Seiichiro Ten-no

R12 methods in explicitly correlated molecular electronic structure theory

The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12. Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelniggs use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12)). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical accuracy (1 kcal/mol) in triple- or even double-zeta basis sets. Using a range of approximations, applications to large molecules become possible. Here, the major developments in the field are reviewed, and recommendations for future directions are presented. By comparing with commonly used extrapolation techniques, it is shown that modern R12 methods can deliver high accuracy dramatically faster than by using conventional methods. Contents PAGE 1. Introduction 429  1.1. The origin of the problem 429  1.2. Two-electron systems 430  1.3. Explicitly correlated MP2 methods 430  1.4. Gaussian geminals 431  1.5. Exponentially correlated Gaussians 432  1.6. The transcorrelated method 433 2. R12 wavefunctions 433  2.1. Definition 434  2.2. Correlation factors 435  2.3. Projection operators 437  2.4. Levels of theory 439  2.5. Methods for open shells 440 3. Approximations of many-electron integrals 441  3.1. Exact evaluation 442  3.2. Approximations: GBC, EBC and 443  3.3. Resolution of the identity 445  3.4. Numerical quadrature 447  3.5. Density fitting 449  3.6. DF combined with RI 451 4. Examples from second-order perturbation theory 452  4.1. Technical details 453  4.2. R12 results in comparison with extrapolated values 454  4.3. Comparison between R12 and F12 results 458 5. Perspectives 461  5.1. Higher level methods 461  5.2. Local approximations 461  5.3. Conclusions 462   5.3.1. Correlation factor 462   5.3.2. Projection operator 462   5.3.3. Formulation of intermediate B 463   5.3.4. Approximating integrals 463   5.3.5. Efficiency improvements 463 Acknowledgements 463 References 464

Reference interaction site model self‐consistent field study for solvation effect on carbonyl compounds in aqueous solution

In the previous study, Chem. Phys. Lett. 214, 391 (1993), we developed a new computational procedure for the solvation effect on the electronic structure of solute based upon the reference interaction site model (RISM) integral equation and the Hartree–Fock equation. The method enables us to calculate the solvent distribution and solute electronic wave functions simultaneously, which is free from such empirical parametrizations as appeared in the usual models based on the dielectric continuum picture. In the present article, we have applied the method to several carbonyl compounds in aqueous solution. The SPC model was used to describe the liquid water. The vertical n→π*, π→π*, and σ→π* transitions of formaldehyde are examined by the RISM‐self‐consistent field formalism coupled with the restricted Hartree–Fock approximation, and then the free energy calculation was performed for the excited state in order to estimate the contributions for the optical fluorescence spectra. The intramolecular energy turned ...

Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures

A rational generator, which fulfills the cusp conditions for singlet and triplet electron pairs, is proposed and applied to explicitly correlated second order Møller-Plesset perturbation theory calculations. It is shown that the generator in conjunction with frozen geminals improves the convergence of correlation energy without introducing any variational parameters in explicitly correlated functions. A new scheme for three-electron integrals based on numerical quadratures is also illustrated. The method is tested for the convergence of reaction enthalpies with various basis sets.

Solution of three-dimensional reference interaction site model and hypernetted chain equations for simple point charge water by modified method of direct inversion in iterative subspace

We proposed a modified procedure of the direct inversion in the iterative subspace (DIIS) method to accelerate convergence in the integral equation theory of liquids. We update the DIIS basis vectors at each iterative step by using the approximate residual obtained in the DIIS extrapolation. The procedure is tested by solving the 3‐dimensional (3‐D) generalization of the reference interaction site model equation together with the hypernetted chain closure, as well as their 1‐D version. We calculated the 3‐D site distribution of water, represented by the simple point charge model, around one water molecule considered as a central particle. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 928–936, 1999

A hybrid approach for the solvent effect on the electronic structure of a solute based on the RISM and Hartree-Fock equations

Abstract A new approach is proposed to evaluate the solvent effect upon the electronic structure of a solute molecule in the liquid phase. The Hartree-Fock and the extended reference interaction site model integral equations are solved in a self-consistent manner to simultaneously optimize the electronic structure of the solute, and the solvent distribution around it. The method is applied to a formaldehyde molecule in water. The result shows a clear indication of enhanced polarization of the solute molecule due to the solvent. The blue-shift induced by the solvent, which is observed in the absorption spectrum corresponding to the vertical 1 A 1 → 1 A 2 transition, is reproduced.

Density fitting for the decomposition of three-electron integrals in explicitly correlated electronic structure theory

It is shown that the convergence of R12-type explicitly correlated electronic structure theories can be improved by rearranging the three-electron integrals before using a resolution of the identity to decompose them into expressions involving only two-electron integrals. The new scheme is illustrated for some test systems within the explicitly correlated second order many-body perturbation theory.

Explicitly correlated electronic structure theory from R12/F12 ansätze

Fundamental aspects of the explicitly correlated R12 and F12 theories are summarized in the perspective of recent advances related to our contribution in this field. Starting from the basics of pair functions and second quantized formulations, the R12/F12 ansätze have been applied to MP2, coupled‐cluster, and equation of motion coupled‐cluster theories. Emphasis is given to approaches that use the rational generator to create the exact cusp conditions (SP ansatz). Computational aspects of the evaluation of many‐electron integrals are also discussed in conjunction with the use of the Slater‐type geminal, which is the predominant choice for the correlation factor in modern R12/F12 theories.

New implementation of second-order Møller-Plesset perturbation theory with an analytic Slater-type geminal

The author introduces a new method for the exchange commutator integrals in explicitly correlated Møller-Plesset second order perturbation theory. The method is well suited with an analytic Slater-type geminal correlation factor. He also explains the scheme for auxiliary integrals needed for the correlation factor. Based on different Ansätze, he analyzes the performance of the method on correlation energies and reaction enthalpies in detail.

A feasible transcorrelated method for treating electronic cusps using a frozen Gaussian geminal

Abstract We develop a feasible transcorrelated method for accelerating the convergence of reproducing the dynamic correlation effects with the size of one-electron basis. The effective Hamiltonian is parameterized in such a way that the Coulomb repulsion is compensated at short inter-electronic distances in terms of a frozen Gaussian geminal. The geminal is chosen to be independent of the position and orientation of pair-electrons. The extra part of the transcorrelated Hamiltonian is also short-ranged, size-consistent, and universal to the states of interest. We preliminarily applied the method to the single-reference many body perturbation theory with some pilot calculations.

Versatile Supramolecular Gelators That Can Harden Water, Organic Solvents and Ionic Liquids

We developed novel supramolecular gelators with simple molecular structures that could harden a broad range of solvents: aqueous solutions of a wide pH range, organic solvents, edible oil, biodiesel, and ionic liquids at gelation concentrations of 0.1-2 wt %. The supramolecular gelators were composed of a long hydrophobic tail, amino acids and gluconic acid, which were prepared by liquid-phase synthesis. Among seven types of the gelators synthesized, the gelators containing L-Val, L-Leu, and L-Ile exhibited high gelation ability to various solvents. These gelators were soluble in aqueous and organic solvents, and also in ionic liquids at high temperature. The gelation of these solvents was thermally reversible. The microscopic observations (TEM, SEM, and CLSM) and small-angle X-ray scattering (SAXS) measurements suggested that the gelator molecules self-assembled to form entangled nanofibers in a large variety of solvents, resulting in the gelation of these solvents. Molecular mechanics and density functional theory (DFT) calculations indicated the possible molecular packing of the gelator in the nanofibers. Interestingly, the gelation of an ionic liquid by our gelator did not affect the ionic conductivity of the ionic liquid, which would provide an advantage to electrochemical applications.