G. I. Pagola

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Calculation of the fourth-rank molecular hypermagnetizability of some small molecules

A computational scheme has been developed within the framework of Rayleigh-Schrödinger perturbation theory to evaluate nonlinear interaction energy contributions for a molecule in the presence of an external spatially uniform, time-independent magnetic field. Terms connected with the fourth power of the perturbing field, representing the fourth-rank hypermagnetizabilities of five small molecules, have been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test, adopting two different coordinate systems to estimate the degree of convergence of theoretical tensor components.

Magnetizabilities of diatomic and linear triatomic molecules in a time-independent nonuniform magnetic field.

The theory of response of a molecule in the presence of a static nonuniform magnetic field with uniform gradient is reviewed and extended. Induced magnetic dipole, quadrupole, and anapole moments are expressed via multipole magnetic susceptibilities. Dependence of response properties on the origin of the coordinate system with respect to which they are defined is investigated. Relationships describing the change of multipole and anapole susceptibilities in a translation of the reference system are reported. For a single molecule, two quantities are invariant and, in principle, experimentally measurable, that is, the induced magnetic dipole and the interaction energy. The trace of a second-rank anapole susceptibility, related to a pseudoscalar obtained by spatial averaging of the dipole-quadrupole susceptibility, of different sign for D and L enantiomeric systems, is origin independent. Therefore, in an isotropic chiral medium a homogeneous magnetic field induces an electronic anapole, having the same magnitude but opposite sign for two enantiomorphs. Calculations have been carried out for a set of diatomic and linear triatomic systems characterized by the presence of magnetic-field induced toroidal electron currents.

Nuclear magnetic resonance J coupling constant polarizabilities of hydrogen peroxide: A basis set and correlation study

In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one‐electron basis sets and electron correlation both at the level of density functional theory as well as second‐order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one‐electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods.

Nonlinear response of the benzene molecule to strong magnetic fields

The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density.

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules.

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector B at the origin of the coordinate system and by the polar vector C=∇×B , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector A . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling B and C via a¯ , one third of the trace of the anapole magnetizability aαβ tensor, that is, WBC=−a¯B·C . Both A and WBC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of a¯ predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals.

Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C=∇×B, is rationalized via a second-rank anapole magnetizability tensor a(αβ), defined as minus the second derivative of the second-order interaction energy with respect to the components C(α) and B(β). The average anapole magnetizability a̅ equals -χ̅, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χ(α,βγ). It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole A(α), having the same magnitude, but opposite sign, for two enantiomorphs.

Calculation of Hypershielding Contribution to Isotropic Nitrogen Shielding in Strong Magnetic Fields.

Hypershielding contributions to magnetic shielding of the nitrogen N nucleus have been evaluated for some nitroso (RNO) and isodiazene (R1R2NN) compounds in the presence of an external spatially uniform, time-independent magnetic field, accounting for cubic response via Rayleigh−Schrodinger perturbation theory. Numerical estimates have been obtained at the coupled Hartree−Fock level of accuracy within the conventional common-origin approach. Medium-size basis sets of gaugeless (that is, without gauge-including phase factors) Gaussian functions have been employed in a numerical test to show that the isotropic hypershielding contribution τNB2, τN = 1/2⟨ΣαβγδN⟩, eqs 2−4 in the text, to average nitrogen shielding in PhNO (τN ≈ 1.1 × 10−5 ppm T−2), (CH3)3CNO (τN ≈ 2.3 × 10−5 ppm T−2), and (CH3)2NN (τN ≈ 4.4 × 10−5 ppm T−2) are similar and quite large. For 15N at the highest currently available high-resolution NMR field strength of 22.3 T (ωH/2π = 950 MHz, ω15N/2π = 96.3 MHz) the change due to the additional sh...

Calculation of the electric hypershielding at the nuclei of molecules in a strong magnetic field

The third-rank electric hypershielding at the nuclei of 14 small molecules has been evaluated at the Hartree-Fock level of accuracy, by a pointwise procedure for the geometrical derivatives of magnetic susceptibilities and by a straightforward use of its definition within the Rayleigh-Schrodinger perturbation theory. The connection between these two quantities is provided by the Hellmann-Feynman theorem. The magnetically induced hypershielding at the nuclei accounts for distortion of molecular geometry caused by strong magnetic fields and for related changes of magnetic susceptibility. In homonuclear diatomics H(2), N(2), and F(2), a field along the bond direction squeezes the electron cloud toward the center, determining shorter but stronger bond. It is shown that constraints for rotational and translational invariances and hypervirial theorems provide a natural criterion for Hartree-Fock quality of computed nuclear electric hypershielding.

Can Induced Orbital Paramagnetism Be Controlled by Strong Magnetic Fields

Magnetic hypersusceptibilities and hypershielding at the nuclei of BH, CH(+), C4H4, and C8H8 molecules in the presence of an external spatially uniform, time-independent magnetic field have been investigated accounting for cubic response contributions via Rayleigh-Schrödinger perturbation theory. Numerical estimates have been obtained at the coupled Hartree-Fock and density-functional levels of theory within the conventional common-origin approach, using extended gaugeless basis sets. The fundamental role of electron correlation effects was assessed. Critical values of the applied magnetic field at which transition from paramagnetic to diamagnetic behavior would occur were estimated. It is shown that perturbative methods may successfully be employed to estimate the interaction energy for big cyclic molecules.