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.

Extending NMR Quantum Computation Systems by Employing Compounds with Several Heavy Metals as Qubits

Nuclear magnetic resonance (NMR) is a spectroscopic method that can be applied to several areas. Currently, this technique is also being used as an experimental quantum simulator, where nuclear spins are employed as quantum bits or qubits. The present work is devoted to studying heavy metal complexes as possible candidates to act as qubit molecules. Nuclei such 113Cd, 199Hg, 125Te, and 77Se assembled with the most common employed nuclei in NMR-QIP implementations (1H, 13C, 19F, 29Si, and 31P) could potentially be used in heteronuclear systems for NMR-QIP implementations. Hence, aiming to contribute to the development of future scalable heteronuclear spin systems, we specially designed four complexes, based on the auspicious qubit systems proposed in our previous work, which will be explored by quantum chemical calculations of their NMR parameters and proposed as suitable qubit molecules. Chemical shifts and spin–spin coupling constants in four complexes were examined using the spin–orbit zeroth-order regular approximation (ZORA) at the density functional theory (DFT) level, as well as the relaxation parameters (T1 and T2). Examining the required spectral properties of NMR-QIP, all the designed complexes were found to be promising candidates for qubit molecules.

Enhancing NMR Quantum Computation by Exploring Heavy Metal Complexes as Multiqubit Systems: A Theoretical Investigation

Assembled together with the most common qubits used in nuclear resonance magnetic (NMR) quantum computation experiments, spin-1/2 nuclei, such as ¹¹³Cd, ¹⁹⁹Hg, ¹²⁵Te, and ⁷⁷Se, could leverage the prospective scalable quantum computer architectures, enabling many and heteronuclear qubits for NMR quantum information processing (QIP) implementations. A computational design strategy for prescreening recently synthesized complexes of cadmium, mercury, tellurium, selenium, and phosphorus (called MRE complexes) as suitable qubit molecules for NMR QIP is reported. Chemical shifts and spin-spin coupling constants (SSCCs) in five MRE complexes were examined using the spin-orbit zeroth order regular approximation (ZORA) at the density functional theory level and the four-component relativistic Dirac-Kohn-Sham approach. In particular, the influence of different conformers, basis sets, exchange-correlation functionals, and methods to treat the relativistic as well as solvent effects were studied. The differences in the chemical shifts and SSCCs between different low energy conformers of the studied complexes were found to be very small. The TZ2P basis set was found to be the optimum choice for the studied chemical shifts, while the TZ2P-J basis set was the best for the couplings studied in this work. The PBE0 exchange-correlation functional exhibited the best performance for the studied MRE complexes. The addition of solvent effects has not improved on the gas phase results in comparison to the experiment, with the exception of the phosphorus chemical shift. The use of MRE complexes as qubit molecules for NMR QIP could face the challenges in single qubit control and multiqubit operations. They exhibit chemical shifts appropriately dispersed, allowing qubit addressability and exceptionally large spin-spin couplings, which could reduce the time of quantum gate operations and likely preserve the coherence.

Solid-State NMR Techniques for the Structural Characterization of Cyclic Aggregates Based on Borane-Phosphane Frustrated Lewis Pairs

Modern solid-state NMR techniques offer a wide range of opportunities for the structural characterization of frustrated Lewis pairs (FLPs), their aggregates, and the products of cooperative addition reactions at their two Lewis centers. This information is extremely valuable for materials that elude structural characterization by X-ray diffraction because of their nanocrystalline or amorphous character, (pseudo-)polymorphism, or other types of disordering phenomena inherent in the solid state. Aside from simple chemical shift measurements using single-pulse or cross-polarization/magic-angle spinning NMR detection techniques, the availability of advanced multidimensional and double-resonance NMR methods greatly deepened the informational content of these experiments. In particular, methods quantifying the magnetic dipole-dipole interaction strengths and indirect spin-spin interactions prove useful for the measurement of intermolecular association, connectivity, assessment of FLP-ligand distributions, and the stereochemistry of adducts. The present review illustrates several important solid-state NMR methods with some insightful applications to open questions in FLP chemistry, with a particular focus on supramolecular associates.

Dihydrogen Splitting by Intramolecular Borane-Phosphane Frustrated Lewis Pairs: A Comprehensive Characterization Strategy Using Solid State NMR and DFT Calculations

Four hydrogenated intramolecular phosphane-borane frustrated Lewis pair (B/P FLP) compounds bearing unsaturated cyclic or aromatic carbon backbones have been synthesized and structurally characterized using ¹¹ B, ³¹ P, ¹ H and ² H solid-state NMR spectroscopy. A comparison of the spectra with those of the corresponding free B/P FLPs shows that both ¹¹ B isotropic chemical shifts as well as nuclear electric quadrupolar coupling constants decrease significantly upon FLP hydrogenation, revealing the breakage of the partial B-P bond present in the starting materials. Likewise, the ³¹ P isotropic chemical shift, the chemical shift anisotropy, and the asymmetry parameter decrease significantly upon FLP hydrogenation, reflecting the formation of a more symmetric, C_3v -like local environment. ¹¹ B{³¹ P} rotational echo double resonance (REDOR) experiments can be used to measure the B-P internuclear distance (about 3.2 Å) of these compounds. Observation of the hydrogen atoms bound to the Lewis centers is best accomplished via ³¹ P{¹ H} and ¹¹ B{¹ H} cross-polarization-heteronuclear correlation experiments or by direct observation of the ² H MAS NMR signals on especially prepared FLP-D₂ adducts. For accurately measuring the phosphorus-deuterium distance via ³¹ P{² H} rotational echo adiabatic passage double resonance (REAPDOR), it is essential to take the secondary dipolar coupling of ³¹ P with the boron-bonded ² H nuclei explicitly into consideration, by simulating a ² H_P -³¹ P-² H_B three-spin system based on structural input. All of the experimental NMR interaction parameters are found in excellent agreement with values calculated by DFT methods, using the geometries obtained either by energy optimization or from single-crystal structures.

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.

Relativistic calculations of magnetic resonance parameters: background and some recent developments

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

Shielding and indirect spin-spin coupling tensors in the presence of a heavy atom: an experimental and theoretical study of bis(phenylethynyl)mercury

Magnetic shielding and indirect spin-spin coupling phenomena are tensorial properties and both their isotropic and anisotropic parts do affect NMR spectra. The involved interaction tensors, σ and J, can nowadays be theoretically calculated, although the reliability of such methods in the case of anisotropic parameters, Δσ and ΔJ, in systems involving heavy nuclei, yet demands testing. In this communication the results of the experimental and theoretical investigations of bis(phenylethynyl)mercury (I) labeled with (13)C isotope at positions neighboring Hg are reported. The theoretical calculations of molecular geometry and values of NMR parameters for I have been performed by the ZORA/DFT method, including the relativistic scalar and spin-orbit coupling contributions, using the PBE0 functional and TZP (or jcpl) basis set. These values have been confronted with the experimentally measured ones. The isotropic parameters have been measured by the standard (13)C and (199)Hg NMR spectra. The shielding anisotropies for the atoms in the central part of molecule I have been determined in a liquid sample using magnetic relaxation measurements. The relaxation data have been interpreted within the rotational diffusion theory, assuming the symmetrical top reorientation model. The anisotropies of one-bond (13)C-(199)Hg and two-bond (13)C-Hg-(13)C spin-spin couplings have been determined exploiting the temperature-dependent (13)C NMR spectra of I in the ZLI1167 liquid-crystal phase. We have found that our theoretical calculations reproduce experimental values of both isotropic and anisotropic NMR parameters very well.

NMR J-coupling constants in cisplatin derivatives studied by molecular dynamics and relativistic DFT

Solvent effects on J((195)Pt-(15)N) one-bond nuclear spin-spin coupling constants (J(PtN)) of cisplatin [cis-diamminedichloroplatinum(II)] and three cisplatin derivatives are investigated using a combination of density functional theory (DFT) based ab initio molecular dynamics (aiMD) and all-electron relativistic DFT NMR calculations employing the two-component relativistic zeroth-order regular approximation (ZORA). Good agreement with experiment is obtained when explicit solvent molecules are considered and when the computations are performed with a hybrid functional. Spin-orbit coupling causes only small effects on J(PtN) . Key factors contributing to the magnitude of coupling constants are elucidated, with the most significant being the presence of solvent as well as the quality of the density functional and basis set combination. The solvent effects are of the same magnitude as J(PtN) calculated for gas-phase geometries. However, the trends of J(PtN) among the complexes are already present in the gas phase. Results obtained with a continuum solvent model agree quite well with the aiMD results, provided that the Pt solvent-accessible radius is carefully chosen. The aiMD results support the existence of a partial hydrogen-bond-like inverse-hydration-type interaction affording a weak (1)J(Pt⋅⋅⋅H(w)) coupling between the complexes and the coordinating water molecule.

Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity

Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

Measurement of delta(1)J((199)Hg, (31)P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury-phosphorus coupling tensors

Using 31P solid-state NMR spectroscopy, anisotropy in the indirect 199Hg-31P spin-spin coupling tensor (DeltaJ) for powdered [HgPCy3(OAc)2]2 (1) has been measured as 4700 +/- 300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that DeltaJ(199Hg, (31)P) arises entirely from the ZORA Fermi-contact-spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of DeltaJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various 199Hg, 31P spin-spin coupling anisotropies is reasonable; however, experimental values of 1J(199Hg, 31P)(iso) are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for 1J(199Hg, 31P)(iso) in [HgPPh3(NO3)2]2 depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the 31P NMR spectrum of 199Hg-31P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.