This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n $\geq1$ and can slightly reduce compute costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. We select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low compute costs to make practical recommendations. Our assessment covers conventional electronic structure methods (DFT and wavefunction) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.
In natural processes involving weak interactions, a violation of spatial parity conservation should appear. Its effects are expected to be observable in molecules using different spectroscopic methodologies, but due to the tiny magnitude of these effects they have never been measured yet. We present a theoretical analysis of four-component relativistic nuclear-spin-dependent parity-violating nuclear spin-rotation and NMR shielding tensors in a set of tetrahedral chiral molecules. This work highlights the crucial role played by the ligands and the electronic structure of the chiral center in th…
Nuclear Magnetic Resonance (NMR) shielding constants of transition metals in solvated complexes are computed at the relativistic density functional theory (DFT) level. The solvent effects evaluated with subsystem-DFT approaches are compared with the reference solvent shifts predicted from supermolecular calculations. Two subsystem-DFT approaches are analyzed -- in the standard frozen density embedding (FDE) scheme the transition metal complexes are embedded in an environment of solvent molecules whose density is kept frozen, in the second approach the densities of the complex and of its enviro…
We describe an accurate and scalable implementation for the computation of molecular nuclear magnetic resonance shieldings, J-couplings, and magnetizabilities within nonrelativistic semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. We compare the convergence to the basis set limit for two established types of NAO basis sets, called NAO-VCC-nZ and FHI-aims-09, to several established Gaussian-type basis sets. The basis set limit is reached faster for the NAO basis sets than for standard correlation consistent Gaussian-type basis sets (cc-pVnZ, aug-cc-p…
We present a simple derivation of the nuclear shielding in paramagnetic molecules, extendable to strong spin-orbit coupling cases of relevance to lanthanides and actinides, as well as encompassing contributions from excited multiplets. While our general formulation does not need electron paramagnetic resonance parameters, using them a simple and practical expression is obtained for the special case of the zero-field-split ground-state manifold, including magnetic (Zeeman and hyperfine) couplings between the sublevels. The latter method is implemented computationally and applied in the context …
We present an implementation of coupled-perturbed complete active space self-consistent field (CP-CASSCF) theory for the computation of nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals and Cholesky decomposed two-electron integrals. The CP-CASSCF equations are solved using a direct algorithm where the magnetic Hessian matrix-vector product is expressed in terms of one-index transformed quantities. Numerical tests on systems with up to about 1300 basis functions provide information regarding both the computational efficiency and limitations of our implementation.
The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for $^1$H, $^{13}$C, and $^{15}$N shieldings in polymorphs of three paradigmatic molecular crystals -- benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typ…
The requirement for accelerated and quantitatively accurate screening of nuclear magnetic resonance spectra across the small molecules chemical compound space is two-fold: (1) a robust `local' machine learning (ML) strategy capturing the effect of neighbourhood on an atom's `near-sighted' property -- chemical shielding; (2) an accurate reference dataset generated with a state-of-the-art first principles method for training. Herein we report the QM9-NMR dataset comprising isotropic shielding of over 0.8 million C atoms in 134k molecules of the QM9 dataset in gas and five common solvent phases. …
Predicting accurate NMR chemical shieldings relies upon cancellation of different types of error in the ab initio methodology used to calculate the shielding tensor of the analyte of interest and the reference. Often the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects, is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral triv…
It is known that the nuclear-spin-dependent parity-violating contributions to the NMR shielding and the nuclear spin-rotation tensors (${\bf σ}^{PV}$ and ${\bf M}^{PV}$, respectively) are formally related each other within the non-relativistic (NR) regime. Such a formal relationship is not any longer valid within the relativistic domain. A new more general formal relationship, that is valid within the relativistic framework is shown here, being developed through the use of the LRESC model. The formalism of polarization propagators is applied to write the different contributions to both propert…
Comment on "Four-component relativistic theory for NMR parameters: Unified formulation and numerical assessment of different approaches" [J. Chem. Phys. 130, 144102 (2009)]
NMR Chemical Shift Computations at Second-Order Møller-Plesset Perturbation Theory Using Gauge-Including Atomic Orbitals and Cholesky-Decomposed Two-Electron Integrals
The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.
We investigate the ability of mechanical and electronic density functional theory (DFT)-based embedding approaches to describe the solvent effects on nuclear magnetic resonance (NMR) shielding constants of the $^{95}$Mo nucleus in the molybdate ion in aqueous solution. From the description obtained from calculations with two- and four-component relativistic Hamiltonians, we find that for such systems spin-orbit coupling effects are clearly important for absolute shielding values, but for relative quantities a scalar relativistic treatment provides a sufficient estimation of the solvent effects…
