase of its magnitude is observed.

In silico prediction of atomic static electric-dipole polarizabilities of the early tetravalent actinide ions:Th4+(5f0),Pa4+(5f1), andU4+(5f2)

The dipole polarizability tensor components of the tetravalent actinide ions ${\mathrm{Th}}^{4+}$, ${\mathrm{Pa}}^{4+}$, and ${\mathrm{U}}^{4+}$ are computed using the numerical finite-field technique. Four-component correlated calculations have been performed to serve as a reference for establishing the accuracy of two- and one-component relativistic methods. A good agreement within all methods is achieved provided that extended basis sets are used to reach the complete basis set limit. The four-component correlated polarizabilities represent a database of reference values of the dipole polarizability for the early tetravalent actinide ions.

Ab initiotheory of metal-insulator interfaces in a finite electric field

We present a novel technique for calculating the dielectric response of metal/insulator heterostructures. This scheme allows, for the first time, the fully first-principles calculation of the microscopic properties of thin-film capacitors at finite bias potential. The method can be readily applied to pure insulators, where it provides an interesting alternative to conventional finite-field techniques based on the Berry-phase formalism. We demonstrate the effectiveness of our method by performing comprehensive numerical tests on a model Ag/MgO/Ag heterostructure.

Spin-orbit-resolved static polarizabilities of group-13 atoms: Four-component relativistic configuration interaction and coupled cluster calculations

This study reports static electric dipole polarizabilities of the group 13 atoms in their lowest $J=\frac{1}{2},\frac{3}{2}$ states including resolution of the property in the corresponding ${M}_{J}$ components. The polarizabilities are obtained by a numerical finite-field technique applying weak external electric fields. Special relativity is accounted for in the four-component Dirac framework. Two large-scale configuration interaction programs which can be applied either including or neglecting spin-dependent terms in the Dirac Hamiltonian, respectively, are used for the treatment of dynamic electron correlation. Coupled cluster calculations are performed for obtaining highly accurate $J=\frac{1}{2}$ ground-state polarizabilities and for calibrating the configuration interaction calculations. The heavier atoms show large differences in the properties for different $J$ states, and the effect of spin-orbit coupling is elucidated by separating it off from scalar relativistic contributions. The impact of spin-orbit interaction is also demonstrated for polarizability anisotropy components.

On the influence of non-additive interactions on the optical properties of the selected subsystems of crystalline urea

The results of many-body analysis of the intermolecular interaction energy for the selected subsystems of the molecular crystal of urea are discussed. In particular, a great importance of cooperative effects in both, the interaction energy and linear and non-linear optical properties are considered. The nature of intermolecular interactions in the urea clusters is investigated applying the hybrid variational–perturbational interaction energy decomposition scheme. Molecular polarizabilities and first-order hyperpolarizabilities are estimated by means of a finite-field technique combined with the Hartree–Fock and the second-order Møller–Plesset perturbation theories. The results of our calculations indicate a substantial influence of the many-body effects on the non-linear response of the studied hydrogen-bonded systems.

Four-component and scalar relativistic Douglas-Kroll calculations for static dipole polarizabilities of the alkaline-earth-metal elements and their ions fromCantoRan(n=0,+1,+2)

Static dipole polarizabilities for the neutral and ionized $M$, ${M}^{+}$, and ${M}^{2+}$ group 2 elements from $M=\mathrm{Ca}$ to Ra are predicted from relativistic coupled-cluster calculations using finite field techniques together with carefully optimized Gaussian-type basis sets. Useful relations between the dipole polarizability and the ionization potential are established.

Second harmonic generation second hyperpolarizability of water calculated using the combined coupled cluster dielectric continuum or different molecular mechanics methods.

In this article we report the first calculations of second harmonic generation second hyperpolarizability of liquid water using coupled cluster/molecular mechanics (CC/MM) methods or coupled cluster/dielectric continuum (CC/DC) methods. The latter approach treats the solvent as an isotropic homogeneous fluid while the former accounts for the discrete nature of the solvent molecules. The CC/MM approach may include or exclude polarization effects explicitly. Alternatively, polarization effects may be included using perturbation theory. The CC descriptions implemented are the coupled cluster second-order approximate singles and doubles (CC2) and coupled cluster singles and doubles models. The second harmonic generation second hyperpolarizabilities are, depending on the model, obtained using either an analytical implementation of the cubic response function or using an analytical implementation of the quadratic response function combined with the finite field technique. The CC/MM results for the second harmonic generation second hyperpolarizability compare excellently with experimental data while a significant overestimation is found when using the CC/DC model. Particular, the cavity radius in the CC/DC calculations have an enormous effects on this fourth-order property.

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Ab initio Hartree–Fock and MP2 calculations of the longitudinal (hyper)polarizability—including the static electronic, static zero-point vibrational average (ZPVA), and pure vibrational (static and dynamic) contributions—have been carried out on a set of seven typical medium size conjugated nonlinear optical (NLO) molecules. The ZPVA is obtained through first-order in mechanical plus electrical anharmonicity. Based on physical “nuclear relaxation” considerations the individual (square bracket) terms that contribute to the pure vibrational (hyper)polarizability are then taken into account through third-, fourth-, or fifth-order depending upon the type of term. In order to carry out the correlated treatment, field-induced coordinates and a special finite field technique are utilized. Correlation leads to very substantial differences in the absolute and relative values of the various contributions. In comparison to the electronic term the ZPVA correction is usually small but in one case is over two-thirds as large. On the other hand, both static and dynamic pure vibrational contributions are commonly of a magnitude that is comparable to, or are larger than, the electronic term. The higher-order pure vibration terms are often large. For dynamic processes they can be almost as important as the lowest-order terms; for static (hyper)polarizabilities they can be more important. Thus, for typical NLO molecules, the initial convergence behavior of the perturbation series in mechanical and electrical anharmonicity requires further investigation.

Quasirelativistic transition moment calculations using the multipartitioning perturbation theory: B0 +( [formula omitted])→X0 +( [formula omitted]) transitions in IF and ICl

A simple method of ab initio quasirelativistic calculations on electronic transition moments in molecules is presented. The description of relativistic effects through effective core potentials is combined with the use of the second-order many-body multipartitioning perturbation theory for correlation treatment. Transition moment estimates are obtained by the finite-field technique. Pilot applications to the B0 +( 3 Π )→X0 +( 1 Σ + ) transitions in IF and ICl are reported and the results are compared to experimental data. A new fit of the observed visible absorption spectra of ICl gives results in excellent agreement with our ab initio results.

Molecular property calculations for excited states using a multireference coupled-cluster approach

Abstract In this Letter, we compute the properties of the ground-state and low-lying excited states of the water molecule dominated by quasi-degenerate single-hole–particle-excited determinants with respect to the restricted Hartree–Fock determinant of the ground state. We use an extensively correlated Fock-space-based multireference version of the coupled-cluster (CC) method. The dipole moments of the ground and low-lying vertically excited states of water at the equilibrium geometry have been calculated using the finite-field technique.

Lifetimes and transition dipole moment functions of NaK low lying singlet states: Empirical and ab initio approach

The paper presents experimental D 1∏ state lifetime τv′J′ data and develops empirical and ab initio approaches concerning D 1∏ and B 1∏ lifetimes, as well as D 1∏–X 1∑+, B 1∏–X 1∑+ and D 1∏–A 1∑+ transition dipole moment functions μ(R) of the NaK molecule. Experimental D 1∏(v′,J′) state τv′J′ values for v′ varying from 1 to 22 have been obtained from experimentally measured electric radio frequency-optical double resonance (rf-ODR) signal contours. The rf-ODR signals have been produced by D 1∏←X 1∑+ laser induced optical transition and rf field (1–900 MHz) induced e–f transition within the D 1∏(v′,J′) level. The possibility to determine empirical absolute μ(R) function in a wide R range from experimental τv′J′ dependence on v′ and J′ has been demonstrated; such an approach has been applied to obtain μ(R) for the B 1∏–X 1∑+ transition on which relative intensity data are absent. The empirical D 1∏–X 1∑+μ(R) function has been considerably improved by simultaneous fitting of relative intensity and lifetime data implicitly accounting for the J′ dependence of measured lifetime values. The finite-field technique combined with the many-body multipartitioning perturbation theory was used for ab initio all-electron transition moment calculations. This approach appeared to be adequate to compute reliable μ(R) functions due to a proper description of core-valence correlations. As a result, excellent agreement between ab initio and empirical B 1∏–X 1∑+ and D 1∏–X 1∑+ transition dipole moment functions has been achieved.

Nuclear relaxation and vibrational contributions to the static electrical properties of polyatomic molecules: beyond the Hartree-Fock approximation

Electronic and nuclear contributions to the static molecular electrical properties, along with the Stark tuning rate ( δ νE ) and the infrared cross section changes ( δ SE) have been calculated at the SCF level and at different correlated levels of theory, using a TZ2P basis set and finite field techniques. Nuclear contributions to these molecular properties have also been calculated using a recent analytical approach that allow both to check the accuracy of the finite field values, and to evaluate the importance of higher-order derivatives. The HF, CO, H 2O, H 2CO, and CH 4 molecules have been studied and the results compared to experimental date when available. The paper shows that nuclear relaxation and vibrational contributions must be included in order to obtain accurate values of the static electrical properties. Two different, combined approaches are proposed to predict experimental values of the electrical properties to an error smaller than 5%.

Calculation of static molecular properties in the framework of the unitary group based coupled cluster approach

The recently developed and implemented state selective, fully spin-adapted coupled cluster (CC) method that employs a single, yet effectively multiconfigurational, spin-free reference and the formalism of the unitary group approach (UGA) to the many-electron correlation problem, has been employed to calculate static electric properties of various open-shell (OS) systems using the finite field (FF) technique. Starting with the lithium atom, the method was applied at the first-order interacting space single and double excitation level (CCSD(is)) to several first- and second-row hydrides having OS ground state, namely to the CH, NH, OH, SiH, PH, and SH radicals. In the case of NH we also considered three OS excited states. In all cases the dipole moment and polarizability were determined using a high quality basis set and compared with the experiment, whenever available, as well as with various configuration interaction results and other theoretical results that are available from the literature. The agreement of our CCSD(is) values with experiment is very satisfactory except for the 3Σ− ground state of the NH radical, where the experimentally determined dipole moment is too small. No experimental data are available for the corresponding polarizabilities. It is also shown that the FF technique is not suitable for calculations of higher order static properties, such as the hyperpolarizability β and γ tensors. For this reason we formulate the linear response version of our UGA-based CCSD approach and discuss the aspects of its future implementation. Key words: static molecular properties, dipole moments, polarizabilities, free radicals, unitary group based coupled cluster method, linear response theory, finite field technique.

State-selective multireference coupled-cluster theory: In pursuit of property calculation

In this work, we examine the efficiency of the recently developed [P. Piecuch et al., J. Chem. Phys. 99, 6732 (1993)] state-selective (SS) multi-reference (MR) coupled-cluster (CC) method for calculation of molecular properties. In our earlier papers, we demonstrated that the SSMRCC method with inclusion of single, double, and internal and semi-internal triple excitations [SSCCSD(T) approach] is capable of providing an accurate description of the ground-state potential energy surfaces. In this paper, we present the dipole moment and polarizability values of the HF molecule at equilibrium and stretched geometries calculated using finite field technique and SSCCSD(T) ansatz. The calculations use double zeta quality basis sets with and without polarization functions. Molecular orbital basis sets include both relaxed and nonrelaxed orbitals.

Relativistic pseudopotential calculations of the ground-state spectroscopic properties of HBr

Spectroscopic properties are predicted for the diatomic HBr using a scalar relativistic pseudopotential approach. The potential curves are discussed at different levels of theory. The dipole moment and static dipole polarizability curves are calculated by using a finite field technique. Rotational, vibrational and isotope effects on molecular properties are investigated. The calculated spectroscopic constants are in good agreement with the available experimental data.