Coupled Perturbed Approach to Dual Basis Sets for Molecules and Solids. II: Energy and Band Corrections for Periodic Systems.

When trying to reach convergence of quantum chemical calculations toward the complete basis set limit, crystalline solids generally prove to be more challenging than molecules. This is due both to the closer packing of atoms─hence, to linear dependencies─and to the problematic behavior of Ewald techniques used for dealing with the infinite character of Coulomb sums. Thus, a dual basis set approach is even more desirable for periodic systems than for molecules.

The shape effect and its consequences for polar surfaces and for heterogeneous catalysis.

In this paper we develop the shape effect, which is relevant for crystalline materials whose size is larger than that of the thermodynamic limit. According to this effect the electronic properties of one surface of a crystal depend upon all of its surfaces, on the overall shape. At first, qualitative mathematical arguments are presented for the existence of this effect based on the conditions for the stability of polar surfaces.

Perturbation Theory Treatment of Spin-Orbit Coupling. III: Coupled Perturbed Method for Solids.

A previously proposed noncanonical coupled-perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment for spin-orbit coupling is here generalized to infinite periodic systems. The scalar-relativistic periodic KS-DFT/HF solution, obtained with a relativistic effective core potential, is taken as the zeroth-order approximation. Explicit expressions are given for the total energy through third-order, which satisfy the 2N + 1 rule (i.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry.

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998.

Perturbation Theory Treatment of Spin-Orbit Coupling, Part I: Double Perturbation Theory Based on a Single-Reference Initial Approximation.

We develop a perturbation theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree-Fock (SR UHF) solution, we carry out a double perturbation expansion in terms of spin-orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two.

Perturbation Theory Treatment of Spin-Orbit Coupling II: A Coupled Perturbed Kohn-Sham Method.

A noncanonical coupled perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment of spin-orbit coupling (SOC) is provided. We take the scalar-relativistic KS-DFT/HF solution, obtained with a relativistic effective core potential, as the zeroth-order approximation. Explicit expressions are given for the total energy through the 4th order, which satisfy the 2 + 1 rule.

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes.

The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real.

The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions).

Coupled Perturbation Theory Approach to Dual Basis Sets for Molecules and Solids. 1. General Theory and Application to Molecules.

We present a new coupled Hartree-Fock(HF)/Kohn-Sham DFT perturbation method that accounts for the effect of enlarging the basis set in electronic structure calculations. In contrast with previous approaches, our dual basis set treatment yields not only a correction for the total energy but also for the orbital eigenvalues and density. The zeroth order solution is obtained from the projection of the small basis set coefficients.

Biradical rotamer states tune electron J coupling and MAS dynamic nuclear polarization enhancement.

Cross Effect (CE) Dynamic Nuclear Polarization (DNP) relies on the dipolar (D) and exchange (J) coupling interaction between two electron spins. Until recently only the electron spin D coupling was explicitly included in quantifying the DNP mechanism. Recent literature discusses the potential role of J coupling in DNP, but does not provide an account of the distribution and source of electron spin J coupling of commonly used biradicals in DNP.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case.

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored.

Surface effects on converse piezoelectricity of crystals.

The contribution of surface units to bulk properties are often neglected in theoretical and computational studies of crystalline systems. We demonstrate that this assumption has to be made with caution in the case of (electric field) polarization. As a generalization of an earlier work on quasi-one-dimensional systems [Springborg, et al.

Calculation of the dynamic first electronic hyperpolarizability β(-ω(σ); ω(1), ω(2)) of periodic systems. Theory, validation, and application to multi-layer MoS2.

We describe our implementation of a fully analytical scheme, based on the 2n + 1 rule, for computing the coupled perturbed Hartree Fock and Kohn-Sham dynamic first hyperpolarizability tensor β(-ωσ; ω1, ω2) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int.

Computation of Second Harmonic Generation for Crystalline Urea and KDP. An ab Initio Approach through the Coupled Perturbed Hartree-Fock/Kohn-Sham Scheme.

The electronic second harmonic generation (SHG) tensor, d, of crystalline urea and potassium dihydrogen phosphate (KDP) is evaluated as a function of frequency using a Gaussian type basis set and the Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) schemes as implemented in the CRYSTAL code. The results of various functionals, including LDA, GGA (PBE), and global and range-separated hybrids (B3LYP, PBE0, LC-BLYP), as well as Hartree-Fock, are compared. It is found that the calculated SHG intensity always decreases as the percentage of exact exchange increases.

Electronic responses of long chains to electrostatic fields: Hartree-Fock vs. density-functional theory: a model study.

The response to an electrostatic field is determined through simple model calculations, within both the restricted Hartree-Fock and density functional theory methods, for long, finite as well as infinite, periodic chains. The permanent dipole moment, μ0, the polarizability, α, and the hyperpolarizabilities β and γ, calculated using a finite-field approach, are extensively analyzed. Our simple model allows for treatment of large systems and for separation of the properties into atomic and unit-cell contributions.

Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis. II. Validation and comparison with experiments.

In this work, we validate a new, fully analytical method for calculating Raman intensities of periodic systems, developed and presented in Paper I [L. Maschio, B. Kirtman, M.

Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis. I. Theory.

We present a fully analytical formulation for calculating Raman intensities of crystalline periodic systems using a local basis set. Numerical differentiation with respect to atomic coordinates and with respect to wavevectors is entirely avoided as is the determination of crystal orbital coefficient derivatives with respect to nuclear displacements. Instead, our method utilizes the orbital energy-weighted density matrix and is based on the self-consistent solution of first- and second-order Coupled Perturbed Hartree-Fock/Kohn-Sham equations for the electronic response to external electric fields at the equilibrium geometry.

Raman spectrum of pyrope garnet. A quantum mechanical simulation of frequencies, intensities, and isotope shifts.

The Raman spectrum of pyrope garnet is simulated in ab initio quantum mechanical calculations, using an all-electron Gaussian-type basis set and the hybrid B3LYP functional. Frequencies calculated for the 25 Raman-active modes are in excellent agreement with the several sets of experimental data, with the mean absolute difference ranging from 4 to 8 cm(-1). Comparison of the computed and experimental spectrum shows excellent agreement for most of the intensities as well.

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities.

A set of exchange-correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM-B3LYP, LC-BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all-trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller-Plesset second-order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals.

A Full Dimensionality Approach to Evaluate the Nonlinear Optical Properties of Molecules with Large Amplitude Anharmonic Tunneling Motions.

Previously, a reduced dimensionality approach was used to determine the vibrational contribution to nonlinear optical properties for molecules with large amplitude anharmonic modes that takes into account tunneling between potential wells (Luis, J. M.; Reis, H.

Ab initio analytical infrared intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method.

A fully analytical method for calculating Born charges and, hence, infrared intensities of periodic systems, is formulated and implemented in the CRYSTAL program, which uses a local gaussian type basis set. Our efficient formalism combines integral gradients with first-order coupled perturbed Hartree-Fock/Kohn Sham electronic response to an electric field. It avoids numerical differentiation with respect to wave vectors, as in some Berry phase approaches, and with respect to atomic coordinates.

Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides.

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B10H14, Li2(•+)TCNQ(•-), and Na2(•+)TCNQ(•-).

Static and dynamic coupled perturbed Hartree-Fock vibrational (hyper)polarizabilities of polyacetylene calculated by the finite field nuclear relaxation method.

The vibrational contribution to static and dynamic (hyper)polarizability tensors of polyacetylene are theoretically investigated. Calculations were carried out by the finite field nuclear relaxation (FF-NR) method for periodic systems, newly implemented in the CRYSTAL code, using the coupled perturbed Hartree-Fock scheme for the required electronic properties. The effect of the basis set is also explored, being particularly important for the non-periodic direction perpendicular to the polymer plane.