Fourth-order Perturbation Theory Research Articles

Gaussian-4 theory using reduced order perturbation theory

Two modifications of Gaussian-4 (G4) theory [L. A. Curtiss et al., J. Chem. Phys. 126, 084108 (2007)] are presented in which second- and third-order perturbation theories are used in place of fourth-order perturbation theory. These two new methods are referred to as G4(MP2) and G4(MP3), respectively. Both methods have been assessed on the G3/05 test set of accurate experimental data. The average absolute deviation from experiment for the 454 energies in this test set is 1.04 kcalmol for G4(MP2) theory and 1.03 kcalmol for G4(MP3) theory compared to 0.83 kcalmol for G4 theory. G4(MP2) is slightly more accurate for enthalpies of formation than G4(MP3) (0.99 versus 1.04 kcalmol), while G4(MP3) is more accurate for ionization potentials and electron affinities. Overall, the G4(MP2) method provides an accurate and economical method for thermochemical predictions. It has an overall accuracy for the G3/05 test set that is much better than G3(MP2) theory (1.04 versus 1.39 kcalmol) and even better than G3 theory (1.04 versus 1.13 kcalmol). In addition, G4(MP2) does better for challenging hypervalent systems such as H(2)SO(4) and for nonhydrogen species than G3(MP2) theory.

Effect of magnons on the 0–π transition in a superconductor/half-metallic ferromagnet/superconductor junction

We study the Josephson effect in an s-wave superconductor/dirty half-metal/s-wave superconductor (SC/HM/SC) junction by taking account of the spin dynamics due to the magnon excitation in the HM. Using the fourth order perturbation theory for the tunneling Hamiltonian and Green’s function method, we formulate the Josephson critical current in a SC/HM/SC junction. In the tunneling process from the SC to the HM and vice versa, we consider the effect of spin flip tunneling due to the magnon excitation at the interface. As a result, it is found that the spin triplet pair correlation propagates into the HM and the Josephson current flows. We find that the Josephson critical current shows the damped oscillation as a function of the thickness of the HM and the 0–π transition occurs. Moreover, we show that the 0–π transition occurs by changing temperature. The 0–π transition results from magnon excitations in the HM. This proposes a new mechanism with respect to the 0–π transition.

0- and π-states in Josephson coupling through magnetic layers

We study the Josephson coupling energy, EJ, between two superconductors (SCs) through magnetic layers, i.e., ferromagnetic metal (FM) and antiferromagnetic insulator (AFI). By the tunneling Hamiltonian approach, analytical formulae of EJ are given in the fourth order perturbation theory as to the tunneling matrix element. In the former case, the EJ exhibits a damped oscillatory dependence on the thickness of the FM, and shows a transition between the 0- and the π-Josephson couplings. In the latter case, the magnetic exchange interaction in the AFI plane suppresses the π-Josephson coupling, and the 0-Josephson coupling leads to coexistence between SC and AFI. It is found that the origin of π-Josephson coupling in the SC/AFI/SC junction is different from that in the SC/FM/SC one.

Role of Magnetic Scattering in 0–π Transitions in a Superconductor/Ferromagnetic Metal/Superconductor Junction

We study the influence of magnetic scattering on the Josephson critical current, Ic, in a superconductor/ferromagnetic metal/superconductor (SFS) junction by a tunneling Hamiltonian approach. An analytical formula of Ic is given in the fourth order perturbation theory as regards the tunneling matrix element. The Ic exhibits the damped oscillatory dependence on the thickness of the ferromagnetic metal, d, and shows the transition between 0- and pi-states with d. When the superconducting transition temperature is comparable to the ferromagnetic Curie temperature, the period of oscillation is obviously changed by increasing temperature, T, due to the magnetic scattering, which induces the 0-pi transition with T. The magnetic scattering provides rich variety of Josephson effect in the SFS junction. Our results present an appropriate condition of a superconductor and a ferromagnetic metal to control the 0- and the pi-states.

Effective Landé factor [formula omitted] of conduction electrons in GaAs and AlSb

Using third and fourth order perturbation theory inside a 14-band and 30-band k ⋅ p model, we have calculated the effective Landé factor g ∗ of Γ 6 C conduction electrons in GaAs and AlSb. A strong variation between both models is observed. We show that the 14-band formalism even in fourth order perturbation theory is not sufficient to predict an experimental data of g ∗ . However, results deduced by the 30-band k ⋅ p model are consistent with experimental data. In particular, the k ⋅ p Hamiltonian parameters are adjusted such that the g ∗ of GaAs and AlSb are respectively −0.391 and 0.81, in excellent agreement with the experimental values of −0.44 and 0.84.

Theory of 0– [formula omitted] transition in a superconductor/ferromagnet/superconductor junction

We study the 0– π transition by taking into account magnetic scattering in a dirty ferromagnet (FM). Using the fourth order perturbation theory for the tunneling Hamiltonian and Green's function method, we formulate the Josephson effect in a SC/FM/SC junction, where SC is a superconductor. It is found that Josephson critical current shows the damped oscillation as a function of the thickness of the ferromagnet and the 0– π transition occurs. Moreover, it is found that the 0– π transition occurs by changing temperature due to the magnetic scattering.

Convergence of the chiral expansion for the nucleon mass

A number of papers recently have used fourth-order chiral perturbation theory to extrapolate lattice data for the nucleon mass; the process seems surprisingly successful even for large pion masses. This paper shows that the inclusion of the fifth-order terms spoils the agreement.

Body-assisted van der Waals interaction between two atoms

Using fourth-order perturbation theory, a general formula for the van der Waals potential of two neutral, unpolarized, ground-state atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is derived. The theory is applied to two atoms in bulk material and in front of a planar multilayer system, with special emphasis on the cases of a perfectly reflecting plate and a semi-infinite half space. It is demonstrated that the enhancement and reduction of the two-atom interaction due to the presence of a perfectly reflecting plate can be understood, at least in the nonretarded limit, by using the method of image charges. For the semi-infinite half space, both analytical and numerical results are presented.

A general formula obtained from induced moments for the retarded van der Waals dispersion energy shift between two molecules with arbitrary electric multipole polarizabilities: I. Ground state interactions

An expression for the dispersion energy shift arising from the interaction of two ground state polarizable molecules of arbitrary electric multipole moment order is obtained. The physical viewpoint adopted is one in which an electric polarizable body subject to vacuum fluctuations associated with an electric displacement field gives rise to an induced multipole moment. The moments induced at each centre couple to the retarded electric multipole–multipole resonant interaction tensor, resulting in a direct evaluation of the generalized formula for the dispersion potential between the pair. The present approach is compared and contrasted to a previous derivation of the interaction energy which required the Casimir–Polder potential as its starting point and employed fourth-order time-dependent perturbation theory. Although the functional forms obtained for the generalized energy shift differ in the two methods, identical expressions result for specific contributions to the dispersion potential. This is shown explicitly for the first few lowest order cases, comprising molecules possessing electric dipole, quadrupole and octupole polarizability characteristics. In this paper, the present approach is used to calculate energy shifts between an excited and an unexcited molecule.

Structure and properties of theNi@Si12cluster from all-electronab initiocalculations

The structural, electronic, and vibrational properties of the $\mathrm{Ni}@{\mathrm{Si}}_{12}$ cluster have been studied using all-electron ab initio calculations in the framework of the density functional theory (DFT) with the hybrid nonlocal exchange and correlation functional of Becke-Lee-Yang-Parr (B3LYP). Perturbation theory was also used for the lowest energy competing structures in order to unambiguously identify the ground state in view of marginal total energy differences at the DFT/B3LYP level of theory. To facilitate possible future experimental identification and to check the stability of the structures, we have performed vibrational analyses that include Raman and infrared spectra for the stable structures. Through the vibrational analysis, we have found that the ${C}_{5v}$ symmetric Frank-Kasper structure, based on an icosahedral structural motif, which for some time was believed as the ground state, is unstable. Our calculations reveal a ground state of ``cubic'' ${D}_{2d}$ symmetry, which at the fourth order of perturbation theory is about $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ lower than the alternative suggested ground state, based on a hexagonal structural motif. This distorted hexagonal structure of ${C}_{\mathrm{S}}$ symmetry at the DFT/B3LYP level of theory is practically isoenergetic to our cubic ${D}_{2d}$ structure, with a marginal energy difference of about $0.04\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. In addition to IR and Raman spectra, we have examined in detail electronic (bonding and binding), structural, and chemical characteristics that could be important for possible future applications of these or derived from these materials. Such characteristics include total and partial density of states, crystal orbital overlap populations, binding energies, ionization potentials, electron affinities, ``chemical hardness,'' and embedding energies.

Intermolecular interactions in a radiation field via the method of induced moments

Molecular quantum electrodynamics is employed to calculate a generalized formula for the energy shift between a pair of molecules that have electric polarizability of arbitrary multipole order and are in the presence of an intense electromagnetic field. In contrast to a previous calculation of the dipole-dipole contribution, which required fourth-order time-dependent perturbation theory for its evaluation, the present approach involves calculating the interaction between the multipole moments induced at each center by the incident beam and the resonant multipole-multipole coupling tensor together with the average value of the spatial correlation function of the displacement field for an $N$-photon state. The theory developed applies to the situation where the molecular pair is held fixed relative to the direction of propagation of the radiation field or is allowed to be completely randomly oriented. Explicit results are obtained for dipole-quadrupole and quadrupole-quadrupole polarizable molecules. For oriented systems the energy shift for linear and circular polarizations is examined for incident radiation propagating in directions parallel and perpendicular to the intermolecular join, and the asymptotic behavior is obtained at the limits of short and large separation distance. After performing a pair orientation average, the energy shift in the near zone is found to exhibit an ${R}^{\ensuremath{-}1}$ power-law behavior with separation distance, while the far zone has a modulated ${R}^{\ensuremath{-}2}$ dependence in all of the cases considered. None of the energy shifts obtained display discriminatory characteristics, with respect to either the handedness of the incident beam or the individual species.

Nonlinear absorption spectrum in the field of a weakly saturating standing wave

The spectrum of a probe field in a three-level system interacting with a standing wave at the adjacent transition is calculated. The expression for a nonlinear resonance profile is obtained taking into account diffusion in the velocity space in the fourth order of perturbation theory in the standing-wave amplitude.

Structure and energy stability of lanthanum and lutetium trihalide dimer molecules

The geometrical parameters of lanthanum and lutetium trihalide dimer molecules Ln2X6 (Ln = La, Lu; X = F, Cl, Br, I) and dissociation energies of Ln2X6 → 2LnX3 were calculated in terms of Mo ller-Plesset fourth order perturbation theory including single, double, triple, and quadruple excitations (SDTQ-MP4). Variation of the properties of molecules in series of compounds Ln2F6 → Ln2Cl6 → Ln2Br6 → Ln2I6 from lanthanum La2X6 to lutetium Lu2X6 compounds and from monomer LnX3 to dimer Ln2X6 molecules has been studied (the parameters of LnX3 molecules were determined in the same SDTQ-MP4 approximation). The lanthanide compression of the metal-halogen internuclear distance Δr(Ln-X) = re(La-X)-re(Lu-X) depends on the nature of the ligand X and coordination number of Ln. The calculated data are compared with previously published experimental and theoretical data on the structure and dissociation energies of Ln2X6 molecules.

Analysis off−pmodel for octupole ordering inNpO2

In order to examine the origin of octupole ordering in NpO2, we propose a microscopic model constituted of neptunium 5f and oxygen 2p orbitals. To study multipole ordering, we derive effective multipole interactions from the f-p model by using the fourth-order perturbation theory in terms of p-f hopping integrals. Analyzing the effective model numerically, we find a tendency toward \Gamma_{5u} antiferro-octupole ordering.

Why Isn′t the N20 Dodecahedron Ideal for Three‐Coordinate Nitrogen?

AbstractFor Abstract see ChemInform Abstract in Full Text.

Higher-orderCndispersion coefficients for the alkali-metal atoms

The van der Waals coefficients, from ${C}_{11}$ through to ${C}_{16}$ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the ${C}_{n}∕{r}^{n}$ potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to ${C}_{10}∕{r}^{10}$ results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than $20{a}_{0}$. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive $({C}_{11},{C}_{13},{C}_{15})$ and attractive $({C}_{12},{C}_{14},{C}_{16})$ dispersion forces.

Structure, vibrational spectra, and energetic stability of LnX 4 − ions (Ln=La, Lu; X=F, Cl, Br, I)

Molecular structure and properties of La and Lu tetrahalide ions LnX 4 − ) are studied by the configuration interaction singles-and-doubles method augmented with quadruple excitation correction (CISD+Q) and by the fourth-order Moller-Plesset perturbation theory with account for single, double, triple, and quadruple excitations (SDTQ-MP4). The atomic inner shells are described by Stevens relativistic effective core potentials. Valence basis sets are augmented with diffuse s-, p-, and polarization d-, f-, and g-functions. The equilibrium configuration of nuclei in LnX 4 − ions was found to be tetrahedral. The equilibrium internuclear distances, quadratic force constants, vibrational frequencies, and IR intensities of LnX 4 − ions are compared with the corresponding parameters of La and Lu trihalide molecules (LnX3), calculated within the same approximations. Regularities in the behavior of molecular parameters on going along the LnF 4 − →LnCl 4 − →LnBr 4 − →LnI 4 − series and from La compounds to Lu compounds are revealed. Heights of the energy barriers to the LnX 4 − inversion through the square planar structures (T d → D 4h →T d ) are evaluated: 100–110 and 130–150 kJ/mol for LaX 4 − and LuX 4 − , respectively. Enthalpies of dissociation reactions LnX 4 − →LnX3+X− are calculated and the results obtained are compared with the available experimental data.

Orientation of single crystals using linear approximations to NMR transits

We have derived analytical expressions for determining the orientation of high-symmetry single crystals from line-crossings in a single rotation plot. We demonstrate the utility of the method using the strontium-87 resonance in strontium nitrate. Employing our new method, which we call orientation of single crystals using linear approximations to NMR transits (OSCULANT), in combination with fourth-order perturbation theory, we obtain a highly accurate value for the quadrupole coupling constant, and an estimate for the chemical shielding anisotropy.

Why Isn't the N20 Dodecahedron Ideal for Three-Coordinate Nitrogen?

Nitrogen molecules are the focus of much attention for their potential as high-energy density materials. The usefulness of such molecules as energy sources depends on the stability of the molecules with respect to dissociation. Many such molecules dissociate too easily to be a stable fuel, and the reasons for such instability are related to the details of structure and bonding of the molecule. Such details will be examined for isomers of the molecule N20. N20 has a highly symmetric isomer in which the 20 atoms occupy the vertexes of a dodecahedron. This isomer is a cage molecule in which all of the faces are regular pentagons that have interior angles of 108 degrees . These angles are very close to the known bond angles in very stable nitrogen compounds such as ammonia. Such a structure with only pentagons should provide an ideal bonding environment for three-coordinate nitrogen. However, by use of theoretical calculations including density-functional theory and fourth-order perturbation theory, along with the Dunning correlation-consistent basis sets, it will be shown that dodecahedral N20 is not the most stable cage for N20. The reasons why will be discussed in terms of the structure and bonding of the molecules.

Borrowing Intensity in Rare Earth Doped Materials; Magnetic Dipole Transitions

A theoretical model of magnetic dipole transitions in crystals doped by the lanthanide ions is based on the fourth-order perturbation theory applied for the Hamiltonian in which two perturbing mechanisms are taken into account. Namely, the impact due to the crystal field potential and also spin-orbit interaction operator is included in the transition amplitude. The analysis is performed in the language of Racah algebra applied for the formulation of the effective operators expressed in terms of unit double tensor operators. The radial integrals of the terms contributing at the fourth order are defined within the perturbed function approach, due to which their values are evaluated for the complete radial basis sets of one-electron states of given symmetry. The numerical analysis performed for the Eu3+ ion provides the information on the relative importance of various effective operators and allows one to establish a hierarchy of important terms contributing to the transition amplitude. The results of the analysis lead also to the verification of possible importance of magnetic dipole transitions in the description of 0 ↔ 0 and 0 ↔ 1 electric dipole transitions via the so-called borrowing mechanism introduced by Wybourne.