Incorporating Electron Correlation Research Articles

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT.

Modeling polaron defects is an important aspect of computational materials science, but the description of unpaired spins in density functional theory (DFT) often suffers from delocalization error. To diagnose and correct the overdelocalization of spin defects, we report an implementation of density-corrected (DC-)DFT and its analytic energy gradient. In DC-DFT, an exchange-correlation functional is evaluated using a Hartree-Fock density, thus incorporating electron correlation while avoiding self-interaction error. Results for an electron polaron in models of titania and a hole polaron in Al-doped silica demonstrate that geometry optimization with semilocal functionals drives significant structural distortion, including the elongation of several bonds, such that subsequent single-point calculations with hybrid functionals fail to afford a localized defect even in cases where geometry optimization with the hybrid functional does localize the polaron. This has significant implications for traditional workflows in computational materials science, where semilocal functionals are often used for structure relaxation. DC-DFT calculations provide a mechanism to detect situations where delocalization error is likely to affect the results.

Valence shell photoelectron angular distributions and vibrationally resolved spectra of imidazole: A combined experimental-theoretical study.

Linearly polarized synchrotron radiation has been used to record polarization dependent valence shell photoelectron spectra of imidazole in the photon energy range 21-100eV. These have allowed the photoelectron angular distributions, as characterized by the anisotropy parameter β, and the electronic state intensity branching ratios to be determined. Complementing these experimental data, theoretical photoionization partial cross sections and β-parameters have been calculated for the outer valence shell orbitals. The assignment of the structure appearing in the experimental photoelectron spectra has been guided by vertical ionization energies and spectral intensities calculated by various theoretical methods that incorporate electron correlation and orbital relaxation. Strong orbital relaxation effects have been found for the 15a', nitrogen lone-pair orbital. The calculations also predict that configuration mixing leads to the formation of several low-lying satellite states. The vibrational structure associated with ionization out of a particular orbital has been simulated within the Franck-Condon model using harmonic vibrational modes. The adiabatic approximation appears to be valid for the X 2A″ state, with the β-parameter for this state being independent of the level of vibrational excitation. However, for all the other outer valence ionic states, a disparity occurs between the observed and the simulated vibrational structure, and the measured β-parameters are at variance with the behavior expected at the level of the Franck-Condon approximation. These inconsistencies suggest that the excited electronic states may be interacting vibronically such that the nuclear dynamics occur over coupled potential energy surfaces.

Roles of electron correlation effects for the accurate determination of gj factors of low-lying states of Cd+113 and their applications to atomic clocks

We investigate roles of electron correlation effects in the determination of $g_j$ factors of the $ns~^2S_{1/2}$ ($n$=5,6,7), $np~^2P_{1/2,3/2}$ ($n$=5,6), $5d~^2D_{3/2,5/2}$, and $4f~^2F_{5/2,7/2}$ states of the singly ionized cadmium (Cd$^+$) ion. Single and double excited configurations along with important valence triple excited configurations through relativistic coupled-cluster (RCC) theory are taken into account for incorporating electron correlation effects in our calculations. We find significant contributions from the triples to the lower $S$ and $P$ states for attaining high accuracy results. The contributions of Breit interaction and lower-order quantum electrodynamics effects, such as vacuum polarization and self-energy corrections, are also estimated using the RCC theory and are quoted explicitly. In addition, we present energies of the aforementioned states from our calculations and compare them with the experimental results to validate $g_j$ values. Using the $g_j$ factor of the ground state, systematical shift due to the Zeeman effect in the microwave clock frequency of the $|5s~^2S_{1/2}, F=0,m_F=0 \rangle \leftrightarrow |5s~^2S_{1/2}, F=1,m_F=0 \rangle$ transition in $^{113}$Cd$^+$ ion has been estimated.

What is semiempirical molecular orbital theory approximating?

We elucidate the approaches used to incorporate electron correlation in existing semiempirical molecular orbital theory (SEMO) methods and compare them with the techniques used in other quantum chemical methods. After analyzing expressions for electron correlation in ab initio wavefunction theory, density functional theory, and density functional-based tight-binding (TB) methods, we suggest a framework for developing hybrid TB-SEMO methods. We provide a numerical proof-of-concept for such a method based on the OM2 method.

ONIOM Investigation of the Second-Order Nonlinear Optical Responses of Fluorescent Proteins.

The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer). We observe that a small high layer can already account for the variations of β as a function of the nature of the FP, provided the low layer is treated at an ab initio level to describe properly the effects of key H-bonds. Then, for semiquantitative reproduction of the experimental values obtained from hyper-Rayleigh scattering experiments, it is necessary to incorporate electron correlation as described at the second-order Møller-Plesset perturbation theory (MP2) level as well as implicit solvent effects accounted for using the polarizable continuum model (PCM). This led us to define the MP2/6-31+G(d):HF/6-31+G(d)/IEFPCM scheme as an efficient ONIOM approach and the MP2/6-31+G(d):HF/6-31G(d)/IEFPCM as a better compromise between accuracy and computational needs. Using these methods, we demonstrate that many parameters play a role on the β response of FPs, including the length of the π-conjugated segment, the variation of the bond length alternation, and the presence of π-stacking interactions. Then, noticing the small diversity of the FP chromophores, these results highlight the key role of the β-barrel and surrounding residues on β, not only because they can locally break the noncentrosymmetry vital to a β response but also because it can impose geometrical constraints on the chromophore.

A valence bond theory treatment of tetrel bonding interactions

Long range noncovalent interactions in H3Y…TrH3X molecules (Y=N, P, As; Tr=C, Si, Ge; X=F, Cl, Br) have been studied using valence bond methods in order to further the understanding of tetrel (group IV) bonding. It is shown that incorporating electron correlation through the breathing orbital valence bond method is required in order to reproduce tetrel bond energy trends obtained by density functional theory. Tetrel bonds are formed by donation of the Y lone pair into a σ-hole on the Tr atom and their strength depends on the donor strength of the Y atom and the Tr/X electronegativity difference. Charge transfer valence bond structures are shown to be important, indicating that electron transfer is the driving force behind tetrel bonds rather than electrostatics.

Theoretical models incorporating electron correlation

Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Moller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is, applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. The independent electron-pair approximation is accurate to second order in a Moller-Plesset expansion, but inaccurate in third order. A series of variational methods is discussed which gives upper bounds for the energy, but which lacks size consistency. Finally, calculations on some small molecules using a moderately large Gaussian basis are presented to illustrate these points. Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are describe substantially better by Moller--Plesset theory to second or third order than by Hartree--Fock theory.

Incremental Solvation of Nonionized and Zwitterionic Glycine

Microsolvation and combined microsolvation-continuum approaches are employed in order to examine the structures and relative energies of nonionized (N) and zwitterionic (Z) glycine clusters. Bridging structures are predicted to be the global minima after 3-5 discrete water molecules are included in the calculations. Calculations incorporating electron correlation stabilize the zwitterionic structures by about 7-9 kcal/mol relative to the N structures regardless of the number of discrete water molecules considered. Continuum calculations stabilize the Z structures relative to N structures; this effect decreases as the number of discrete water molecules is increased. Eight water molecules do not appear to fully solvate glycine.

Theoretical Study of the Insertion Reactions of Zr+ into HF, HCl, H2O, H2S, NH3, PH3, CH4, and SiH4

The insertion reactions of transition metal cation doublet Zr+(2D) into HF, HCl, H2O, H2S, NH3, PH3, CH4, and SiH4 have been studied by means of ab initio molecular orbital calculations incorporating electron correlation with the Møller−Plesset perturbation theory up to the second and the fourth orders and the hybrid density functional method, B3LYP. Three regions of the potential surface have been investigated, an ion−molecule complex, followed by a three-center, four-electron transition state, and then an insertion product. It is found that all insertion reactions are exothermic and all transition states are below the energy surfaces of the reactants. For the ion−molecule complexes, the binding energies of the same-row hydrides increase from right to left, with the exception of CH4 and SiH4, whose binding energies decline considerably; while to the same-group hydrides the ion−molecule complexes in the up row are more bound than those in the down row. The stability of the insertion product H−Zr+−RHn-1 decreases from right to left across the row and falls from up to down across the column. The reaction barrier follows the same trend; i.e., the more exothermic the insertion reaction is, the lower is the reaction barrier. All these observed trends could be understood by a combined effect of the electrostatic interaction and the covalent interaction.

Four-component relativistic calculations on the mono-ammine complexes of trivalent f 0, f 7, and f 14 ions

Mono-ammine complexes of trivalent f 0, f 7, and f 14 ions were investigated by using all-electron four-component relativistic calculations based on the Dirac–Hartree–Fock (DHF) method. Relativistic second-order Møller–Plesset perturbation (RMP2) calculations were also performed to incorporate electron correlation for the closed-shell systems. A comparison with the previous data of the aqua complexes showed that the ammine complex provides longer metal–ligand distance, larger stabilization energy, and larger amount of electron donation than the aqua complex does for a certain metal ion.

Four-component relativistic calculations on the complexes between a water molecule and trivalent lanthanoid and actinoid ions

Complexes between a water molecule and trivalent lanthanoid and actinoid ions were investigated by all-electron four-component relativistic calculations using the Dirac–Hartree–Fock (DHF) method. DHF-based relativistic second-order M øller–Plesset perturbation (RMP2) calculations were also performed to incorporate electron correlation for the closed-shell systems. Non-relativistic calculations using the HF and MP2 methods were carried out in parallel to compare with the DHF and RMP2 results. Metal–oxygen distances and stabilization energies were evaluated, and a separability between relativity and correlation was found. Mulliken population analysis and spinor projection were used to analyze the wave functions, and a nature of coordinate bond was revealed.

Ab Initio Study of Chlorosilanes: Dipole Moments and Charge Distributions

Dipole moments of chlorosilane derivatives have been investigated at SCF, MP2, CISD, and CCD levels of ab initio theories with various basis sets. Calculated dipole moments of chlorosilanes are quite dependent on the size of the basis sets, and most calculations with modest basis sets significantly overestimate the experimental values. To predict dipole moments of chlorosilanes reasonably, extremely large sizes of the basis set, for example, 6-311++G(3df,2p), are required. Incorporation of electron correlation improves calculated dipole moments somewhat, but the degree of the improvement seems to be limited without an employment of remarkably large basis sets. Our analyses by using electrostatic potentials and CHELPG charges show that the magnitudes of calculated dipole moments in chlorosilanes have a close relation with the degree of the charge separation across polar bonds, including the Si−Cl bond.

Theoretical study on the insertion reactions of Ti+(2F) with HF, HCl, H2O, H2S, NH3, PH3, CH4, and SiH4

The insertion reactions of transition metal cation doublet Zr+(2D) into HF, HCl, H2O, H2S, NH3, PH3, CH4, and SiH4 have been studied by means of ab initio molecular orbital calculations incorporating electron correlation with the Moller−Plesset perturbation theory up to the second and the fourth orders and the hybrid density functional method, B3LYP. Three regions of the potential surface have been investigated, an ion−molecule complex, followed by a three-center, four-electron transition state, and then an insertion product. It is found that all insertion reactions are exothermic and all transition states are below the energy surfaces of the reactants. For the ion−molecule complexes, the binding energies of the same-row hydrides increase from right to left, with the exception of CH4 and SiH4, whose binding energies decline considerably; while to the same-group hydrides the ion−molecule complexes in the up row are more bound than those in the down row. The stability of the insertion product H−Zr+−RHn-1 de...

Theoretical Study on the Silylidyne Insertion into NH3, H2O, HF, PH3, H2S, and HCl

The reaction paths of the silylidyne insertion into NH3, H2O, HF, PH3, H2O, HF, and HCl have been studied by means of ab initio molecular orbital calculations incorporating electron correlation with Moller−Plesset perturbation theory up to the second and fourth order and using polarization basis sets augmented by diffuse functions. All these reactions involve the initial formation of an intermediate complex followed by a hydrogen-migration process via a transition state. Analyses for the reactivity of the six substrates in the SiH insertion reactions indicate that the reaction with the hydride of the right-hand group has a less stable complex and is more exothermic than with the hydride of the left-hand group and that the reaction with the second-row hydride has a lower overall barrier and is less exothermic than with the first-row hydride. Comparison with the CH and SiH2 insertion reactions has been made, and it is noted that the CH, SiH2, and SiH insertion reactions have similar reaction processes. The energetic results (for the barriers and reaction enthalpies) indicate that the SiH radical is less reactive than the CH radical in the insertion reactions.

Theoretical study on the insertion reaction of CH(X2Π) with CH4

The CH + CH4 reaction has been studied by means of ab initio molecular orbital calculations incorporating electron correlation with Møller–Plesset perturbation theory up to second and fourth orders with the 6-31G(d,p) and 6-311++G(2d,p) basis sets. An energetically feasible insertion reaction path has been found in the potential energy surface that confirms the experimental proposal for the mechanism of the CH + CH4 reaction. The feature of the mechanism for the CH + CH4 insertion reaction is found to be different from the feature of the mechanisms for the CH + NH3, CH + H2O, and CH + HF insertion reactions, but somewhat similar to that for the CH2 + CH4 insertion reaction. Energetic results for the CH + CH4 reactions are in agreement with experiment. Keywords: CH radical, methane, reaction mechanism.

Electron momentum density distribution in iridium by Compton scattering technique

The isotropic Compton profile of iridium, measured using 59.54 keVγ-rays, is reported in this paper. The results are compared with the theoretical Compton profiles from APW method with and without incorporating electron correlation effects. It is seen that correlation effects improve the agreement between the experiment and theory. Comparison with the renormalized-free-atom (RFA) model calculations has also been made. Behaviour ofd-band electrons in Ir and some other 5d transition metals is discussed in terms of broadening in their Compton profiles.

An ab initio study on the insertion reactions of CH [X2II] with NH3, H2O, and HF

The mechanisms of the reactions of CH (X2II) with NH3, H2O, and HF have been studied by means of ab initio molecular orbital calculations incorporating electron correlation with Møller–Plesset perturbation theory up to the second order. For each of the three CH reactions, the insertion path has been found in the potential energy surface; in the calculated insertion path there exists an intermediate complex prior to the transition state that has a lower energy than the reactants. Energetic results indicate that insertion paths are favourable channels for these CH reactions, which is in line with proposals based on kinetic experiments. Key words: CH radical, ammonia, water, hydrogen fluoride, reaction mechanism.

Unimolecular rearrangement of α-silylcarbenium ions. An ab initio study

The unimolecular rearrangements of hydrogen, methyl and phenyl groups at the Si atom in α-silylcarbenium ions have been investigated using an ab initio molecular orbital method. MP2/6–31 + G ∗//HF/6–31G ∗ calculations predict that all three groups migrate from the Si to an adjacent C α with no energy barrier. Thus, the silicenium ion is the only stable species in each potential energy surface. The conformation of the benzylsilicenium ion, (C 6H 5)CH 2−SiH 2 +, indicates that the phenyl ring is significantly bent toward the silyl cationic center in order to interact with the vacant 3p(Si +) orbital. In contrast to MP2 results, Hartree-Fuck calculations (both HF/3–21G ∗ and HF/6–31G ∗ levels) predict small energy barriers for 1,2-migrations of H and Me (1.4 kcal mol −1 for H migration, and 1.5 kcal mol −1 for Me migration, respectively, at the HF/6–31G ∗ level). This difference provides convincing evidence that the incorporation of electron correlation is of particular importance in describing the potential energy surface for the rearrangement of α-silylcarbenium ions to silicenium ions. The results of the calculations have also been applied to the possible rearrangement mechanism of α-chlorosilanes to chlorosilanes, assuming that the experimental conditions are favorable toward the generation of ionic species. Various factors which may govern the migratory aptitudes of various R groups, i.e. (1) activation energies, (2) overall reaction energies and (3) the conformational preference of reactants have been investigated. The calculated activation energy obtained, namely the energy for the generation of the silicenium ion and the C −1 ion from an α-chlorosilane, is consistent with the experimental migratory aptitude in the gas phase observed in mass spectrometers.

SCRF/Monte Carlo Study of Solvent Effects on a Polar [2+2] Cycloaddition

Solvent effects on the polar [2+2] cycloaddition of 1,1-dicyanoethylene (DCNE) and methyl vinyl ether (MVE) have been studied using ab initio self-consistent reaction field (SCRF) and Monte Carlo (MC) statistical mechanics calculations. Emphasis is placed on the dependence of transition-state structure and energetics on solvation and on the impact of using different charge sets and geometries from the SCRF calculations in the MC simulations. The ab initio calculations were performed with dielectric constants e of 1.0, 2.23 (CCl4), and 35.94 (CH3CN) with the 6-31G* basis set at the Hartree−Fock (HF) level and incorporating electron correlation through MP2 and Becke3LYP density functional methods. Computed dipole moments of 10−17 D for the transition structures overlap estimates based on the solvent effects observed by Steiner and Huisgen. However, the mechanistic picture that emerges is medium dependent. In the gas phase and nonpolar solvent, the results here indicate a concerted (single barrier) process w...