Calculation Of Molecular Magnetic Properties Research Articles

RotGT-2023: A benchmark data set of rotational g tensors.

The largest ever set, RotGT-2023, of statistically validated experimental components of rotational g tensors and respective vibrational corrections, has been created. The experimental values were collected from literature data. The vibrational corrections for obtaining equilibrium molecular g values have been calculated at the highest affordable coupled cluster level of theory. The set comprises 278 parameters from 129 molecules, including their isotopologues. Statistical assessment of the data has been performed to exclude unreliable parameters. A benchmarking of two theoretical approximations, based on coupled cluster and density functional theories, has been performed. The determined weighted mean and weighted standard deviations of the relative errors in calculated equilibrium g values are 1.09% and 2.07% for the ae-CCSD(T)/x2c-TZVPPall-s//ae-CCSD(T)/cc-pwCVTZ level. The obtained results can be used for predicting the rotational Zeeman effect, correcting rotational constants in spectroscopic studies and in molecular structure refinements. The latter has been demonstrated on the refinement of the molecular structure of silane SiH4, which resulted in rese(Si-H) = 1.473 323 1(27) Å. The other tested theoretical protocol, PBE0/x2c-TZVPPall-s//PBE0-D3BJ/def2-QZVPP, showed considerably worse statistical properties. The RotGT-2023 data set and the developed in this work statistical model are recommended for benchmarking of theoretical approximations for calculations of molecular magnetic properties.

On the development of the exact two-component relativistic method for calculating indirect NMR spin-spin coupling constants

Recently, to obtain the proper basis functions of small component spinors from the basis functions of large component spinors, the restricted magnetic balance (RMB) has been used in relativistic calculations of molecular magnetic properties, instead of the restricted kinetic balance (RKB). In this study, we attempt to develop the RMB-based exact two-component relativistic method, i.e., RMB-based normalized elimination of the small component (RMB-NESC) method for calculating indirect NMR spin-spin coupling constants (SSCCs), as well as the RKB-NESC method. The RMB-NESC SSCC formulas require complicated one-electron integrals, unlike the RKB-NESC SSCC formulas. However, the standard integral evaluation method for the complicated integrals has not yet been established, while we calculate them by using the finite-size nuclear model and partial integration. By comparison with the RKB-NESC and experimental SSCC values, we discuss whether the RMB-NESC results are valid. Finally, we conclude that our calculation for the complicated integrals must have some problems.

Non-perturbative calculation of molecular magnetic properties within current-density functional theory.

We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

The Rotational g Tensor as a Benchmark for Density-Functional Theory Calculations of Molecular Magnetic Properties.

The rotational g factor for a large number of organic compounds has been investigated with density-functional theory. Rapid convergence toward the basis-set limit is ensured by the use of London atomic orbitals. A statistical analysis of the results has been carried out in comparison with accurate experimental data. It is shown that gradient-corrected and hybrid functionals reproduce experimental results most closely, with the Keal-Tozer KT2 functional being the most accurate.

Coupled Hartree–Fock calculations of molecular magnetic properties annihilating the transverse paramagnetic current density

The reliability of the continuous transformations of origin of the current density method, which makes the transverse paramagnetic current vanish (CTOCD-PZ), for the prediction of nearly gauge-origin independent molecular magnetic susceptibility and gauge-origin independent nuclear magnetic shielding, is proved on the basis of a fairly large number of calculations. It is shown that, within the computational scheme provided by the coupled Hartree–Fock perturbation theory (CHF), convergence towards the presumed Hartree–Fock limit, for magnetic susceptibility and proton magnetic shielding, is systematically reached using basis sets which are smaller than those required by conventional common origin and CTOCD-DZ techniques. For second-row nuclear magnetic shieldings a variant of the CTOCD-PZ method, which shifts the origin of the current towards the nearest nucleus for points close to nuclei, as suggested originally by Keith and Bader with the CSDGT method [T. A. Keith and R. F. W. Bader, Chem. Phys. Lett. 210, 223 (1993)], gives likewise good results with affordable basis sets.

Improvement of STO and GTO Basis Set Quality in Calculations of Magnetic Properties by the Coupled and Uncoupled Hartree−Fock Perturbation Theory

Two methods of physically justified improvement of the STO and GTO basis set quality are suggested for ab initio calculations of molecular magnetic properties. They are based on the analysis of analytical expressions for the first-order correction (response) functions to the unperturbed basis AO's. The response functions have been obtained by solution of the inhomogeneous Schrodinger equation for the model problem “a one-electron atom in an external uniform field”, by the closed representation of the Green's function. It has been shown that unlike the London orbitals for magnetic field the Green's function method enables us to get the general solutions of the inhomogeneous Schrodinger equation. The methods elaborated have been applied in test calculations of magnetic susceptibilities and nuclear shielding constants of the first- and second-row hydrides and diatomics in STO-NG, split-valence CGTO basis sets, and extended ones constructed on their base. Analysis of results obtained has allowed us to determi...

Method of basis set construction in ab initio calculations of molecular magnetic properties

A physically justified method of construction of basis sets of the Slater- and Gauss-type functions for calculations of the molecular magnetic susceptibilities (χ) and NMR shielding constants (σ) is suggested. It is based upon the inclusion of those response functions into the basis set, which were generated from the initial basis set functions by the electron angular momentum operator. The χ and σ test calculations have been carried out for the ten-electron hydride molecules within the coupled scheme of the Hartree-Fock perturbation theory.

Calculation of molecular magnetic properties in the isoelectronic series PH 2−, PH 3 and PH 4+

Ab initio coupled Hartree-Fock perturbation theory has been used to evaluate magnetic susceptibility and magnetic shielding tensors of 31P and 1H nuclei in PH 2 −, PH 3 and PH 4 +. Good agreement between theoretical and experimental data and a satisfactory degree of origin independence of computed values has been found by adopting large polarized basis sets developed ad hoc for magnetic properties.

Calculation of molecular magnetic properties within the Landau gauge in hydrogen fluoride, ammonia, and methane molecules

The magnetic susceptibility and the nuclear magnetic shielding tensors of HF, NH3, and CH4 molecules in the presence of a spatially uniform time-independent magnetic field have been calculated within the Landau gauge for the vector potential. The random-phase approximation has been used, adopting flexible Gaussian basis sets of large size. Magnetic susceptibilities are quite harder to evaluate accurately in the Landau gauge than in Coulomb gauge. Calculated nuclear magnetic shieldings are close to the Hartree–Fock limit. Sum rules for charge conservation and origin independence of magnetic susceptibility and nuclear magnetic shieldings are fairly well satisfied by basis sets of extended size.

Electron-correlated calculations of magnetic properties

A method for the calculation of molecular magnetic properties is developed. Of significance is the inclusion of electron correlation (at the MP2 level). In order to validate the method, the magnetizabilities of H2 and HF are determined. These exploratory results indicate that further applications will be successful.

Calculation of molecular magnetic properties within the Landau gauge.

A theoretical procedure for calculating magnetic susceptibility and nuclear magnetic shieldings in molecules in the presence of a spatially uniform time-independent magnetic field, within the Landau gauge for the vector potential, is described. Sum rules for charge and current conservation and gauge invariance have been derived. A computational scheme based on the random-phase approximation has been used to calculate magnetic susceptibility and shielding tensors in the water molecule, adopting fairly flexible Gaussian basis sets of large size. The results show that very accurate molecular wave functions are needed to obtain paramagnetic contributions to the magnetic susceptibility of the same quality as those obtainable within the Coulomb gauge for the vector potential. The theoretical nuclear magnetic shielding tensors in the Landau gauge are characterized by the same quality as those in the Coulomb gauge.

Magnetic properties of molecules with Gauss-type function depending on perturbation

A new analytical method of the quantum mechanical calculations of molecular magnetic properties in gaseous phase is suggested. The method is based on taking into account of the Gauss-type basis set dependence on a perturbation. Effectiveness of the given method in the test calculations of the nuclear magnetic shielding constants for some of the small molecules in a minimal basis set of the atomic functions is demonstrated.

An electronic Hamiltonian for origin independent calculations of magnetic properties

A gauge origin independent formalism for the calculation of molecular magnetic properties is presented. Origin independence is obtained by using London’s gauge invariant atomic orbitals, expanding the second quantization Hamiltonian in the external magnetic field and nuclear magnetic moments, and using the resulting expansion terms as perturbation operators in response function calculations. To ensure orthonormality of the molecular orbitals, a field-dependent symmetrical orthonormalization is employed. In this way the gauge dependence of the London orbitals is transferred to the Hamiltonian. The resulting perturbation operators may be used to calculate magnetic properties from any approximate ab initio wave function.

Generation of a basis set for the calculation of molecular magnetic properties

Completeness conditions have been applied in the theory of molecular magnetic properties to determine the best gauge for a given basis set. They can similarly be used to optimise the basis for a fixed gauge origin. Test results indicate that the gauge dependence of the calculated properties can be significantly reduced in this way.

Optimal gauge in approximate calculations of molecular magnetic properties

A variational procedure is suggested for determining optimal gauge parameters (such as gauge origin etc.) in calculations of molecular magnetic properties with a finite basis set.

On the improvement of the gauge invariance in finite basis set coupled hartree—fock calculations of molecular magnetic properties

Finite basis set coupled Hartree—Fock calculations of molecular magnetic susceptibilities and nuclear shielding constants show a very large gauge dependence (i.e., a dependence on the origin of the magnetic vector potential). The best agreement with experiment is expected for a gauge origin at the electronic centroid for which choice the so-called paramagnetic cotributions to the above properties are small. However, with a finite basis set agreement with experiment may be fortuitous and some estimate of the contribution of the unknown functions is required. A general scheme is presented for dealing with the above problems. The essence of the method is to apply an average energy approximation to the unknown functions and to determine this energy by enforcing the gauge invariance requirement. Consequently the technique can still be categorised as an ab initio method and a close approach to the Hartree—Fock limit is achieved without the need to employ very large basis sets with extensive optimisation. The method is applied to the hydrogen fluoride molecule which provides numerical justification of the proposed scheme.