Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals

A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three-dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Röhse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Röhse et al. using a low order polynomial fitting procedure.

A heterogeneous conductorlike solvation model (conductorlike screening model/conductorlike polarizable continuum model) that uses different local effective dielectrics for different portions of the solute cavity surface is implemented for quantum chemical Hartree-Fock and Kohn-Sham methods. A variational treatment is used to form the heterogeneous solvation operator, so a simple analytic expression of the energy gradients, which are vital for geometry optimization and molecular dynamics simulation, is derived and implemented. Using the new Fixed Points with Variable Areas surface tessellation scheme, continuous and smooth potential energy surfaces as well as analytic gradients are obtained for this heterogeneous model. Application of the heterogeneous solvation model to a realistic quantum model consisting of 101 atoms for the type-1 Cu center in rusticyanin shows that the desolvation due to protein burial can likely raise the reduction potential by approximately 200 mV and, including the heterogeneity in geometry optimization, can likely affect the results by approximately 2 kcal/mol or approximately 70 mV.

The high cost of computing the Hartree-Fock exchange energy has resulted in a limited use of hybrid density functionals in solid-state and condensed phase calculations. Approximate methods based on the use of localized orbitals have been proposed as a way to reduce this computational cost. In particular, Boys orbitals (or maximally localized Wannier functions in solids) were recently used in plane wave, first-principles molecular dynamics simulations of water. Recently, the recursive subspace bisection (RSB) method was used to compute orbitals localized in regular rectangular domains of varying shape and size, leading to efficient calculations of the Hartree-Fock exchange energy in the plane-wave, pseudopotential framework. In this paper, we use the RSB decomposition to analyze orbital localization properties in inhomogeneous systems (e.g., solid/liquid interfaces) in which localized orbitals have widely varying extent. This analysis reveals that some orbitals cannot be significantly localized and thus cannot be truncated without incurring a substantial error in computed physical properties, while other orbitals can be well localized to small domains. We take advantage of the ability to systematically reduce the error in RSB calculations through a single parameter to study the effect of orbital truncation. We present the errors in PBE0 ground state energies, ionic forces, band gaps, and relative energy differences between configurations for a variety of systems, including a tungsten oxide/water interface, a silicon/water interface, liquid water, and bulk molybdenum. We show that the RSB approach can adapt to such diverse configurations by localizing orbitals in different domains while preserving a 2-norm upper bound on the truncation error. The resulting approach allows for efficient hybrid DFT simulations of inhomogeneous systems in which the localization properties of orbitals vary during the course of the simulation.

The electronic structure and some electron transfer properties of a model mixed-valence Spiro molecular cation have been investigated at CAS-SCF, CAS+S, and CAS+SD levels starting from canonical and localized orbitals, using SZ, DZ, and TZP basis sets. The potential energy surfaces of the adiabatic ground and the lowest three excited electronic states have been computed, within a two-state model, and a double-well potential has been obtained for the ground electronic state. We have demonstrated the low coupling interaction between the two redox moieties of this molecular cation by following the charge localization/delocalization in the valence pi system through the reaction coordinate of the intramolecular charge transfer. The effect of dynamical correlation, using either localized or canonical orbitals, was found to be crucial for a quantitative description of the electronic structure and some important electron transfer parameters of this mixed-valence system.

The importance of negative (anionic) hyperconjugation

To circumvent the cubic scaling and convergence difficulties encountered in the standard top-down localization of the global canonical molecular orbitals (CMOs), a bottom-up localization scheme is proposed based on the idea of "from fragments to molecule". That is, the global localized MOs (LMOs), both occupied and unoccupied, are to be synthesized from the primitive fragment LMOs (pFLMOs) obtained from subsystem calculations. They are orthonormal but are still well localized on the parent fragments of the pFLMOs and can hence be termed as "fragment LMOs" (FLMOs). This has been achieved by making use of two important factors. Physically, it is the transferability of the locality of the fragments that serves as the basis. Mathematically, it is the special block-diagonalization of the Kohn-Sham matrix that allows retention of the locality: The occupied-occupied and virtual-virtual diagonal blocks are only minimally modified when the occupied-virtual off-diagonal blocks are annihilated. Such a bottom-up localization scheme is applicable to systems composed of all kinds of chemical bonds. It is then shown that, by a simple prescreening of the particle-hole pairs, the FLMO-based time-dependent density functional theory (TDDFT) can achieve linear scaling with respect to the system size, with a very small prefactor. As a proof of principle, representative model systems are taken as examples to demonstrate the accuracy and efficiency of the algorithms. As both the orbital picture and integral number of electrons are retained, the FLMO-TDDFT offers a clear characterization of the nature of the excited states in line with chemical/physical intuition.

Elastic properties and electronic structures of L12 Co3(Ge,W)

Chemical phenomena involving near-degenerate electronic states, such as conical intersections or avoided crossing, can be properly described using quasi-degenerate perturbation theory. This study proposed a highly scalable quasi-degenerate second-order N-electron valence state perturbation theory (QD-NEVPT2) using the local pair-natural orbital (PNO) method. Our recent study showed an efficient implementation of the PNO-based state-specific NEVPT2 method using orthonormal localized virtual molecular orbitals (LVMOs) as an intermediate local basis. This study derived the state-coupling (or off-diagonal) terms to implement QD-NEVPT2 in an alternative manner to enhance efficiency based on the internally contracted basis and PNO overlap matrices between different references. To facilitate further acceleration, a local resolution-of-the-identity (RI) three-index integral generation algorithm was developed using LMOs and LVMOs. Although the NEVPT2 theory is considered to be less susceptible to the intruder-state problem (ISP), this study revealed that it can easily suffer from ISP when calculating high-lying excited states. We ameliorated this instability using the imaginary level shift technique. The PNO-QD-NEVPT2 calculations were performed on small organic molecules for the 30 lowest-lying states, as well as photoisomerization involving the conical intersection of 1,1-dimethyldibenzo[b,f] silepin with a cis-stilbene skeleton. These calculations revealed that the PNO-QD-NEVPT2 method yielded negligible errors compared to the canonical QD-NEVPT2 results. Furthermore, we tested its applicability to a large photoisomerization system using the green fluorescent protein model and the ten-state calculation of the large transition metal complex, showcasing that off-diagonal elements can be evaluated at a relatively low cost.

K. C. Thompson and M. A. Collins, J. Chem. Soc., Faraday Trans., 1997, 93, 871 DOI: 10.1039/A606038B

Generalized gradient calculations of magneto-electronic properties for diluted magnetic semiconductors ZnMnS and ZnMnSe

Conformational studies on timolol: A β-blocker by PCILO and NMR methods

Half-metallic ferromagnetic features of V-doped Cu2O alloys: TB-mBJ and DFT + U insights

Electronic structure and optical properties of noncentrosymmetric LiGaSe2: Experimental measurements and DFT band structure calculations

Electronic structure of cadmium selenogallate CdGa 2Se 4 as studied using ab initio calculations and X-ray photoelectron spectroscopy

Zirconium aluminides studied with first principles calculations: Hyperfine interactions and site preference of dopants