Finite-field Perturbation Theory Research Articles

Enhancement of the parity-violating energy difference of H2X2 molecules by electronic excitation

The parity-violating energy difference (PVED) between two enantiomers of a chiral molecule is caused by the weak interaction. Because of the smallness of the PVED, nonzero PVED is yet to be discovered in experimental searches. To detect the PVED, the search for molecules with large PVED values is important. Previously, one of the authors proposed that the PVED may be significantly enhanced in ionized or excited states. The significant enhancement of the PVED in some electronic excited states is proven in this study using H$_2$X$_2$ (X=O, S, Se, Te) molecules as examples. The maximum enhancement was an about 360-fold increase for H$_2$Se$_2$. For the PVED calculation, we employ the finite-field perturbation theory (FFPT) within the equation-of-motion coupled-cluster theory based on the exact two-component molecular-mean field Hamiltonian. The relation between the enhancement of the PVED and the contribution to the PVED from the highest occupied molecular orbital is also examined. The effects of computational elements, such as parameters related to the electron correlation and FFPT on PVED values in excited states of H$_2$X$_2$ molecules are studied.

Dipole polarizability of alkali-metal (Na, K, Rb)-alkaline-earth-metal (Ca, Sr) polar molecules: prospects for alignment.

Electronic open-shell ground-state properties of selected alkali-metal-alkaline-earth-metal polar molecules are investigated. We determine potential energy curves of the (2)Σ(+) ground state at the coupled-cluster singles and doubles with partial triples (CCSD(T)) level of electron correlation. Calculated spectroscopic constants for the isotopes ((23)Na, (39)K, (85)Rb)-((40)Ca, (88)Sr) are compared with available theoretical and experimental results. The variation of the permanent dipole moment (PDM), average dipole polarizability, and polarizability anisotropy with internuclear distance is determined using finite-field perturbation theory at the CCSD(T) level. Owing to moderate PDM (KCa: 1.67 D, RbCa: 1.75 D, KSr: 1.27 D, RbSr: 1.41 D) and large polarizability anisotropy (KCa: 566 a.u., RbCa: 604 a.u., KSr: 574 a.u., RbSr: 615 a.u.), KCa, RbCa, KSr, and RbSr are potential candidates for alignment and orientation in combined intense laser and external static electric fields.

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence 1,3n-π*, 1,3π-π*, and 1,3σ-π* excited states and Rydberg 1,3n-3s, 1,3π-3 , 1,3n-3py and 1,3π-3py states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C2v symmetry of the ground state is lowered to the Cs symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.

Ab initiostudy of permanent electric dipole moment and radiative lifetimes of alkaline-earth-metal--Li molecules

We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: ${}^{24}$Mg${}^{7}$Li, ${}^{40}$Ca${}^{7}$Li, ${}^{88}$Sr${}^{7}$Li, and ${}^{138}$Ba${}^{7}$Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $\ensuremath{\nu}$ $=$ 0 state (${}^{24}$Mg${}^{6}$Li: 22 s, ${}^{40}$Ca${}^{6}$Li: 39 s, ${}^{88}$Sr${}^{6}$Li: 380 s, and ${}^{138}$Ba${}^{6}$Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10$%$.

13C−H and 13C−13C Spin Coupling Behavior in Aldofuranosyl Rings from Density Functional Theory

Ab initio molecular orbital calculations using density functional theory (DFT) have been conducted on the aldopentofuranose, 2-deoxy-{beta}-D-erythro-pentofuranose (1) to evaluate the performance of DFT methodology in structural optimization and NMR spin-spin coupling constant determinations prior to its application in more complex carbohydrate-containing systems. Computed molecular parameters (bond lengths, bond angles, bond torsions) and NMR spin-spin coupling constants (J) in the 10 geometrically optimized envelope forms of 1 are compared to those reported previously from HF/6-31G*-optimized geometries. In earlier work, {sup n}J{sub CH} values were first computed at the HF level using finite-field perturbation theory and a basis set specially designed to economically recover the Fermi-contact contribution to J. Electron correlation effects on the coupling constants were then introduced via second-order Moeller-Plesset perturbation (MP2) calculations. The derived correlation corrections (i.e., the MP2-HF values) were scaled by factors obtained from more elaborate quadratic configuration interaction (QCISD) calculations on related, though necessarily smaller, systems. In the present study, the Fermi-contact components of the J values were computed directly via DFT, presumably recovering the important effects of electron correlation and thus obviating the need for scaling. J{sub CH} values (one-, two-, and three-bond) derived from the DFT treatment are compared to scaled couplings obtained more » previously using HF/MP2 methods. The effect of structural relaxation on J is assessed by direct comparison of HF values for the {sup 13}C-{sup 1}H couplings in both HF- and DFT-optimized geometries. {sup 1}J{sub CC}, {sup 2}J{sub CC}, {sup 3}J{sub CC}, and {sup 2+3}J{sub CC} values are computed (DFT) in 1 as a function of ring conformation for the first time, correlation corrections are evaluated by direct comparison with HF calculations, and new structural interpretations of these couplings are provided. « less

Ab initio finite-field transition moment calculations

The finite-field perturbation theory is applied to the ab initio calculations of electronic transition dipole moments in molecules. The results are less sensitive to the level of electron correlation treatment than the directly computed electric dipole off-diagonal matrix elements. The finite-field approach can provide a substantial gain in accuracy when simple MCSCF electronic wavefunctions are used.

Three-Bond C−O−C−C Spin-Coupling Constants in Carbohydrates: Development of a Karplus Relationship

A range of 13C-labeled carbohydrates containing C−O−C−C coupling pathways having different structures and dihedral angles has been prepared and used to identify structural factors affecting 3JCOCC, especially those across the O-glycosidic linkages of oligosaccharides. Model mono- and disaccharides were geometrically optimized using density functional methods, and scalar couplings involving carbon were calculated using a similar approach coupled with finite-field perturbation theory. Experimental and calculated 3JCOCC values were in close agreement, thus allowing use of the latter to better define the effect of carbohydrate structure on 3JCOCC magnitude. In addition to dihedral angle, the disposition of terminal electronegative substituents along the C−O−C−C coupling pathway significantly affects 3JCOCC values, and structural motifs have been identified where these effects may be encountered in oligosaccharides. A simple Karplus equation for trans-O-glycoside 3JCOCC values is proposed and has been applied in the reanalysis of trans-O-glycosidic couplings in 13C-labeled methyl β-lactoside and sucrose. The behavior of trans-O-glycosidic 2JCOC and 3JCOCH values, which provide structural information complementary to that derived from 3JCOCC values, is also discussed.

An accurate in-plane force field for porphine. A scaled quantum mechanical study

The ground state geometry, force field, and vibrational intensity data of free-base porphine were determined by density functional theory. Calculations were carried out with the Becke-Lee-Yang-Parr composite exchange-correlation functional and 6-31G ∗ basis set. The calculations predict a stable structure of D 2h symmetry. The resulting force field was transformed to internal coordinates and scaled by transferable scale factors from our previous work. There is very good agreement between the calculated and experimental frequencies and intensities, and between experimental and simulated spectra. The assignment of the in-plane modes is discussed and some reassignments are proposed. Finite field perturbation theory was used to obtain the Raman intensities.

An accurate in-plane force field for porphine. A scaled quantum mechanical study

The ground state geometry, force field, and vibrational intensity data of free-base porphine were determined by density functional theory. Calculations were carried out with the Becke-Lee-Yang-Parr composite exchange-correlation functional and 6-31G ∗ basis set. The calculations predict a stable structure of D 2h symmetry. The resulting force field was transformed to internal coordinates and scaled by transferable scale factors from our previous work. There is very good agreement between the calculated and experimental frequencies and intensities, and between experimental and simulated spectra. The assignment of the in-plane modes is discussed and some reassignments are proposed. Finite field perturbation theory was used to obtain the Raman intensities.

Ab initio computations close to the one-particle basis set limit on the weakly bound van der Waals complexes benzene–neon and benzene–argon

The equilibrium geometries and binding energies of the van der Waals (vdW) complexes benzene–neon and benzene–argon have been calculated at the level of second-order Mo/ller–Plesset perturbation theory (MP2). Terms linear in the interelectronic distances r12 were used in the MP2 treatment to converge fast to the one-particle basis set limit. This new method, MP2-R12 as implemented in the sore program, was applied with high quality basis sets derived from Dunning’s aug-cc-pVXZ (X=D,T,Q,5) sets. In reward of the efforts to reach the basis set limit, it is found that the calculated binding energies for the vdW complexes were computed virtually free of a basis set superposition error (BSSE). The key MP2-R12 results are De=154 cm−1 and re=3.32 Å for benzene–neon and De=553 cm−1 and re=3.41 Å for benzene–argon. The permanent dipole moments of the vdW complexes have been computed by finite field perturbation theory. Coupled-cluster calculations of type CCSD(T), although performed with considerably smaller basis sets than the MP2-R12 calculations, show that, to improve the MP2-R12 results, it is inevitable to consider correlation effects due to connected triple excitations which go beyond the MP2 description.

Electron-correlated calculations of the nuclear shielding constants and shielding polarizabilities for H2, N2, HF and CO

The nuclear magnetic shielding σ in a molecule is changed by the presence of an external uniform electric field. This change may be expressed in terms of the shielding polarizabilities σ′ and σ″. Values of σ′ and σ″ have been evaluated for H2, N2, HF and CO using a combination of the second order Moller-Plesset theory (MP2) and the finite-field perturbation theory. The effects of electron correlation on the σ′ and σ″ tensors for N2, HF and CO are seen to be sufficiently large that a higher-order theory than MP2 will be necessary to account for them fully.

Ab initio quadratic configuration interaction calculation of indirect NMR spin-spin coupling constants

Finite-field perturbation theory is combined with the quadratic configuration interaction method of ab initio electronic structure theory to calculate the Fermi-contact component of the indirect spin-spin coupling constant between adjacent carbon nuclei in a range of bonding environments. Basis set requirements for accuracy are first investigated in ethane and a small modification of the outer-core, inner-valence region of the standard Dunning double-ζ contraction is shown to be satisfactory

Isotropic coupling constant for the nitrogen atom from correlated calculations based on spin-unrestricted wave functions

The isotropic hyperfine coupling constant for the ground electronic state of the nitrogen atom is computed from the quadratic configuration interaction correlation procedure based on a single unrestricted Hartree–Fock (UHF) determinant. The splitting is determined from the normalized spin density at the nucleus, derived by finite-field perturbation theory. Results obtained are compared with previous work based on spin-restricted reference spaces. Close accord is found between present estimates and full configuration interaction values for small basis sets. Contributions from shells of higher angular momentum functions in the basis set are similar in both approaches and for the largest unrestricted calculation the correlated results are in good accord with experiment. The UHF wave function is shown to provide a reasonable account of the K-shell contribution to the isotropic coupling and hence the UHF-based correlated calculations show much less sensitivity to the neglect of core–electron correlation than the dramatic effects observed in spin-restricted treatments.

Ab initio coupled-cluster calculations of isotropic hyperfine splitting in some diatomic hydrides

Ab initio calculations of the isotropic hyperfine coupling constants in the electronic ground states of some diatomic hydride radicals and their radical cations are reported using highly correlated wave functions. An augmented coupled-cluster doubles procedure, including an approximate account of the effects of the inclusion of amplitudes due to single and triple replacements in the unrestricted Hartree-Fock (UHF) reference determinant, is employed. Contact spin densities are estimated by finite-field perturbation theory. Coupling at oxygen in OH and OH{sup +} and at fluorine in FH{sup +} is well described by a basis set of triple-{zeta} quality including two shells of polarization (d) functions. Accurate computation of the nitrogen splitting in NH and NH{sup +} and particularly the carbon splitting in CH appears to be more demanding. A modest double-{zeta}-basis set on hydrogen is sufficient to quantitatively reproduce the observed trends in the coupling constants at that nucleus.

A b i n i t i o calculation of the hyperfine coupling constants in B2

Hyperfine coupling constants for the ground electronic state of the B2 molecule, [3∑−g] , are computed using correlation procedures based on spin-unrestricted wave functions. Two distinct methods have been employed. Firstly, a variational configuration mixing approach with all configurations arising from single and double replacements in the reference wave function has been augmented by an approximate size-consistency correction. Secondly, a many-body perturbation theory procedure based on the coupled–cluster expansion with infinite-order doubles has been approximately corrected for single and triple excitations through fourth order. Both isotropic and dipolar coupling constants have been obtained as expectation values over the appropriate wave functions for the unrestricted Hartree–Fock (UHF) and the variational configuration-interaction (CI) methods. The anisotropic coupling is already satisfactorily accounted for at the UHF level, while even with the approximate correction for the effect of higher excitations, the variational CI approach still underestimates the isotropic splitting by a factor of 2. The origin of this deficiency is traced using the other correlation method in which the isotropic coupling is derived from the normalized spin density at the nucleus, obtained by finite-field perturbation theory. The effect of the inclusion of triple excitations from the UHF wave function is seen to contribute about one third of the observed value. Such excitations are not accounted for in the size-consistency corrected variational CI approach. This conclusion is confirmed by a similar finding in a full fourth-order Mo/ller–Plesset (MP) calculation.

Ab initio calculations of the Raman intensities of fundamental vibrations of polyatomic molecules using the improved virtual orbital technique

The SOS-IVO method previously successfully applied to the calculation of molecular dipole polarizabilities at equilibrium geometry is used, in conjunction with the finite difference approach for the evaluation of polarizability derivatives, to calculate scattering coefficients and depolarization ratios of vibrational Raman bands. A large basis set, based on Dunning's double and triple zeta s-p basis, is used in which polarization and diffuse functions are introduced ([DTZ/DPP]). Use is also made, in view of its success in equilibrium polarizability calculations, of a reduced basis ([DTZ/DP]) in which only a limited number of polarization functions, simulated by spherical Gaussian orbitals, are included based on symmetry considerations about the polarizability tensor components. The theory is applied to a series of molecules belonging to the C 2v (H 2O, H 2CO), C 3v (NH 3, CH 3CN), C ∞v and D ∞h (HF and N 2) point groups, for which experimental gas phase intensity data are available and for which, in most cases, calculations using more demanding methods (finite field perturbation theory, analytical gradient method) were already available in the literature. Except for shortcomings in the cases of vibrational modes involving the elongation of a triple bond, a satisfactory agreement between theoretical and experimental intensities is obtained, indicating an average deviation factor of about 1.4 between theoretical and experimental polarizability derivative tensor components. The reduced basis performs well, except in the case of some very weak bending modes where recently an extremely high basis set sensitivity has been noticed.

Raman intensity calculations of formamide with the CNDO method

Within the polarizability theory, absolute and relative Raman scattering cross sections are calculated using a variational method and the finite field perturbation theory. The calculations are performed within the CNDO approximation and the basis set in the variational scheme is extended to include polarization functions. Satisfactory numerical results are obtained for the formamide molecule with the variational procedure. The FFP theory which was used up to now only for calculating relative Raman scattering cross sections is adequate in reproducing the relative values for formamide. The absolute scattering cross sections are too small. Because we are interested in calculations of biological relevant molecules, it is necessary to consider also the FFP method in the standard CNDO version, which is much more economical with respect to computer time and capacity than the variational method.

Molecules in electric fields

Finite field perturbation theory coupled with configuration interaction techniques have been used to evaluate the components of the polarisability tensor of H2 at and near its equilibrium internuclear separation. The values are fitted to a polynomial which then yields the derivatives of the polarisability with respect to internuclear distance. Our results compare favourably with theoretical values obtained by the use of highly accurate correlated wavefunctions.