Nuclear spin–spin coupling in the acetylene isotopomers calculated fromab initiocorrelated surfaces for 1J(C, H), 1J(C, C), 2J(C, H), and 3J(H, H)

Exploring Alternate Methods for the Calculation of High-Level Vibrational Corrections of NMR Spin-Spin Coupling Constants

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications

An accurate quantum chemical (QC) modeling of ⁷⁷ Se and ¹²⁵ Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of ⁷⁷ Se and ¹²⁵ Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of ⁷⁷ Se and ¹²⁵ Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Efficient calculation of NMR isotopic shifts: Difference-dedicated vibrational perturbation theory

We present difference-dedicated second-order vibrational perturbation theory (VPT2) as an efficient method for the computation of nuclear magnetic resonance (NMR) isotopic shifts, which reflect the geometry dependence of the NMR property in combination with different vibration patterns of two isotopologues. Conventional calculations of isotopic shifts, e.g., by standard VPT2, require scanning the geometry dependence over the whole molecule, which becomes expensive rapidly as the molecule size increases. In DD-VPT2, this scan can be restricted to a small region around the substitution site. At the heart of DD-VPT2 is a set of localized vibration modes common to the two isotopologues and designed such that the difference between the vibration patterns is caught by a small subset of them (usually fewer than 10). We tested the DD-VPT2 method for a series of molecules with increasing size and found that this method provides results with the same quality as VPT2 and in good agreement with the experiment, with computational savings up to 95% and less numerical instabilities. The method is easy to automatize and straightforward to generalize to other molecular properties.

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

Theoretical calculations of carbon-hydrogen spin-spin coupling constants

Structural applications of theoretical calculations of carbon-hydrogen spin-spin coupling constants are reviewed covering papers published mainly during the last 10-15 years with a special emphasis on the most notable studies of hybridization, substitution and stereoelectronic effects together with the investigation of hydrogen bonding and intermolecular interactions. The wide scope of different applications of calculated carbon-hydrogen couplings in the structural elucidation of particular classes of organic and bioorganic molecules is reviewed, concentrating mainly on saturated, unsaturated, aromatic and heteroaromatic compounds and their functional derivatives, as well as on natural compounds and carbohydrates. The review is dedicated to Professor Emeritus Michael Barfield in view of his invaluable pioneering contribution to this field.

Importance of Triples Contributions to NMR Spin-Spin Coupling Constants Computed at the CC3 and CCSDT Levels

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin-spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1-3%, but much higher corrections were found for ¹J_CN in FCN, 15.7%, and ¹J_OF in OF₂, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for ³J_FH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster expansion are accounted for at the CC3 level. Thus, we believe that the CC3 method will become the standard approach for the calculation of reference values of nuclear spin-spin coupling constants.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Communication: Localized molecular orbital analysis of the effect of electron correlation on the anomalous isotope effect in the NMR spin-spin coupling constant in methane

We discuss the effect of electron correlation on the unexpected differential sensitivity (UDS) in the (1)J(C-H) coupling constant of CH4 using a decomposition into contributions from localized molecular orbitals and compare with the (1)J(N-H) coupling constant in NH3. In particular, we discuss the well known fact that uncorrelated coupled Hartree-Fock (CHF) calculations are not able to reproduce the UDS in methane. For this purpose we have implemented for the first time a localized molecular orbital analysis for the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes--SOPPA(CCSD) in the DALTON program. Comparing the changes in the localized orbital contributions at the correlated SOPPA and SOPPA(CCSD) levels and at the uncorrelated CHF level, we find that the latter overestimates the effect of stretching the bond between the coupled atoms on the contribution to the coupling from the localized bonding orbital between these atoms. This disturbs the subtle balance between the molecular orbital contributions, which lead to the UDS in methane.

Computational NMR coupling constants: shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one-bond carbon-hydrogen spin-spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97-2 and M06-L) and basis sets (TZVP, HIII-su3, EPR-III, aug-cc-pVTZ-J, ccJ-pVDZ, ccJ-pVTZ, ccJ-pVQZ, pcJ-2 and pcJ-3) using 68 organic molecular systems with 88 (1)JCH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of (1)JCH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root-mean-square deviations lie between 4.7 and 16.4 Hz and are reduced to 4-6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97-2 functionals in combination with HIII-su3, aug-cc-pVTZ-J and pcJ-2 basis sets.

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.

Optimized basis sets for the calculation of indirect nuclear spin-spin coupling constants involving the atoms B, Al, Si, P, and Cl

The aug-cc-pVTZ-J series of basis sets for indirect nuclear spin-spin coupling constants has been extended to the atoms B, Al, Si, P, and Cl. The basis sets were obtained according to the scheme previously described by Provasi et al. [J. Chem. Phys. 115, 1324 (2001)]. First, the completely uncontracted correlation consistent aug-cc-pVTZ basis sets were extended with four tight s and three tight d functions. Second, the s and p basis functions were contracted with the molecular orbital coefficients of self-consistent-field calculations performed with the uncontracted basis sets on the simplest hydrides of each atom. As a first illustration, we have calculated the one-bond indirect spin-spin coupling constants in BH(4)(-), BF, AlH, AlF, SiH(4), SiF(4), PH(3), PF(3), H(2)S, SF(6), HCl, and ClF at the level of density functional theory using the Becke three parameter Lee-Yang-Parr and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes.

Structural trends of 77Se-1H spin-spin coupling constants and conformational behavior of 2-substituted selenophenes

Experimental measurements and second-order polarization propagator approach (SOPPA) calculations of (77)Se-(1)H spin-spin coupling constants together with theoretical energy-based conformational analysis in the series of 2-substituted selenophenes have been carried out. A new basis set optimized for the calculation of (77)Se-(1)H spin-spin coupling constants has been introduced by extending the aug-cc-pVTZ-J basis for selenium. Most of the spin-spin coupling constants under study, especially vicinal (77)Se-(1)H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2-position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds.

Prediction of spin-spin coupling constants in solution based on combined density functional theory/molecular mechanics

We present theory and implementation of calculation of spin-spin coupling constants within combined quantum mechanics/molecular mechanics methods. Special attention is given to the role of explicit solvent polarization as well as the molecular consequences due to hydrogen bonding. The model is generally applicable but is here implemented for the case of density functional theory. First applications to liquid water and acetylene in aqueous solution are presented. Good agreement between theory and experiment is obtained in both cases, thereby showing the strength of our approach. Finally, spin-spin coupling constants across hydrogen bonds are discussed considering for the first time the role of an explicit solvent on this class of spin-spin couplings.

Interpretation of Hydrogen/Deuterium Isotope Effects on NMR Chemical Shifts of [FHF]− Ion Based on Calculations of Nuclear Magnetic Shielding Tensor Surface

Using ab initio calculations of 1H, 19F magnetic shielding tensors of hydrogen difluoride ion as the functions of three coordinates of symmetry, an attempt is made to estimate the contributions of different vibrational isotope effects to H/D NMR isotope shifts referred in the literature. It is shown that the contributions of the amplitudes of proton stretching and bending vibrations dominate whereas the contribution of the totally symmetric vibration can be neglected. Different signs of the H/D isotope effects on hydron and fluorine chemical shifts are caused by very strong angle dependence of the fluorine magnetic shielding. The agreement of the calculated and measured values is nearly quantitative. An unusually strong paramagnetic deshielding of hydrogen for the equilibrium geometry of the [FHF]− ion is noted.

A Comparison of Møller-Plesset and Coupled Cluster Linear Response Theory Methods for the Calculation of Dipole Oscillator Strength Sum Rules and C6 Dispersion Coefficients

Four correlated linear response theory methods - the second order polarization propagator approximation (SOPPA), the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), the CC2 and coupled cluster singles doubles (CCSD) linear response theory - were used to determine the dipole oscillator strength sum rules of the hydrogen halides HX (with X = F, Cl, Br and I) and the C6 dispersion coefficient for all pairs of interacting HX molecules via numerical integration of the Casimir-Polder formula. The dependence of the polarizabilities, their frequency dependence and the C6 coefficients on the level of correlation and the dependence of the C6 coefficients on the two intramolecular bond lengths were studied.

Stereochemical study of iminodihydrofurans based on experimental measurements and SOPPA calculations of (13)C-(13)C spin-spin coupling constants

Configurational assignment and conformational analysis of a series of iminodihydrofurans obtained from cyanoacetylenic alcohols were performed on the basis of experimental measurements and high-level ab initio calculations of their (13)C-(13)C spin-spin coupling constants. The title compounds were shown to form and exist in solution as the individual Z isomers, adopting the orthogonal orientation of the amino, alkylamino and dialkylamino groups and the s-trans orientation of the CONH(2) group at the C(4) position of the 2,5-dihydro-2-iminofuran moiety.

Configurational assignment of carbon, silicon and germanium containing propynal oximes by means of 13C-1H, 13C-13C and 15N-1H spin-spin coupling constants

Configurational assignment of five carbon, silicon and germanium containing propynal oximes has been carried out by means of experimental measurements and high-level ab initio calculations of their 13C-1H, 13C-13C and 15N-1H spin-spin coupling constants. The title compounds were shown to exist in the nonequilibrium mixture of E and Z isomers with the energy difference of less than 0.3 kcal/mol calculated at the MP2/6-311G** level.

Theory and computation of nuclear magnetic resonance parameters

The art of quantum chemical electronic structure calculation has over the last 15 years reached a point where systematic computational studies of magnetic response properties have become a routine procedure for molecular systems. One of their most prominent areas of application are the spectral parameters of nuclear magnetic resonance (NMR) spectroscopy, due to the immense importance of this experimental method in many scientific disciplines. This article attempts to give an overview on the theory and state-of-the-art of the practical computations in the field, in terms of the size of systems that can be treated, the accuracy that can be expected, and the various factors that would influence the agreement of even the most accurate imaginable electronic structure calculation with experiment. These factors include relativistic effects, thermal effects, as well as solvation/environmental influences, where my group has been active. The dependence of the NMR spectra on external magnetic and optical fields is also briefly touched on.

Geometry Dependence of Spin–Spin Couplings in Cyanamide by DFT Analysis

There have been numerous theoretical and experimental investigations examining NMR parameters related to non-amino N-H...N H-bonded moieties in both biological and chemical contexts. In contrast, little information on the geometry dependence of NMR parameters related to the biologically important H-bond donor amino group is available. Herein, the geometric dependencies of the one-bond amino N-H spin-spin coupling constants [(1)J(NH)] in the cyanamide monomer and dimer have been computed with B3LYP and the aug-cc-pVTZ-su0 basis set. In an isolated planar cyanamide molecule, the |(1)J(NH)| couplings were found to increase as the N-H bond lengthened. In contrast, in the planar cyanamide dimer the size of the H-bonded amino N-H coupling (|(1)J(N(d)H(d))|) decreased with increasing N(d)H(d) bond length. The |(1)J(N(d)H(d))| coupling was larger than the |(1)J(N(d)H(free))| coupling for N(d)H(d) distances up to 1.18 A (for a fixed N(d)H(free) distance of 1.006 A). Hence, the decrease of |(1)J(NH)| with increasing N-H distance, as well as the larger value of |(1)J(N(d)H(d))| compared to |(1)J(N(d)H(free))|, were only observed for situations where the amino group is involved in an H-bonding interaction. This is attributed to electron redistribution induced by the presence of the second cyanamide molecule. Similar electron-redistribution effects are thought to be responsible for the observed distance dependence of computed (1)J(NH) couplings of H-bonded amino groups in near-planar G-quartet structures. Here, the |(1)J(NH)| couplings of the amino N-H bonds decreased with increasing N-H bond length whereas the |(1)J(N(d)H(d))| couplings are approximately 7 Hz larger than the |(1)J(N(d)H(free))| couplings, despite the longer N(d)-H(d) bond length.

Conformational study of 2-arylazo-1-vinylpyrroles

Conformational study of 2-phenylazo-1-vinylpyrrole and 2-(4-bromophenyl)azo-5-methyl-1-vinylpyrrole was performed on the basis of the experimental measurements and high-level ab initio calculations of their 13C--13C and 13C--1H spin-spin coupling constants, showing marked stereochemical behaviour upon the internal rotation of the vinyl group and the pyrrolyl moiety. In liquid phase, both compounds were found to adopt predominant s-trans-s-trans conformation with the noticeable population (ca. 30%) of the higher-energy s-cis-s-trans conformation in the latter compound. As follows from the X-ray data, 2-phenylazo-1-vinylpyrrole crystallizes in s-trans-s-trans conformation while the crystalline molecular structure of 2-(4-bromophenyl)azo-5-methyl-1-vinylpyrrole is s-cis-s-trans.