Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.     

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: L?wdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.     

Spin-spin coupling tensors in fluoromethanes

All spin-spin coupling tensors J of the fluoromethanes CH3F, CH2F2, and CHF3 are obtained theoretically by multiconfiguration self-consistent field linear response (MCSCF LR) ab initio calculations. Furthermore the principal values and the orientation of the principal axis systems of each theoretical J tensor are specified. Experimental liquid crystal NMR (LC NMR) data on the tensorial properties of the CF spin spin coupling in CH3F and CH2F2, and the FF spin-spin coupling in CHF3 are also reported. In the analysis of the experiments, the contributions from molecular vibrations, as well as that of the correlation of vibrational and rotational motion to the experimental anisotropic couplings, D(exp), are taken into account. The information of the anisotropic indirect coupling, 1/2J(aniso), is detected as the difference between D(exp) and the calculated dipolar coupling, D(calc). The extracted indirect contributions, 1/2J(aniso), are in fair agreement with the ab initio results. All relative (experimental and theoretical) CF and FF indirect contributions, 1/2J(aniso)/D(exp), are negative and under 1.7% in magnitude, when the observed molecular orientations are used. Therefore, in the one bond CF couplings and in the two bond FF couplings, the indirect contribution can normally be ignored without introducing serious error to the determination of molecular orientation and/or structure. However, a more accurate method is to partially correct for the indirect contribution by utilising the transferability of the spin-spin coupling tensors in related molecules. This is due to the fact that even small contributions may be significant, if the order parameter of the internuclear direction is negligibly small, leading to dominating indirect contributions. The very good agreement of the experimental values with the calculated coupling constants and the reasonable agreement in the anisotropic properties, which are experimentally much more difficult to define, indicates that the MCSCF LR method is capable of producing reliable J tensors for these systems, contrary to the case of density-functional theory.     

Approximate MCSCF optimization for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of CO,HCN, HNC,H2CO,and O3

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. The initial state used in MCSTEP is typically a small complete active space (CAS) with multiconfigurational self‐consistent field (MCSCF) state. In some cases, because of our use of a small CAS in MCSTEP, the Lagrangian eigenvalues of the MCSCF reference state are in an undesired order (u). The desired order (d) can usually be obtained by excluding one or more orbital rotations in MCSCF optimization between the doubly occupied and partially occupied orbitals. We systematically examine several cases where the undesired order occurs for the low‐lying vertical MCSTEP ionization potentials (IPs) of the molecules CO, HCN, HNC, H₂CO, and O₃ with our recently established CAS choices for MCSCF/MCSTEP. By excluding one or more orbital rotations between the partially and doubly occupied orbitals, an approximate MCSCF reference state with the same CAS choice is obtained for use in standard MCSTEP calculations that, in general, gives more reliable vertical MCSTEP IPs. © 2007 Wiley Periodicals, Inc. J Quantum Chem, 2008     

DFT study of the NMR properties of xenon in covalent compounds and van der waals complexes-implications for the use of 129Xe as a molecular probe

The NMR properties (chemical shift and spin-spin coupling constants) of (129)Xe in covalent compounds and weakly bound complexes have been investigated by DFT methods including relativistic effects. For covalent species, a good agreement between experimental and calculated results is achieved without scalar relativistic effects, but their inclusion (with a triple-zeta, double-polarization basis set) leads to some improvement in the quality of the correlation. The spin-orbit coupling term has a significant effect on the shielding constant, but makes a small contribution to the chemical shift. Coupling constants contain substantial contributions from the Fermi contact and paramagnetic spin-orbit terms; unlike light nuclei the spin-dipole term is also large, whereas the diamagnetic spin-orbit term is negligible. For van der Waals dimers, the dependence of the xenon chemical shift and anisotropy is calculated as a function of the distance. Small (<1 Hz) but non-negligible through-space coupling constants between (129)Xe and (13)C or (1)H are predicted. Much larger couplings, of the order of few Hz, are calculated between xenon and (17)O in a model silicate residue.     

The unrestricted natural orbital-restricted active space method: methodology and implementation

The full configuration interaction method in the space of fractionally occupied unrestricted natural orbitals (UNO-CAS method) is extended to excited states as well as to strongly correlated and reactive systems with large active spaces. This is accomplished by␣using restricted active space (RAS) wave functions introduced by Olsen et al. [(1988) J Chem Phys 89: 2185] and using the UNOs without the expensive orbital optimization step. In RAS, the space of active orbitals is subdivided into three groups: a group with essentially doubly occupied orbitals (RAS1), the usual CAS space (RAS2), and a space with weakly occupied active orbitals (RAS3). We select these spaces on the basis of the occupation numbers of the UNOs. All possible electron distributions are allowed in the usual CAS space, but the number of vacancies is limited in RAS1 and the number of electrons is limited in RAS3. We discuss an efficient algorithm for generating a RAS wave function. This is based on the Handy-Knowles determinantal expansion with an addressing scheme adopted for the restricted expansion. Results for both ground and excited states of azulene and free base porphyrin are presented. Received: 16 July 1998 / Accepted: 7 August 1998 / Published online: 19 October 1998     

Evaluation of a new procedure for quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A new procedure for quantum-chemical estimates of the constants of isotropic hyperfine coupling (IHFC) with protons using the orbital spin populations calculated in the basis set of symmetrically orthogonalized (according to Löwdin) atomic orbitals is tested taking 16 well-studied simplest π-electron and σ-electron radicals as examples. The most probable reasons for and possible ways of correcting large deviations of calculated IHFC constants from experimental values are considered. The efficiency of the semiempirical MNDORU scheme, which makes it possible to consistently estimate the delocalization and spin-polarization contributions to the constants of IHFC with protons in free radicals, is demonstrated.     

A pair-excitation MCSCF calculation based on CNDO/INDO approximation I

Second-order multiconfigurational self-consistent field (MCSCF ) calculation has been programmed on the basis of CNDO /INDO molecular orbital bases, in which the configuration space employed is restricted within pair-excitations. Test calculations have been carried out for 17 small molecules. All the MCSCF ground states of these molecules have been successfully converged to their respective optimal states by employing a simple weighting scheme. This procedure provides a great savings in computer time. The MCSCF calculation on azetidine required only 27 min on a HITAC M-680H. The MCSCF energies of HF, F₂, and BH show improved behaviors up to large atomic distances (～7au).     

Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method

We have analyzed the basis function series in molecular systems by optimization of orbital exponents in Gaussian-type functions (GTFs) including the electron correlation effects with multiconfiguration self-consistent field (MCSCF) and M?ller?CPlesset second-order perturbation (MP2) methods. First, we have derived and implemented the gradient formulas of MCSCF and MP2 energies with respect to GTF exponent, as well as GTF center and nuclear geometry, based on the fully variational molecular orbital (FVMO) method. Second, we have applied these electron-correlated FVMO methods to H₂, LiH, and hydrocarbon (CH₄, C₂H₆, C₂H₄, and C₂H₂) molecules. We have clearly demonstrated that the optimized exponent values with electron-correlated methods are different from those with simple Hartree?CFock method, since adequate basis functions for adequate virtual orbitals are indispensable to describe the accurate wave function and geometry for electron-correlated calculations.     

About the calculation of exchange coupling constants using density-functional theory: the role of the self-interaction error

The effect of the correction of the self-interaction error on the calculation of exchange coupling constants with methods based on density-functional theory has been tested in simple model systems. The inclusion of the self-interaction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transition-metal complexes, such as meta-GGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated J values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.     

Complete prediction of the 1H NMR spectrum of organic molecules by DFT calculations of chemical shifts and spin-spin coupling constants

1H NMR chemical shifts and coupling constants for several aromatic and aliphatic organic molecules have been calculated with DFT methods. In some test cases (furan, o-dichlorobenzene and n-butyl chloride) the performance of several functionals and basis sets has been analyzed, and the various contributions to spin-spin coupling (Fermi-contact, diamagnetic and paramagnetic spin-orbit) have been evaluated. The latter two components cancel each other, so that the calculation of the contact term only is sufficient for an accurate evaluation of proton-proton couplings. Such calculated values are used to simulate the 1H NMR spectra of organic molecules with complicated spin systems (e.g. naphthalene, o-bromochlorobenzene), obtaining a generally very good agreement with experimental spectra with no prior knowledge of the involved parameters.     

NMR偶合常数的从头算级别自然杂化轨道研究

为了研究自然杂化轨道计算结果与核自旋偶合常数的相关性,本文进行了从头算级别的自然杂化轨道计算。采用STO－3G基组,利用Lowdin正交化原子轨道基组下的密度矩阵,得到了分子中各原子的杂化轨道、净电荷与^13C-H、^13C-^13C键自旋偶合常数^1Jcn和^1Jcc之间关系式。利用这些式子计算得到的结果与实验数据非常一致。     

Improving the calculation of Electron Paramagnetic Resonance hyperfine coupling tensors for d-block metals

Calculation of hyperfine coupling constants (HFCs) of Electron Paramagnetic Resonance from first principles can be a beneficial complement to experimental data in cases where the molecular structure is unknown. We have recently investigated basis set convergence of HFCs in d-block complexes and obtained a set of basis functions for the elements Sc-Zn, which were saturated with respect to both the Fermi contact and spin-dipolar components of the hyperfine coupling tensor [Hedeg?rd et al., J. Chem. Theory Comput., 2011, 7, 4077-4087]. Furthermore, a contraction scheme was proposed leading to very accurate, yet efficient basis sets for the elements Sc-Zn. Here this scheme is tested against a larger test set of molecules and a wider range of DFT functionals. We further investigate the regular aug-cc-pVTZ and core-valence correlation aug-cc-pCVTZ basis sets as well as another core-property basis set, CP(PPP). While aug-cc-pVTZ-J provides hyperfine coupling constants that are almost identical to the converged series (aug-cc-pVTZ-Juc), we observe that not only the regular but also the core-valence correlation basis sets provide results far from the converged results. The usage of specialized core-basis sets leads to a large and highly significant improvement of the calculated hyperfine couplings in comparison with experimental data.     

Nuclear spin–spin coupling and nuclear motion

The vibration and rotation of molecules affects nuclear spin–spin coupling constants. This manifests itself as a temperature dependence of the coupling and also as an isotope effect (after allowing, where necessary, for differing magnetogyric ratios of the two nuclei involved in the isotopic substitution). Within the Born–Oppenheimer approximation, a nuclear spin–spin coupling surface can be defined for each pair of coupled nuclei. This surface is sampled by the nuclei as they undergo the excursions about equilibrium geometry that are governed by the force field. An accurate ab initio carbon–proton spin–spin coupling surface for the methane molecule has been calculated. This was obtained by summing the surfaces for each of the four contributions—Fermi contact, spin–dipolar, orbital paramagnetic, and orbital diamagnetic—expressed as power series in terms of symmetry coordinates. Preliminary calculations for ¹³CH₄ and ¹³CD₄ give a difference of only 6% between the calculated and observed nuclear motion contributions. The observed temperature dependence is also accounted for by the calculations. For these isotopomers, bond stretching plays the dominant role. © 1994 John Wiley & Sons, Inc.     

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

The efficacy of several multiconfiguration self-consistent field (MCSCF) methods in the subsequent spin-orbit coupling calculations was studied. Three MCSCF schemes to generate molecular orbitals were analyzed: state-specific, state-averaged, and dynamically weighted MCSCF. With Sn(2)(+) as the representative case, we show that the state-specific MCSCF orbitals lead to discontinuities in potential energy curves when avoided crossings of electronic states occur; this problem can be solved using the state-averaged or dynamically weighted MCSCF orbitals. The latter two schemes are found to give similar results when dynamic electron correlation is considered, which we calculated at the level of multiconfigurational quasidegenerate perturbation theory (MCQDPT). We employed the recently developed Douglas-Kroll spin-orbit adapted model core potential, ZFK3-DK3, and the dynamically weighted MCSCF scheme to calculate the spectroscopic constants of the mono-hydrides and compared them to the results obtained using the older set of potentials, MCP-TZP. We also showed that the MCQDPT tends to underestimate the dissociation energies of the hydrides and discussed to what extent coupled-cluster theory can be used to improve results.     

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 prediction and assignment of vicinal 1H-1H coupling constants of diastereomeric 3-alkoxy-6,7-epoxy-2-oxabicyclo[3.3.0]octanes

Spin-spin coupling constants between nuclei in NMR spectroscopy reflect their spatial arrangement. A number of calculation methods, applying different levels of theory, have been developed to support the stereochemical assignment of novel compounds. Nevertheless, revisions of the assignment of structures in the literature are not rare. In the present work, the reliability of the calculation methods amenable for a theoretical prediction of spin-spin coupling constants of vicinal protons to support correct stereochemical assignment of substitution at five-membered rings of 3-alkoxy-6,7-epoxy-2-oxabicyclo[3.3.0]octanes was studied. Experimental (3)J(H,H) coupling constants were compared with the coupling constants calculated for all possible diastereomers. The fully quantum chemical approach provided theoretical (3)J(H,H) coupling constants with an absolute deviation of no more than 1.1 Hz for 91% of the experimentally studied coupled spins, whereas the methods without quantum chemical geometry optimization resulted in completely unreliable predictions. Consequently, for a reliable stereochemical assignment of small and medium size molecules, the protocol for calculating the coupling constants based on the results of the quantum chemical geometry optimization is recommended.     

The calculation of indirect nuclear spin-spin coupling constants in large molecules

We present calculations of indirect nuclear spin-spin coupling constants in large molecular systems, performed using density functional theory. Such calculations, which have become possible because of the use of linear-scaling techniques in the evaluation of the Coulomb and exchange-correlation contributions to the electronic energy, allow us to study indirect spin-spin couplings in molecules of biological interest, without having to construct artificial model systems. In addition to presenting a statistical analysis of the large number of short-range coupling constants in large molecular systems, we analyse the asymptotic dependence of the indirect nuclear spin-spin coupling constants on the internuclear separation. In particular, we demonstrate that, in a sufficiently large one-electron basis set, the indirect spin-spin coupling constants become proportional to the inverse cube of the internuclear separation, even though the diamagnetic and paramagnetic spin-orbit contributions to the spin-spin coupling constants separately decay as the inverse square of this separation. By contrast, the triplet Fermi contact and spin-dipole contributions to the indirect spin-spin coupling constants decay exponentially and as the inverse cube of the internuclear separation, respectively. Thus, whereas short-range indirect spin-spin coupling constants are usually dominated by the Fermi contact contribution, long-range coupling constants are always dominated by the negative diamagnetic spin-orbit contribution and by the positive paramagnetic spin-orbit contribution, with small spin-dipole and negligible Fermi contact contributions.     

Calculations of the orbital diamagnetic contribution to nuclear spin-spin coupling constants for molecules with multiple bonds

Ab initio SCF and Cl calculations of the orbital diamagnetic contribution to nuclear spin-spin coupon constants have been performed for a series of molecules containing multiple bonds. A striking feature of the results is the prediction of consistently large contributions to vicinal (trans) and geminal proton-proton couplings which oppose and dominate the corresponding orbital paramagnetic contributions.     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.