The use of localized molecular orbitals and the polarization propagator to identify transmission mechanisms in nuclear spin-spin couplings

An extension of the IPPP (inner projections of the polarization propagator) method to theoretically analyze transmission mechanisms of indirect nuclear spin-spin couplings is presented. The localization technique used is modified so that all the canonical molecular orbitals of a compound may be localized to represent chemical bonds, lone pairs, and the corresponding antibonding molecular orbitals. These localized molecular orbitals, together with the polarization propagator, are used to obtain an intuitive picture of how a coupling is generated as a sum of terms, each one consisting of two particle-hole single excitations. This picture can be used to identify underlying transmission mechanisms and quantitatively evaluate their importance toward the total coupling. The paramagnetic spin-orbit and the spin-dipole interactions are studied in detail.     

Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Algebraic-diagrammatic construction polarization propagator approach to indirect nuclear spin-spin coupling constants

A new polarization propagator approach to indirect nuclear spin-spin coupling constantans is formulated within the framework of the algebraic-diagrammatic construction (ADC) approximation and implemented at the level of the strict second-order approximation scheme, ADC(2). The ADC approach possesses transparent computational procedure operating with Hermitian matrix quantities defined with respect to physical excitations. It is size-consistent and easily extendable to higher orders via the hierarchy of available ADC approximation schemes. The ADC(2) method is tested in the first applications to HF, N(2), CO, H(2)O, HCN, NH(3), CH(4), C(2)H(2), PH(3), SiH(4), CH(3)F, and C(2)H(4). The calculated indirect nuclear spin-spin coupling constants are in good agreement with the experimental data and results of the second-order polarization propagator approximation method. The computational effort of the ADC(2) scheme scales as n(5) with respect to the number of molecular orbitals n, which makes this method promising for applications to larger molecules.     

Relativistic effects on the nuclear magnetic shieldings of rare-gas atoms and halogen in hydrogen halides within relativistic polarization propagator theory

In this work an analysis of the electronic origin of relativistic effects on the isotropic dia- and paramagnetic contributions to the nuclear magnetic shielding sigma(X) for noble gases and heavy atoms of hydrogen halides is presented. All results were obtained within the 4-component polarization propagator formalism at different level of approach [random-phase approximation (RPA) and pure zeroth-order approximation (PZOA)], by using a local version of the DIRAC code. From the fact that calculations of diamagnetic contributions to sigma within RPA and PZOA approaches for HX(X=Br,I,At) and rare-gas atoms are quite close each to other and the finding that the diamagnetic part of the principal propagator at the PZOA level can be developed as a series [S(Delta)], it was found that there is a branch of negative-energy "virtual" excitations that contribute with more than 98% of the total diamagnetic value even for the heavier elements, namely, Xe, Rn, I, and At. It contains virtual negative-energy molecular-orbital states with energies between -2 mc2 and -4 mc2. This fact can explain the excellent performance of the linear response elimination of small component (LR-ESC) scheme for elements up to the fifth row in the Periodic Table. An analysis of the convergency of S(Delta) and its physical implications is given. It is also shown that the total contribution to relativistic effects of the innermost orbital (1s1/2) is by far the largest. For the paramagnetic contributions results at the RPA and PZOA approximations are similar only for rare-gas atoms. On the other hand, if the mass-correction contributions to sigma(p) are expressed in terms of atomic orbitals, a different pattern is found for 1s1/2 orbital contributions compared with all other s-type orbitals when the whole set of rare-gas atoms is considered.     

Derivatives of the polarization propagator including orbital relaxation effects

In this article, we relate derivatives of the polarization propagator used in many-body theory to the nonlinear (quadratic) polarization propagator, and we relate derivatives of the quadratic polarization propagator to the nonlinear propagator of the next higher order, the cubic polarization propagator. We restrict the analysis to differentiation with respect to parameters eta for which the derivative of the Hamiltonian can be written as a sum of one-electron operators. Geometrical derivatives are obtained by specializing to the parameter eta to the alpha coordinate of nucleus I. We treat orbital relaxation explicitly by allowing for the eta dependence of creation and annihilation operators in the propagators. This treatment entails an extension of the geometrical derivative relations among response functions proven by Olsen and Jorgensen [J. Chem. Phys. 82, 3235 (1985)], because the propagator derivatives may involve changes in the one-electron orbitals that do not appear in the susceptibility derivatives. These results underlie the relations between Raman intensities and electric-field shielding tensors, which have been explained in terms of nonlocal polarizability and hyperpolarizability densities. The results suggest an alternative computational route to geometrical or other derivatives of both linear- and nonlinear-response functions: these derivatives can be evaluated without numerical differentiation, directly from the propagator of the next higher order.     

The appearance of an interval of energies that contain the whole diamagnetic contribution to NMR magnetic shieldings

Working within relativistic polarization propagator approach, it was shown in a previous article that the electronic origin of diamagnetic contributions to NMR nuclear magnetic shielding, sigmad, are mostly excitations that fit in a well defined interval of energies such that 2mc2相似文献   

The antisymmetrized geminal power approximation to the excitation propagator

A consistent propagator approximation, denoted as the excitation propagator, is introduced. This propagator describes excitations between N-particle states and its approximation has properties required of consistent random phase approximation schemes. Several properties of this propagator are explored when based on a generalized antisymmetrized geminal power wavefunction. How singularities in the metric occur and how to remove them is discussed in detail. The excitation propagator is also contrasted with the principal (polarization) propagator.     

13C-13C Coupling Constants in Structural Studies: XXXII. Additivity of Spin-Spin Couplings in Sterically Strained Heterocycles

Calculations in terms of the self-consistent finite perturbation theory (SCPT) and analysis of contributions of localized molecular orbitals in terms of the polarization propagator theory (CLOPPA) indicate additivity of ¹³C-¹³C coupling constants in saturated sterically strained heterocycles. Their fused derivatives, especially those containing 3rd Period elements, show considerable deviations of the calculated coupling constants from the additive values.     

A generalized any particle propagator theory: Assessment of nuclear quantum effects on electron propagator calculations

In this work we propose an extended propagator theory for electrons and other types of quantum particles. This new approach has been implemented in the LOWDIN package and applied to sample calculations of atomic and small molecular systems to determine its accuracy and performance. As a first application of the method we have studied the nuclear quantum effects on electron ionization energies. We have observed that ionization energies of atoms are similar to those obtained with the electron propagator approach. However, for molecular systems containing hydrogen atoms there are improvements in the quality of the results with the inclusion of nuclear quantum effects. An energy term analysis has allowed us to conclude that nuclear quantum effects are important for zero order energies whereas propagator results correct the electron and electron-nuclear correlation terms. Results presented for a series of n-alkanes have revealed the potential of this method for the accurate calculation of ionization energies of a wide variety of molecular systems containing hydrogen nuclei. The proposed methodology will also be applicable to exotic molecular systems containing positrons or muons.     

Four-component Hartree-Fock calculations of magnetic-field induced circular birefringence--Faraday effect--in noble gases and dihalogens

The effects of relativity on the magnetic-field induced circular birefringence, or Faraday effect, in He, Ne, Ar, Xe, Rn, F2, Cl2, Br2, and I2 have been determined at the four-component Hartree-Fock level of theory. A measure of the birefringence is given by the Verdet constant, which is a third-order molecular property and thus relates to quadratic response functions. A fully analytical nonlinear polarization propagator approach is employed. The results are gauge invariant as a consequence of the spatial symmetries in the molecular systems. The calculations include electronic as well as vibrational contributions to the property. Comparison with experiment is made for He, Ne, Ar, Xe, and Cl2, and, apart from neon, the theoretical values of the Verdet constant are within 10% of the experimental ones. The inclusion of nonrelativistically spin-forbidden excitations in the propagator parametrization has significant effects on the dispersion in general, but such effects are in the general case largely explained by the use of a resonant-divergent propagator theory. In the present work we do, however, observe noticeable relativistic corrections to the Verdet constant in the off-resonant regions for systems with light elements (F2 and Cl2), and nonrelativistic results for the Verdet constant of Br2 are in error by 25% in the low-frequency region.     

Trimer based polarization as a multibody molecular model. Application to hydrogen fluoride

A molecular modeling approach is introduced as a way to treat multibody (more than two molecules) contributions to the intermolecular potential. There are two key features to the method. First, it employs polarizable electrostatics on the molecules, but converges the charges and fields for only three molecules at a time, taken separately for all trimers (three molecules falling within a cutoff distance) in the system. This feature introduces significant computational savings when applied in Monte Carlo simulation (in comparison to a full N-body polarization treatment), as movement of a single molecule does not require re-converging of the polarization of all molecules, and it achieves this without approximations that cause the value of the energy to depend on the history of the simulation. Second, the approach defines the polarization energy in excess of the pairwise contribution, meaning that the trimer energy has subtracted from it the sum of the energies obtained by converging the polarization of each molecule pair in the trimer. This feature is advantageous because it removes the need (often found in polarizable models) to stiffen inappropriately the repulsive part of the pair potential. The polarization contribution is thus a purely three-body potential. The approach is applied to model hydrogen fluoride, which in experiments exhibits unusual properties that have proven difficult to capture well by molecular models. The new HF model is shown to be much more successful than previous modeling efforts in obtaining agreement with a broad range of experimental data (volumetric properties, heat effects, molecular structure, and vapor-liquid equilibria).     

Quantum-chemical foundations of the topological substructural molecular design

The topological substructural molecular design (TOPS-MODE) approach is formulated as a tight-binding quantum-chemical method. The approach is based on certain postulates that permit to express any molecular property as a function of the spectral moments of certain types of molecular and environment-dependent energies. We use several empirical potentials to account for these intrinsic and external molecular energies. We prove that any molecular property expressed in terms of a quantitative structure-property and structure-activity relationships (QSPR/QSAR) model developed by using the TOPS-MODE method can be expressed as a bond additivity function. In addition, such a property can also be expressed as a substructural cluster expansion function. The conditions for such bond contributions being transferable are also analyzed here. Several new statistical-mechanical electronic functions are introduced as well as a bond-bond thermal Green's function or a propagator accounting for the electronic hopping between pairs of bonds. All these new concepts are applied to the development and application of a new QSAR model for describing the toxicity of polyhalogenated-dibenzo-1,4-dioxins. The QSAR model obtained displays a significant robustness and predictability. It permits an easy structural interpretation of the structure-activity relationship in terms of bond additivity functions, which display some resemblances with other theoretical parameters obtained from first principle quantum-chemical methods.     

Self-consistent approximation to the polarization propagator

A theorem is presented that characterizes approximate states and truncated operator manifolds associated with self-consistent approximate propagators. This theorem establishes a natural relationship between Hermiticity, stationarity, nonredundance and completeness of operator manifolds, model time evolution, and the vacuum condition. For the case of the polarization propagator we describe algorithms by which we can construct states and manifolds that satisfy this theorem and the vacuum condition.     

Calculations of the indirect nuclear spin–spin coupling constants of PbH4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH₄ using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation. Received: 16 November 1998 / Accepted: 30 March 1999 / Published online: 14 July 1999     

Theoretical additivity in multipath 13C, 1H coupling constants

Different path contributions to the Fermi contact term of carbon-hydrogen coupling constants in several bicycloalkanes were calculated using the ‘inner projections of the polarization propagator’ (IPPP) approach. The ground-state wave functions were calculated at the INDO level of approximation. Three and four-bond contributions to the couplings, and the through-space transmission via the rear lobes of the C? X (X ? H, F) bonds attached to the bridgehead carbon atoms, were calculated. The additivity of these contributions compared with the total INDO couplings is good. Similar paths in different molecules give dissimilar contributions to the couplings.     

XCC2--a new coupled cluster model for the second-order polarization propagator

A new coupled cluster model of the polarization propagator, denoted as XCC2, is presented. The XCC2 approach employs time-independent coupled cluster theory of polarization propagators of Moszynski et al. [Collect. Czech. Chem. Commun., 2005, 70, 1109] and excitation operators from the time-dependent (TD) CC2 method. The performance of XCC2 was investigated by calculating static and dynamic dipole polarizabilities for a test set of over 20 molecules and comparing them with TD-CCSD results. The quality of XCC2 dispersion coefficients for several noncovalent molecular complexes was also tested against the benchmark values. This numerical study reveals that the average percent error of XCC2 is significantly reduced in comparison to the TD-CC2 method (4-fold reduction for the mean polarizabilities and 2-fold reduction for anisotropic polarizabilities is observed). Since the computational requirements of both XCC2 and TD-CC2 methods are virtually the same, the new XCC2 method can be viewed as a practical alternative for TD-CC2 for property calculations, giving the second-order polarization propagators of near-CCSD quality in many cases, but retaining at the same time the lower computational cost of the TD-CC2 model.     

Extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms. I. Methodological developments

An extension of a simplified method for molecular correlation energy calculations to molecules containing third row atoms is presented. In addition to the use of pseudo-potentials in the calculations, the consequences of this extension on the different components of the energy partition which is the basic idea of the method, is analysed. Particular emphasis is placed on the specific role played by the 3d orbitals in each of the energy components. First, at the zeroth order, the energy is found to be very sensitive to the optimization of the 3d polarization functions. Secondly, the internal correlation energy, calculated by CI, requires the optimization of distinct 3d correlation orbitals to describe adequately the strong near-degeneracy effects that occur within the valence space. Finally it is shown that the 3d orbitals contribute partially to the non-internal correlation energy and that, the atoms-in-molecule structures corresponding typically to all-external contributions are negligible. The concept of error energy is introduced in place of the non-internal correlation energy: it includes the relativistic contributions within the semi-empirical tables. Such tables are presented for second row atoms and for the chlorine atom. From these tables, predicted values for some atomic term energies, experimentally undetermined, are derived. The methodological tests are limited here to the chlorine atom which is chosen for further applications in the next paper of this series. The conclusions concerning the applicability of the method to third row atoms are however quite general.Boursier I.R.S.I.A     

Determination of excitation energies and transition moments in a second order polarization propagator approach. Application to the Be atom and the CH+ molecule

Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH⁺ show a change of 2–5% for the transition moments and of 0–20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH⁺ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH⁺ in a second order polarization propagator approach.     

Second-order polarization propagator calculations of indirect nuclear spin-spin coupling tensors in the water molecule

The contribution to indirect nuclear spin-spin coupling tensors provided by the Fermi contact, the spin-dipolar, the Fermi contact/spin-dipolar crossterm, and the paramagnetic spin-orbit interactions are investigated in a zeroth-, first- (the same as the coupled Hartree-Fock method), and second-order polarization propagator approach. Numerical applications to the water molecule show that the second-order results for both the HO and the HH coupling constants are in good agreement with experimental data - especially if vibrational corrections and the diamagnetic spin-orbit contributions are taken into account. We find that the correlation corrections beyond coupled Hartree-Fock are important. We also report how the second-order results are influenced by neglect of some of the most time-consuming steps in the calculation.