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.     

Optimization of augmentation functions for correlated calculations of spin-spin coupling constants and related properties

A new hierarchy of augmented basis sets optimized for the calculation of molecular properties such as indirect spin-spin coupling constants is presented. Based on the Dunning hierarchy of cc-pVXZ (X = D, T, Q, and 5) basis sets augmentation functions with tight exponents have been optimized for coupled-cluster calculations of indirect spin-spin coupling constants. The optimal exponents for these tight functions have been obtained by optimizing the sum of the absolute values of all contributions to the coupling constant. On the basis of a series of test cases (CO, HF, N(2), F(2), H(2)O, NH(3), and CH(4)) we propose a set of tight s, p, and d functions to be added to the uncontracted Dunning basis sets, and, subsequently, to recontract. The resulting ccJ-pVXZ (X = D, T, Q, and 5) basis sets demonstrate excellent cost efficiency in benchmark calculations. These new basis sets should generally be applicable for the calculation of spin-spin coupling constants and other properties that have a strong dependence on powers of 1r or even contain a delta distribution for correlated ab initio methods.     

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.     

An NMR and relativistic DFT investigation of one-bond nuclear spin-spin coupling in solid triphenyl group-14 chlorides

A solid-state nuclear magnetic resonance and zeroth-order regular approximation density functional theory, ZORA-DFT, study of one-bond nuclear spin-spin coupling between group-14 nuclei and quadrupolar 35/37Cl nuclei in triphenyl group-14 chlorides, Ph3XCl (X = C, Si, Ge, Sn and Pb), is presented. This represents the first combined experimental and theoretical systematic study of spin-spin coupling involving spin-pairs containing quadrupolar nuclei. Solid-state NMR spectra have been acquired for all compounds in which X has a spin-1/2 isotope--13C, 29Si, [117/119]Sn and 207Pb-at applied magnetic fields of 4.70, 7.05 and 11.75 T. From simulations of these spectra, values describing the indirect spin-spin coupling tensor-the isotropic indirect spin-spin coupling constant, 1J(X, 35/37Cl)iso and the anisotropy of the J tensor, Delta1J(X, 35/37Cl)--have been determined for all but the lead-chlorine spin-pair. To better compare the indirect spin-spin coupling parameters between spin-pairs, 1J(iso) and Delta1J values were converted to their reduced coupling constants, 1K(iso) and Delta1K. From experiment, the sign of 1K(iso) was found to be negative while the sign of Delta1K is positive for all spin-pairs investigated. The magnitude of both 1K(iso) and Delta1K was found to increase as one moves down group-14. Theoretical values of the magnitude and sign of 1K(iso) and Delta1K were obtained from ZORA-DFT calculations and are in agreement with the available experimental data. From the calculations, the Fermi-contact mechanism was determined to provide the largest contribution to 1K(iso) for all spin-pairs while spin-dipolar and paramagnetic spin-orbit mechanisms make significant contributions to the anisotropy of K. The inclusion of relativistic effects was found to influence K(Sn,Cl) and K(Pb,Cl).     

Computed coupling constants in X(CH3)nH(4-n) moieties where X = 13C and 15N+, and n = 0-4: comparisons with experimental data

Seventy-three unique spin-spin coupling constants have been analyzed for the ten species in the two series X(CH3)nH(4-n), where the central atom X is 13C or 15N+. Thirty-seven experimental values have been obtained from the literature, and several new coupling constants have been measured for the methyl-substituted ammonium ions. Both DFT with the B3LYP functional and ab initio EOM-CCSD calculations have been carried out on these same systems. Coupling constants computed by these two methods are in agreement with experimental values. Some problems related to coupling constants for the cationic ammonium systems have been resolved when these were recomputed at EOM-CCSD for complexes in which NH4+ is hydrogen-bonded to H2O molecules.     

Non-empirical calculations of NMR indirect carbon-carbon coupling constants. Part 8--monocycloalkanes

Carbon-carbon and carbon-hydrogen spin-spin coupling constants were calculated in the series of the first six monocycloalkanes using SOPPA and SOPPA(CCSD) methods, and very good agreement with the available experimental data was achieved, with the latter method showing slightly better results in most cases, at least in those involving calculations of J(C,C). Benchmark calculations of all possible 21 coupling constants J(C,C), J(C,H) and J(H,H) in chair cyclohexane revealed the importance of using the appropriate level of theory and adequate quality of the basis sets. Many unknown couplings in this series were predicted with high confidence and several interesting structural trends (hybridization effects, multipath coupling transmission mechanisms, hyperconjugative interactions) were elucidated and are discussed based on the present calculations of spin-spin couplings.     

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.     

Indirect NMR spin-spin coupling constants 3J(P,C) and 2J(P,H) across the P-O...H-C link can be used for structure determination of nucleic acids

Calculated indirect NMR spin-spin coupling constants (3)J(P,C) and (2)J(P,H) were correlated with the local structure of the P-O...H-C linkage between the nucleic acid (NA) backbone phosphate and the H-C group(s) of a nucleic acid base. The calculations were carried out for selected nucleotides from the large ribosomal subunit (Ban et al. Science 2000, 289, 905) with the aim of identifying NMR parameters suitable for detection of certain noncanonical RNA structures. As calculations in the model system, dimethyl-phosphate-guanine, suggest, the calculated indirect spin-spin couplings across the linkage are sensitive to the mutual orientation and distance between the phosphate and nucleic acid base. A short distance between the nucleic acid base and phosphate group and the angles C...P-O and P...C-H smaller than 50 degrees are prerequisites for a measurable spin-spin interaction of either coupling (|J| > 1 Hz). A less favorable arrangement of the P-O...H-C motif, e.g., in nucleotides of the canonical A-RNA, results in an effective dumping of both spin-spin interactions and insignificant values of the NMR coupling constants. The present work indicates that quantum chemical calculations of the indirect spin-spin couplings across the P-O...H-C motif can help detect some rare but important backbone topologies, as seen for example in the reverse kink-turn. Measuring of (3)J(P,C) and (2)J(P,H) couplings can therefore provide critical constraints on the NA base and phosphate geometry and help to determine the structure of NAs.     

Methodological aspects in the calculation of parity-violating effects in nuclear magnetic resonance parameters

We examine the quantum chemical calculation of parity-violating (PV) electroweak contributions to the spectral parameters of nuclear magnetic resonance (NMR) from a methodological point of view. Nuclear magnetic shielding and indirect spin-spin coupling constants are considered and evaluated for three chiral molecules, H2O2, H2S2, and H2Se2. The effects of the choice of a one-particle basis set and the treatment of electron correlation, as well as the effects of special relativity, are studied. All of them are found to be relevant. The basis-set dependence is very pronounced, especially at the electron correlated ab initio levels of theory. Coupled-cluster and density-functional theory (DFT) results for PV contributions differ significantly from the Hartree-Fock data. DFT overestimates the PV effects, particularly with nonhybrid exchange-correlation functionals. Beginning from third-row elements, special relativity is of importance for the PV NMR properties, shown here by comparing perturbational one-component and various four-component calculations. In contrast to what is found for nuclear magnetic shielding, the choice of the model for nuclear charge distribution--point charge or extended (Gaussian)--has a significant impact on the PV contribution to the spin-spin coupling constants.     

A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides

Relativistic density functional theory (DFT) calculations of nuclear spin-spin coupling constants and shielding constants have been performed for selected transition metal (11th and 12th group of periodic table) and thallium cyanides. The calculations have been carried out using zeroth-order regular approximation (ZORA) Hamiltonian and four-component Dirac-Kohn-Sham (DKS) theory with different nonrelativistic exchange-correlation functionals. Two recent approaches for representing the magnetic balance (MB) between the large and small components of four-component spinors, namely, mDKS-RMB and sMB, have been employed for shielding tensor calculations and their results have been compared. Relativistic effects have also been analysed in terms of scalar and spin-orbit contributions at the two-component level of theory, including discussion of heavy-atom-on-light-atom effects for (1)J(CN), σ(C), and σ(N). The results for molecules containing metals from 4th row of periodic table show that relativistic effects for them are small (especially for spin-spin coupling constants). The biggest effects are observed for the 6th row where nonrelativistic theory reproduces only about 50%-70% of the two-component ZORA results for (1)J(MeC) and about 75% for heavy metal shielding constants. It is important to employ a full Dirac picture for calculations of heavy metal shielding constants, since ZORA reproduces only 75%-90% of the DKS results. Smaller discrepancies between ZORA-DFT and DKS are observed for nuclear spin-spin coupling constants. No significant differences are observed between the results obtained using mDKS-RMB and sMB approaches for magnetic balance in four-component calculations of the shielding constants.     

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     

Vibrational corrections to magneto-optical rotation: a computational study

Vibrational corrections to the Verdet constants of nine molecules (H2, N2, CO, H2O, CH4, benzene, toluene, p-xylene, and o-xylene) were calculated with pure density functional theory (DFT), hybrid DFT, and an approximate coupled-cluster theory. Comparisons are made for the accuracy of the vibrational averages among different methods and with respect to experimental data where available. It is found that vibrational corrections to magneto-optical rotation can be as large as 10% of the equilibrium value. Hybrid DFT with the B3LYP hybrid functional offers reasonable accuracy at a relatively inexpensive computational cost for accurate calculations of vibrationally averaged Verdet constants.     

1H and 13C NMR chemical shifts and spin-spin coupling constants in trans- and cis-decalins

The NMR parameters characterizing the spectra of trans- and cis-decalins were determined from theoretical calculations and experimental spectra. The calculated values of the shielding constants are in good agreement with the measured chemical shifts, with a small but noticeable difference in accuracy for the bridgehead atoms. Of all the spin-spin coupling constants, only most of (1)J(C,C) and (1)J(C,H) values could be extracted from the spectra, and the corresponding computed values are in good agreement with experiment. It appears that the applied density functional theory (DFT) approach overestimates slightly the J(C,C) coupling and underestimates the differences between one-bond (1)J(C,H) coupling constants. For all these constants [J(C,C), J(C,H) and J(H,H)] through one to three bonds, which could not be obtained experimentally, the predicted values are in good agreement with the general rules relating spin-spin coupling to the number and spatial arrangement of the intervening bonds.     

Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD

Accurate calculations of NMR indirect nuclear spin-spin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as N(6), where N is the number of orbitals, which prevents routine applications to molecules with more than 10-15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as N(5), like the original SOPPA-method. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spin-spin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spin-spin coupling constants, namely the HuzIV-su4, ccJ-pVTZ, and ccJ-pVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.     

Anharmonic vibrational frequencies and vibrationally averaged structures and nuclear magnetic resonance parameters of FHF-

The anharmonic vibrational frequencies of FHF(-) were computed by the vibrational self-consistent-field, configuration-interaction, and second-order perturbation methods with a multiresolution composite potential energy surface generated by the electronic coupled-cluster method with various basis sets. Anharmonic vibrational averaging was performed for the bond length and nuclear magnetic resonance indirect spin-spin coupling constants, where the latter computed by the equation-of-motion coupled-cluster method. The calculations placed the vibrational frequencies at 580 (nu(1)), 1292 (nu(2)), 1313 (nu(3)), 1837 (nu(1) + nu(3)), and 1864 cm(-1) (nu(1) + nu(2)), the zero-point H-F bond length (r(0)) at 1.1539 A, the zero-point one-bond spin-spin coupling constant [(1)J(0)(HF)] at 124 Hz, and the bond dissociation energy (D(0)) at 43.3 kcal/mol. They agreed excellently with the corresponding experimental values: nu(1) = 583 cm(-1), nu(2) = 1286 cm(-1), nu(3) = 1331 cm(-1), nu(1) + nu(3) = 1849 cm(-1), nu(1) + nu(2) = 1858 cm(-1), r(0) = 1.1522 A, (1)J(0)(HF) = 124+/-3 Hz, and D(0) = 44.4+/-1.6 kcal/mol. The vibrationally averaged bond lengths matched closely the experimental values of five excited vibrational states, furnishing a highly dependable basis for correct band assignments. An adiabatic separation of high- (nu(3)) and low-frequency (nu(1)) stretching modes was examined and found to explain semiquantitatively the appearance of a nu(1) progression on nu(3). Our calculations predicted a value of 186 Hz for experimentally inaccessible (2)J(0)(FF).     

A theoretical study of the fine and hyperfine interactions in the NCO and CNO radicals

The geometries, the harmonic vibrational frequencies, and the Renner-Teller parameter have been reported for the NCO(+)(X (3)Sigma(-)), NCO(X (2)Pi,A (2)Sigma(+),B (2)Pi,2 (2)Sigma(+)), NCO(-)(X (1)Sigma(+)), CNO(+)(X), CNO(X (2)Pi,A (2)Sigma(+),B (2)Pi,2 (2)Sigma(+)), and CNO(-)(X (1)Sigma(+)) systems at the full valence-complete active space self-consistent-field (fv-CASSCF) level of theory. The (2)Pi electronic states of the NCO and CNO radicals have two distinct real vibrational frequencies for the bending modes and these states are subject to the type A Renner-Teller effect. The total energy of CNO(+) without zero point energy correction of the linear geometry is approximately 31 cm(-1) higher than the bent geometry at the fv-CASSCF level and the inversion barrier vanishes after the zero point energy correction; therefore, the ground state of the CNO(+) may possess a quasilinear geometry. The spin-orbit coupling constants estimated using atomic mean field Hamiltonian at the fv-CASSCF level of theory are in better agreement with the experimental values. The excitation energies, the electron affinity, and the ionization potential have been computed at the complete active space second order perturbation theory (CASPT2) and the multireference singles and doubles configuration (MRSD-CI) levels of theory. The computed values of the electric hyperfine coupling constants for the (14)N atom in the ground state of the NCO radical agree well with the experimental data. The magnetic hyperfine coupling constants (HFCC's) have been estimated employing the configuration selected MRSD-CI and the multireference singles configuration interaction (MRS-CI) methods using iterative natural orbitals (ino) as one particle basis. Sufficiently accurate value of the isotropic contribution to the HFCC's can be obtained using an MRS-CI-ino procedure.     

Electronic influences on 3J(C,H) coupling constants via -S-, -S(O)- and -SO2-: their determination, calculation and comparison of detection methods

3J(C,H) coupling constants via a sulfur atom in two series of compounds, both including a sulfide, a sulfoxide and a sulfone, were detected experimentally and calculated by quantum mechanical methods. In the first series (1-3) the coupling between a hydrogen, bonded to an sp3 carbon, and an sp2 carbon is treated; the second series (4-6) deals with the coupling between a hydrogen, bonded to an sp3 carbon, and an sp3 carbon. Different pulse sequences (broadband HMBC, SelJres, 1D HSQMBC, J-HMBC-2, selective J-resolved long-range experiment and IMPEACH-MBC) proved to be useful in determining the long-range 3J(C,H) coupling constants. However, the dynamic behaviour of two of the compounds (4 and 6) led to weighted averages of the two coupling constants expected (concerning equatorial and axial positions of the corresponding hydrogens). DFT calculations proved to be useful to calculate not only the 3J(C,H) coupling constants but also the different contributions of FC, PSO, DSO and SD terms; the calculation of the Fermi contact term (FC) was found to be sufficient for the correct estimation of 3J(C,H) coupling constants.     

Theoretical prediction of the spin-spin coupling constants between an axis and macrocycle of a rotaxane

The indirect nuclear spin-spin coupling constants between nuclei belonging to the axis and to the macrocycle of three structurally related rotaxanes have been calculated by means of density functional theory. It has been shown that the through-space axis-macrocycle proton-proton coupling constants can be as large as 0.4-0.5 Hz and therefore of measurable values. The largest through-space axis-macrocycle carbon-proton and nitrogen-proton coupling constants are 0.2-0.3 Hz. Visualization of coupling pathways by means of the coupling energy density method indicates that the larger proton-proton couplings are indeed transmitted through the space between the coupled nuclei. Thus, it seems that measurement of such couplings should be possible and that indirect spin-spin couplings can be actually transmitted through-space, with no covalent or hydrogen bonds between the coupled nuclei.     

Seven dimensional quantum dynamics study of the H2+NH2-->H+NH3 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H2+NH2-->H+NH3 reaction using a seven dimensional model on an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values and nonreactive NH2 group keeps C2v symmetry and the rotation-vibration coupling in NH2 is neglected. The total reaction probabilities are calculated when the two reactants are initially at their ground states, when the NH2 bending mode is excited, and when H2 is on its first vibrational excited state, with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants and equilibrium constants are calculated for the temperature range of 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the reaction is dominated by ground-state reactivity and the main contribution to the thermal rate constants is thought to come from this state, (b) the excitation energy of H2 was used to enhance reactivity while the excitation of the NH2 bending mode hampers the reaction, (c) the calculated thermal rate constants are very close to the experimental data and transition state theory results at high and middle temperature, while they are ten times higher than that of transition state theory at low temperature (T=200 K), and (d) the equilibrium constants results indicate that the approximations applied may have different roles in the forward and reverse reactions.     

Illumination of the effect of the overlap of lone-pairs on indirect nuclear spin-spin coupling constants

The effect of electron lone-pairs on the Fermi-contact (FC) contribution to indirect nuclear spin-spin coupling constants is analyzed using new tools for their interpretation. In particular, visualization of spin-spin coupling pathways using the coupling deformation density (CDD) has been employed. Furthermore, the recently developed perturbation-stable localization procedure has been applied for decomposition of CDD and the calculated value of couplings into contributions from localized molecular orbitals (LMOs). Correlation between the overlap of densities of LMOs representing lone-pairs and the Fermi-contact contribution to spin-spin coupling constants has been demonstrated. A new way for analyzing spin-spin couplings using the expansion of CDD as a linear combination of the products of molecular orbitals has been suggested. The considered examples include two- and three-bond phosphor-phosphor couplings. Significance of the obtained insight is not restricted to spin-spin couplings of nuclei possessing lone-pairs, as demonstrated in the example of vicinal hydrogen-hydrogen coupling in ethane.