The Experts below are selected from a list of 24855 Experts worldwide ranked by ideXlab platform
Friedrich Grein - One of the best experts on this subject based on the ideXlab platform.
-
quadrupole octopole and hexadecapole Electric Moments of σ π δ and φ electronic states cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum
Journal of Chemical Physics, 2007Co-Authors: Pablo J Bruna, Friedrich GreinAbstract:The number of independent components, n, of traceless Electric 2l-multipole Moments is determined for C∞v molecules in Σ±, Π, Δ, and Φ electronic states (Λ=0,1,2,3). Each 2l pole is defined by a rank-l irreducible tensor with (2l+1) components Pm(l) proportional to the solid spherical harmonic rlYml(θ,φ). Here we focus our attention on 2l poles with l=2,3,4 (quadrupole Θ, octopole Ω, and hexadecapole Φ). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Λ. For Σ±(Λ=0) states, all 2l poles have one independent parameter (n=1). For spatially degenerate states—Π, Δ, and Φ (Λ=1,2,3)—the general rule reads n=1 for l<2∣Λ∣ (when the 2l-pole rank lies below 2∣Λ∣) but n=2 for higher 2l poles with l⩾2∣Λ∣. The second nonzero term is the off-diagonal matrix element ⟨ψ+Λ∣P∣m∣=2Λ(l)∣ψ−Λ⟩. Thus, a Π(Λ=1) state has one dipole (μz) but two independent 2l poles for l⩾2—starting with the quadrupole [Θzz,(Θxx−Θyy)]. A Δ(Λ=2) state has n=1 for 2(1,2,3...
-
quadrupole octopole and hexadecapole Electric Moments of σ π δ and φ electronic states cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum
Journal of Chemical Physics, 2007Co-Authors: Pablo J Bruna, Friedrich GreinAbstract:The number of independent components, n, of traceless Electric 2(l)-multipole Moments is determined for C(infinity v) molecules in Sigma(+/-), Pi, Delta, and Phi electronic states (Lambda=0,1,2,3). Each 2(l) pole is defined by a rank-l irreducible tensor with (2l+1) components P(m)((l)) proportional to the solid spherical harmonic r(l)Y(m)(l)(theta,phi). Here we focus our attention on 2(l) poles with l=2,3,4 (quadrupole Theta, octopole Omega, and hexadecapole Phi). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Lambda. For Sigma(+/-)(Lambda=0) states, all 2(l) poles have one independent parameter (n=1). For spatially degenerate states--Pi, Delta, and Phi (Lambda=1,2,3)--the general rule reads n=1 for l or=2/Lambda/. The second nonzero term is the off-diagonal matrix element [formula: see text]. Thus, a Pi(Lambda=1) state has one dipole (mu(z)) but two independent 2(l) poles for l>or=2--starting with the quadrupole [Theta(zz),(Theta(xx)-Theta(yy))]. A Delta(Lambda=2) state has n=1 for 2((1,2,3)) poles (mu(z),Theta(zz),Omega(zzz)) but n=2 for higher 2((l>or=4)) poles--from the hexadecapole Phi up. For Phi(Lambda=3) states, it holds that n=1 for 2(1) to 2(5) poles but n=2 for all 2((l>or=6)) poles. In short, what is usually stated in the literature--that n=1 for all possible 2(l) poles of linear molecules--only applies to Sigma(+/-) states. For degenerate states with n=2, all Cartesian 2(l)-pole components (l>or=2/Lambda/) can be expressed as linear combinations of two irreducible multipoles, P(m=0)((l)) and P/m/=2 Lambda)((l)) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Theta, Omega, and Phi Moments calculated for Lambda=0-3 states of selected diatomics (in parentheses): X (2)Sigma(+)(CN), X (2)Pi(NO), a (3)Pi(u)(C(2)), X (2)Delta(NiH), X (3)Delta(TiO), X (3)Phi(CoF), and X (4)Phi(TiF). States of Pi symmetry are most affected by the deviation from axial symmetry.
Mario Piris - One of the best experts on this subject based on the ideXlab platform.
-
molecular Electric Moments calculated by using natural orbital functional theory
arXiv: Chemical Physics, 2016Co-Authors: Ion Mitxelena, Mario PirisAbstract:The molecular Electric dipole, quadrupole and octupole Moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-$\zeta$ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 Electric Moments agree satisfactorily with the corresponding experimental data, and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles (CCSD) and multi-reference single and double excitation configuration interaction (MRSD-CI) methods.
-
molecular Electric Moments calculated by using natural orbital functional theory
Journal of Chemical Physics, 2016Co-Authors: Ion Mitxelena, Mario PirisAbstract:The molecular Electric dipole, quadrupole, and octupole Moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-ζ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 Electric Moments agree satisfactorily with the corresponding experimental data and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles and multi-reference single and double excitation configuration interaction methods.
George Maroulis - One of the best experts on this subject based on the ideXlab platform.
-
a note on the Electric quadrupole and higher Electric Moments of ozone o3
Chemical Physics Letters, 2012Co-Authors: George MaroulisAbstract:Abstract We have obtained accurate ab initio and density functional theory values for the quadrupole, octopole and hexadecapole Electric Moments of the cyclic and open forms of ozone. Our best values have been calculated at the coupled cluster level of theory with molecule-specific basis sets. For the quadrupole moment (Θ αβ / ea 0 2 ) they are Θ yy = −1.366 (cyclic), Θ xx = −1.202, Θ yy = 1.426 and Θ xx = −0.223 (open). For the octopole (Ω αβγ / ea 0 3 ) and hexadecapole (Φ αβγδ / ea 0 4 ) Moments our best results are Ω zzz = 2.25, Φ yyyy = 19.53 (cyclic), Ω xxz = 3.28, Ω zzz = −2.97, Φ xxxx = −6.00, Φ yyyy = −3.90 and Φ zzzz = −3.54 (open).
-
accurate Electric multipole moment static polarizability and hyperpolarizability derivatives for n2
Journal of Chemical Physics, 2003Co-Authors: George MaroulisAbstract:We report accurate values of the Electric Moments, static polarizabilities, hyperpolarizabilities and their respective derivatives for N2. Our values have been extracted from finite-field Moller–Pleset perturbation theory and coupled cluster calculations performed with carefully designed basis sets. A large [15s12p9d7f] basis set consisting of 290 CGTF is expected to provide reference self-consistent-field values of near-Hartree–Fock quality for all properties. The Hartree–Fock limit for the mean hyperpolarizability is estimated at γ=715±4e4a04Eh−3 at the experimental bond length Re=2.074 32a0. Accurate estimates of the electron correlation effects were obtained with a [10s7p6d4f] basis set. Our best values are Θ=−1.1258ea02 for the quadrupole and Φ=−6.75ea04 for the hexadecapole moment, ᾱ=11.7709 and Δα=4.6074e2a02Eh−1 for the mean and the anisotropy of the dipole polarizability, C=41.63e2a04Eh−1 for the mean quadrupole polarizability and γ=927e4a04Eh−3 for the dipole hyperpolarizability. The latter v...
-
Electric quadrupole and hexadecapole moment dipole and quadrupole polarizability second Electric dipole hyperpolarizability for p2 and a comparative study of molecular polarization in n2 p2 and as2
Journal of Physical Chemistry A, 2003Co-Authors: George Maroulis, Demetrios XenidesAbstract:We have obtained Electric properties of P⋮P from finite-field Moller−Plesset perturbation theory, density functional theory and coupled cluster techniques. Reference, near-Hartree−Fock values have been obtained with a very large (20s15p10d5f) uncontracted basis set consisting of 300 Gaussian-type functions. At the experimental equilibrium bond length of Re = 1.8934 A we obtain self-consistent field values of 1.0682 ea02 for the quadrupole moment (ϑ), −41.68 ea04 for the hexadecapole moment (Φ), 51.16 for the mean ( ) and 28.58 e2a02Eh-1 for the anisotropy of the dipole polarizability, and 16.5 × 103 e4a04Eh-3 for the mean second dipole hyperpolarizability ( ). Electron correlation reduces strongly the magnitude of the Electric Moments. Both components of the dipole polarizability are reduced by electron correlation, but a small increase is observed for the dipole hyperpolarizability. Our best post-Hartree−Fock values have been obtained with a [9s7p5d3f] basis set at the CCSD(T) level of theory: ϑ = 0.485...
Pablo J Bruna - One of the best experts on this subject based on the ideXlab platform.
-
quadrupole octopole and hexadecapole Electric Moments of σ π δ and φ electronic states cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum
Journal of Chemical Physics, 2007Co-Authors: Pablo J Bruna, Friedrich GreinAbstract:The number of independent components, n, of traceless Electric 2l-multipole Moments is determined for C∞v molecules in Σ±, Π, Δ, and Φ electronic states (Λ=0,1,2,3). Each 2l pole is defined by a rank-l irreducible tensor with (2l+1) components Pm(l) proportional to the solid spherical harmonic rlYml(θ,φ). Here we focus our attention on 2l poles with l=2,3,4 (quadrupole Θ, octopole Ω, and hexadecapole Φ). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Λ. For Σ±(Λ=0) states, all 2l poles have one independent parameter (n=1). For spatially degenerate states—Π, Δ, and Φ (Λ=1,2,3)—the general rule reads n=1 for l<2∣Λ∣ (when the 2l-pole rank lies below 2∣Λ∣) but n=2 for higher 2l poles with l⩾2∣Λ∣. The second nonzero term is the off-diagonal matrix element ⟨ψ+Λ∣P∣m∣=2Λ(l)∣ψ−Λ⟩. Thus, a Π(Λ=1) state has one dipole (μz) but two independent 2l poles for l⩾2—starting with the quadrupole [Θzz,(Θxx−Θyy)]. A Δ(Λ=2) state has n=1 for 2(1,2,3...
-
quadrupole octopole and hexadecapole Electric Moments of σ π δ and φ electronic states cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum
Journal of Chemical Physics, 2007Co-Authors: Pablo J Bruna, Friedrich GreinAbstract:The number of independent components, n, of traceless Electric 2(l)-multipole Moments is determined for C(infinity v) molecules in Sigma(+/-), Pi, Delta, and Phi electronic states (Lambda=0,1,2,3). Each 2(l) pole is defined by a rank-l irreducible tensor with (2l+1) components P(m)((l)) proportional to the solid spherical harmonic r(l)Y(m)(l)(theta,phi). Here we focus our attention on 2(l) poles with l=2,3,4 (quadrupole Theta, octopole Omega, and hexadecapole Phi). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Lambda. For Sigma(+/-)(Lambda=0) states, all 2(l) poles have one independent parameter (n=1). For spatially degenerate states--Pi, Delta, and Phi (Lambda=1,2,3)--the general rule reads n=1 for l or=2/Lambda/. The second nonzero term is the off-diagonal matrix element [formula: see text]. Thus, a Pi(Lambda=1) state has one dipole (mu(z)) but two independent 2(l) poles for l>or=2--starting with the quadrupole [Theta(zz),(Theta(xx)-Theta(yy))]. A Delta(Lambda=2) state has n=1 for 2((1,2,3)) poles (mu(z),Theta(zz),Omega(zzz)) but n=2 for higher 2((l>or=4)) poles--from the hexadecapole Phi up. For Phi(Lambda=3) states, it holds that n=1 for 2(1) to 2(5) poles but n=2 for all 2((l>or=6)) poles. In short, what is usually stated in the literature--that n=1 for all possible 2(l) poles of linear molecules--only applies to Sigma(+/-) states. For degenerate states with n=2, all Cartesian 2(l)-pole components (l>or=2/Lambda/) can be expressed as linear combinations of two irreducible multipoles, P(m=0)((l)) and P/m/=2 Lambda)((l)) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Theta, Omega, and Phi Moments calculated for Lambda=0-3 states of selected diatomics (in parentheses): X (2)Sigma(+)(CN), X (2)Pi(NO), a (3)Pi(u)(C(2)), X (2)Delta(NiH), X (3)Delta(TiO), X (3)Phi(CoF), and X (4)Phi(TiF). States of Pi symmetry are most affected by the deviation from axial symmetry.
Ion Mitxelena - One of the best experts on this subject based on the ideXlab platform.
-
molecular Electric Moments calculated by using natural orbital functional theory
arXiv: Chemical Physics, 2016Co-Authors: Ion Mitxelena, Mario PirisAbstract:The molecular Electric dipole, quadrupole and octupole Moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-$\zeta$ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 Electric Moments agree satisfactorily with the corresponding experimental data, and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles (CCSD) and multi-reference single and double excitation configuration interaction (MRSD-CI) methods.
-
molecular Electric Moments calculated by using natural orbital functional theory
Journal of Chemical Physics, 2016Co-Authors: Ion Mitxelena, Mario PirisAbstract:The molecular Electric dipole, quadrupole, and octupole Moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-ζ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 Electric Moments agree satisfactorily with the corresponding experimental data and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles and multi-reference single and double excitation configuration interaction methods.