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.     

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.     

Basis-set dependence of nuclear spin-spin coupling constants

The convergence of NMR indirect spin-spin coupling constants with the extension of the basis set is analyzed, based on calculations carried out at the multiconfigurational self-consistent-field level for the HF and H₂O systems. For the dominant and difficult Fermi-contact contribution, the standard correlation-consistent basis sets of electronic-structure theory are not suitable, lacking flexibility in the core region. Improved but not satisfactory convergence of the couplings is observed when decontracting the s functions of the correlation-consistent cc-pVXZ basis sets for 2≤X≤6. Next, by systematically extending these basis sets with tight s functions, new sets are obtained that are sufficiently flexible for accurate calculations of indirect nuclear spin-spin couplings, without sacrificing the smooth convergence behavior of the correlation-consistent basis sets. Received: 22 September 1997 / Accepted: 30 December 1997     

Calculation of indirect nuclear spin-spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.     

Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.     

MBOHO calculations of phosphorus-carbon nuclear spin-spin coupling constants

Summary The novel generalized correlation of the nuclear spin-spin coupling constants with the atomic hybrids and net charges is employed to give a new relationship for calculating the directly bonded phosphorus-carbon coupling constants by use of the maximum bond order hybrid orbital procedure together with the extended Hückel molecular orbital calculation. The calculated coupling constants of phosphorus-carbon are all in good agreement with the experimental data, which shows that the new relationship obtained in the present paper is quite satisfactory for calculation of the phosphorus-carbon coupling constants.The project was supported by the National Natural Science Foundation of China and the Excellent University Teacher's Foundation of State Education Commission of China     

NDDO MO calculations: isotropic hyperfine coupling constants and nuclear spin-spin coupling constants

The nonempirical NDDO MO method in its unrestricted form has been used to evaluate isotropic hyperfine coupling constants and nuclear spin-spin coupling constants. Satisfactory agreement with INDO and experimental results is obtained.     

Interaction energies and NMR indirect nuclear spin-spin coupling constants in linear HCN and HNC complexes

The cooperativity effects on both the electronic energy and NMR indirect nuclear spin-spin coupling constants J of the linear complexes (HCN)n and (HNC)n (n = 1-6) are discussed. The geometries of the complexes were optimized at the MP2 level by using the cc-pVTZ basis sets. The spin-spin coupling constants were calculated at the level of the second-order polarization propagator approximation with use of the local dense basis set scheme based on the cc-pVTZ-J basis sets. We find strong correlations in the patterns of different properties such as interaction energy, hydrogen bond distances, and spin-spin coupling constants for both series of compounds. The intramolecular spin-spin couplings are with two exceptions dominated by the Fermi contact (FC) mechanism, while the FC term is the only nonvanishing contribution for the intermolecular couplings. The latter do not follow the Dirac vector model and are important only between nearest neighbors.     

Comments on calculations of nuclear spin-spin coupling constants using the blinder operator

It is pointed out that the finite second-order hyperfine self-coupling energies, obtained by the Blinder operator, are unphysical and 10² times too large. The additional terms in the first-order matrix element are also unphysical. Therefore the Blinder operator gives no improvement over the simple delta function. The consequences on the recent calculations by Paviot and Hoarau and by Sänger and Voitländer are discussed.     

Coupled hartree-fock and second order polarization propagator calculations of indirect nuclear spin-spin coupling constants for diatomic molecules

We report ab initio calculation of indirect nuclear spin-spin coupling constants for the HD, FH, CO and CH⁺ molecules using the first (coupled Hart     

Density functional theory calculation of indirect nuclear magnetic resonance spin-spin coupling constants in C(70)

We calculate NMR spin-spin coupling constants in the C70 fullerene by means of density functional theory. We show that using a hybrid density functional (B3LYP) and an adequate basis set (cc-pCVDZ-sd), excellent agreement with experimental values can be achieved for one-bond couplings. These benchmark calculations suggest that theoretical predictions of NMR spin-spin couplings can be extremely valuable for discerning structural information of fullerenes.     

Electric field effects on one-bond indirect spin-spin coupling constants and possible biomolecular perspectives

Electric field (EF) induced changes of one-bond indirect spin-spin coupling constants are investigated on a wide range of molecules including peptide models. EFs were both externally applied and internally calculated without external EF application by the hybrid density functional theory method. Reliable agreement with experimental data has been obtained for calculated one-bond J-couplings. The role of the EF sign and direction, internal and induced components, hydrogen bonding, internuclear distance and hyperconjugative interactions on the one-bond J-coupling vs EF interconnection is analyzed. A linear dependence of 1J on EF projection along the bond is obtained, if the bound atoms possess different enough electron densities and an EF determined by the electronic polarization exists along the bond. Accentuating the 1JNH couplings as possible EF sensitive parameters, a systematic study is done in two sets of molecules with a large variation of the native internal EF value. The most EF affected component of the 1JNH coupling constant is the spin-dipole term of Ramsey's formulation; however, in the total J-coupling formation, the EF influence on the Fermi contact term is the most significant. The induced EF projection along the bond is 6.7 times weaker in magnitude than the simulated external uniform field. The absolute EF dependence of the one-bond J-coupling involves only the internal field, which is the sum of the induced field (if the external field exists) and the internuclear field determined by the native polarization. That linear and universal dependence joins the corresponding couplings in a diverse set of molecules under various electrostatic conditions. Many types of the one-bond J-couplings can be potentially measured in biomolecules, and the study of their relation with the electrostatic properties at the corresponding sites opens a new avenue to the full exploitation of the NMR measurable parameters with novel and exciting applications.     

Ab initio study of the J(CC) indirect nuclear spin-spin coupling constants in cyclobutane and related systems

Non-empirical calculations using the equations-of-motion approach, which incorporates the main portion of the electron correlation effects, are reported for the carbon-carbon nuclear spin-spin coupling constants in cyclobutane, bicyclobutane, tricyclobutane, cyclobutene, cyclobutyne, cyclobutadiene, bicyclobutene, methylenecyclopropane, and methylenecyclopropene. The results provide an overall picture of the influences exerted on sign and magnitude of the J(CC) by progressive condensation, unsaturation, and branching rearrangement of the cyclobutane frame.     

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.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

Nonempirical calculations of NMR indirect spin-spin coupling constants. Part 15: pyrrolylpyridines

Conformational study of 2-(2-pyrrolyl)pyridine and 2,6-di(2-pyrrolyl)pyridine was performed on the basis of the experimental measurements and high-level ab initio calculations of the one-bond 13C-13C, 13C-1H and 15N-1H spin-spin coupling constants showing marked stereochemical behavior upon the internal rotation around the pyrrole-pyridine interheterocyclic bonds. Both compounds were established to adopt predominant s-cis conformations with no noticeable out-of-plane deviations.     

An ab initio study of the nuclear spin-spin coupling constants in the second-row hydrides

Ab initio SCF perturbation theory calculations have been performed for the contact, orbital and dipolar contributions to the nuclear spin—spin coupling constants in A1H₃, SiH₄ PH₃, H₂S and HCl, using large, stable gaussian basis sets. The results for J(XH) are in reasonably good agreement with experiment, those for. J(HH) are rather less good.     

Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations: SOPPA and SOPPA(CCSD)

We present correlated calculations of the indirect nuclear spin-spin coupling constants of HD, HF, H₂O, CH₄, C₂H₂, BH, AlH, CO and N₂ at the level of the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes – SOPPA(CCSD). Attention is given to the effect of the so-called W ₄ term, which has not been included in previous SOPPA spin-spin coupling constant studies of these molecules. Large sets of Gaussian basis functions, optimized for the calculation of indirect nuclear spin-spin coupling constants, were used instead of the in general rather small basis sets used in previous studies. We find that for nearly all couplings the SOPPA(CCSD) method performs better than SOPPA. Received: 6 July 1998 / Accepted: 8 September 1998 / Published online: 23 November 1998