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The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree–Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.

In the present study, we investigate the use of the ΔSCF method and Slater’s transition state (STS) theory to calculate the binding energies of the 2s and 2p electrons of third-period elements (P, S, and Cl). Both the Hartree–Fock (HF) and Kohn–Sham (KS) approximations are examined. The STS approximation performs well in reproducing the ΔSCF values. However, for the ΔSCF method itself, while the binding energy of the 2p electrons is accurately predicted, the results for 2s are fairly sensitive to the functional, exhibiting significant variations due to self-interaction errors (SIE). Nonetheless, the variations in chemical shifts between different species remain relatively small, and the values agree with experiments due to the cancellation of SIE. A notable observation is that the chemical shifts of the 2s and 2p electrons are similar, indicating a perturbation caused by the valence electrons. The error in the absolute binding energy of KS ΔSCF against the experiment is nearly constant for the same element in different molecules, and it depends largely on the functional owing to SIE. A shifting scheme previously developed can be employed to reproduce the experimental 2s and 2p binding energies, with dependence on the functional and atom but not on the molecule even for 2s KS ΔSCF binding energies. Upon obtaining the corrected binding energies, we find that the gap between 2s and 2p binding energy is nearly independent of chemical environment for a given element: 57.5, 63.9, and 70.9 eV for the elements P, S, and Cl, respectively.

We present an approximate approach for the calculation of ionization potential (IP) and electron affinity (EA) by exploiting the complementary energy non-linearity errors for a species M and its one-electron-ionized counterpart (M+). Reasonable IPs and EAs are thus obtained by averaging the orbital energies of M and M+, even with a low-level method such as BLYP/6-31G(d). By combining the corrected IPs and EAs, we can further obtain reasonable excitation energies. The errors in uncorrected valence IPs and uncorrected virtual-orbital energies show systematic trends. These characteristics provide a convenient and computationally efficient avenue for qualitative estimation of these properties with single corrections for multiple IPs and excitation energies.

In the present study, we have investigated the applicability of long-range-corrected (LC) functionals to a Kohn–Sham (KS) Koopmans’-type theorem. Specifically, we have examined the performance of optimally tuned LCgau-core functionals (in combination with BOP and PW86-PW91 exchange-correlation functionals) by calculating the ionization potential (IP) within the context of Koopmans’ prediction. In the LC scheme, the electron repulsion operator, 1/r12, is divided into short-range and long-range components using a standard error function, with a range separation parameter μ determining the weight of the two ranges. For each system that we have examined (H2O, CO, benzene, N2, HF, H2CO, C2H4, and five-membered ring compounds cyclo-C4H4X, with X = CH2, NH, O, and S, and pyridine), the value of μ is optimized to minimize the deviation of the negative HOMO energy from the experimental IP. Our results demonstrate the utility of optimally tuned LC functionals in predicting the IP of outer valence levels. The accuracy is comparable to that of highly accurate ab initiotheory. However, our Koopmans’ method is less accurate for the inner valence and core levels. Overall, our results support the notion that orbitals in KS-DFT, when obtained with the LC functional, provide an accurate one-electron energy spectrum. This method represents a one-electron orbital theory that is attractive in its simple formulation and effective in its practical application.

The core electron binding energies (CEBEs) and core-level excitation energies of thymine, adenine, cytosine, and uracil are studied by the Kohn–Sham (KS) method with long-range corrected (LC) functionals. The CEBEs are estimated according to the Koopmans-type theorem for density functional theory. The excitation energies from the core to the valence π* and Rydberg states are calculated as the orbital energy differences between core-level orbitals of a neutral parent/cation and unoccupied π* or Rydberg orbitals of its cation. The model is intuitive, and the spectra can easily be assigned. Core excitation energies from oxygen 1s, nitrogen 1s, and carbon 1s to π* and Rydberg states, and the chemical shifts, agree well with previously reported theoretical and experimental data. The straightforward use of KS orbitals in this scheme carries the advantage that it can be applied efficiently to large systems such as biomolecules and nanomaterials.

Previously proposed theoretical schemes for estimating one-electron excitation energies using Kohn–Sham (KS) solutions with long-range corrected (LC) functionals are applied to the charge-transfer (CT) excitations of the ethylene···tetrafluoroethylene (C2H4-C2F4) system, and the CT complex between an aromatic donor (Ar = benzene, toluene, o-xylene, naphthalene, anthracene, and various meso-substituted anthracenes) and the tetracyanoethylene (TCNE) acceptor. The CT excited state is described well as a single-electron excitation between specific orbitals of donor and acceptor. Thus, CT excitation energies are well approximated by the orbital energies because of the satisfaction of the Koopmans-type theorem and the asymptotic behavior of the LC functional. We have examined three computational schemes: scheme 1 employs the orbital energies for the neutral and cationic systems, scheme 2 utilizes orbital energies of just the cation, and in scheme 3, because the electron affinity of a molecule is the ionization energy of its anion, a scale factor is applied to enforce this identity. The present schemes reproduce the correct asymptotic behavior of CT excitation energy of C2H4···C2F4for the long intermolecular distances and give good agreement with accurate ab initioresults. Calculated CT excitation energies for Ar-TCNE are compared with those of TD-DFT and ΔSCF methods. Scheme 1 with the optimal range-separation parameter μ accurately reproduces CT excitation energies for all Ar-TCNE systems and gives good agreement with the best TD-DFT calculations and experiment. Scheme 1, scheme 3, and TD-DFT show similar tendencies with respect to the variation in μ. Scheme 2 and ΔSCF approaches are rather insensitive to changes in μ, but both considerably underestimate the CT excitation energies for these systems. KS orbital energies are physically meaningful and they are practically useful; if the range-separation parameter is tuned, then good results can be obtained.

In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree–Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.

We have previously reported that, whereas conventional density functional theory (DFT) functionals have provided poor calculations on the alkane isodesmic reaction energy and isomerization reaction energy of organic molecules that include C, N, and O atoms, our developed long-range corrected (LC)- and LC including Gaussian attenuation (LCgau)-DFT + local response dispersion (LRD) functionals, which can accurately calculate inter- and intramolecular weak interactions, give accurate isomerization energies on these reactions. In this work, we found that B3LYP-D3, LC-ωPBE-D3, and ωB97XD, known for their good descriptions of weak interaction calculations, fail to reproduce the isomerization reaction energies of the molecules that include the S atom, such as methyl-thiourea, ethyl-thiourea, and propyl-thiourea. In contrast, LC- and LCgau-BOP+LRD functionals provide isomerization reaction energies that are very close to those produced by highly accurate wave function methods. These results show that an accurate description of the intramolecular weak interaction between the alkyl group and the S atom, unlike in the case of urea, is significant to reproduce the correct energy of the molecules with an alkyl group and S atom.

Fullerenes are sheets of sp2carbon atoms wrapped around to form spheres. With this simple consideration, we have in the present study devised and (with over 3600 DFT data points) successfully validated a simple model, termed R+D, for estimating the relative energies of fullerenes. This model contains a resonance component to account for the intrinsic differences between the π-energies of different fullerenes, and a deformation component for treating the distortions from planarity. Notably, we find that both terms (and they alone) are required to obtain good relative energies, which lends support to the formulation of the R+D model. An interesting finding is that for some medium-sized IPR fullerenes, their isomers show similar variations in the two components. We deduce that these fullerenes may represent a good opportunity for tuning molecular properties for practical applications. We hope that the promising results of the present study will encourage further investigations into fullerenes from a fundamental perspective.

The photoinduced phase transition (PIPT) mechanism of tetrathiafulvalene-p-chloranil (TTF-CA) molecular crystal was theoretically investigated using the long-range corrected time-dependent density functional theory (LC-TDDFT) combined with a local response dispersion (LRD) method, which enables us to quantitatively reproduce charge transfer (CT) excitations of van der Waals clusters. By calculating the excitation spectrum and potential energy surface, we found that the PIPT of TTF-CA crystal may proceed through the angle change of the molecular planes. We also found that the CT excitation of one TTF-CA pair helps other neighboring TTF-CA pairs to become excited. Consequently, we theoretically proposed the initial structural change in the neutral-to-ionic PIPT of TTF-CA crystal, which is consistent with experiments.

Reproducibilities of d–π bonds were investigated on calculating complexes of first-row transition-metal cation (M+) and benzene (Bz). Calculations were carried out for half-sandwich MBz+and sandwich MBz2+complexes with several types of density functional theories (DFTs) and single-configurational wave function theories (WFTs). As a result, it was concluded that electron correlations are required to give the binding energies of d–π bonds even qualitatively, and DFTs would reproduce d–π bonds with quantitative accuracies only if electron correlations and long-range exchange interactions were both taken into consideration in exchange-correlation functionals used. In MBz+calculations, WFTs fairly underestimated the binding energies for early transition metals (M = Sc–Cr) because of multiconfigurational effects. In contrast, DFTs overestimated them for late transition metals (M = Fe–Cu) due to insufficient long-range interactions in exchange functionals. For MBz2+, DFTs and WFTs gave similar binding energies for MBz2+, although WFTs slightly overestimated them for late transition metals. Furthermore, it was suggested that the experimental binding energies of CrBz2+and MnBz2+are probably misestimated.

In order to investigate static quantum isotope effects on the stability of proton-transferred structures, we defined an effective quantal potential energy hypersurface (EQPES), which includes mass-dependent quantum effects. We demonstrated the difference between the ordinary potential energy surface and EQPES of the double well potential as a simple example. The minimum energy path on EQPES describes the zero-point energy-corrected structures and tunneling motion, which is characterized as a classically forbidden motion. We also performed the EQPES analysis of model proton-transfer reactions in DNA base pairs. It was found that the double proton-transferred structure of an adenine–thymine (AT) pair is quantum mechanically unstable and that of a guanine–cytosine (GC) pair is stable within a least uncertainty regime. In order to investigate dynamic quantum isotope effects on the stability of the proton-transferred structures, we performed quantal cumulant dynamics (QCD) simulations of the GC pair. Results show that the proton-transferred structure of the protonated isotopomer is dynamically unstable though the EQPES analysis predicts its stability. It is relevant to include dynamic effects in the investigation of the quantum isotope effects on geometric stability of systems with a small energy gap between global and metastable structures.

Enhancement of the Raman scattering and IR absorption activities due to the electron-attachment was investigated for water systems by DFT calculations. DFT calculation of a 6-ring water cluster system that included the diffusive nature of electrons well reproduced the Raman enhancement effects and Raman shifts of the OH stretching modes observed in experiments. Based on the same model and calculations, enhancement of the IR absorption activity was also studied and was found to also be improved. Furthermore, the same calculation revealed that the enhancement can be also expected not only in the OH stretching but also in the lower wavenumber region. The enhancement factors for the various vibrational modes of the OH groups range from 102- 105thanks to the electron addition. Based on the coincidence between the theoretical model and the experimental results for the Raman signals and theoretical prediction for IR absorption, new enhancement techniques based on an electron-attachment in both Raman scattering and IR absorption, denoted as “electron-enhanced vibrational spectroscopy (EEVS)”, is proposed, where molecular polarizability itself is modulated by the strong electrostatic field induced by neighboring electrons.

The recovery of the basic qualitative concepts of the chemical language into the quantum treatment is a rather challenging problem because the desirable simplicity is easily lost in the black box of technical mechanisms of computation, e.g.among the ingredients of post-orbital methods of correlation effects. We present here several clues for bringing the hybridization and aromaticity concepts in a nontrivial and non-redundant conjunction with both quantum chemical quantities and the chemists’ tools of intuition. A rather inedited structural correlation that works as an experimental proof of the hybridization is discussed. The main idea is to exploit the intermediate symmetries, where the hybridization is no longer tautological because of the symmetry. For instance in a MA2B2tetrahedron, if the hybridization not existed as real engine of the stereochemistry, the AMA and BMB angles should be arbitrarily independent. In turn, if the hybridization acts, there is a certain trigonometric relationship between the two angles. The existence of this correlation is noticed and discussed in prototypic series. A new understanding and analysis of strain in cycles and clusters (with particular emphasis on organometallic structures) is constructed as continuation of discussed models. The problem of aromaticity in chelates, rings and clusters is approached by means of specific models. The careful attention devoted to the structural details rewards the theory with an extended understanding of various bonding regimes and at the same time enriches the experimentalists’ perspectives beyond the geometric description and taxonomic systematization of X-ray molecular structure and crystal packing data.The recovery of the basic qualitative concepts of the chemical language into the quantum treatment is a rather challenging problem because the desirable simplicity is easily lost in the black box of technical mechanisms of computation, e.g.among the ingredients of post-orbital methods of correlation effects. We present here several clues for bringing the hybridization and aromaticity concepts in a nontrivial and non-redundant conjunction with both quantum chemical quantities and the chemists’ tools of intuition. A rather inedited structural correlation that works as an experimental proof of the hybridization is discussed. The main idea is to exploit the intermediate symmetries, where the hybridization is no longer tautological because of the symmetry. For instance in a MA2B2tetrahedron, if the hybridization not existed as real engine of the stereochemistry, the AMA and BMB angles should be arbitrarily independent. In turn, if the hybridization acts, there is a certain trigonometric relationship between the two angles. The existence of this correlation is noticed and discussed in prototypic series. A new understanding and analysis of strain in cycles and clusters (with particular emphasis on organometallic structures) is constructed as continuation of discussed models. The problem of aromaticity in chelates, rings and clusters is approached by means of specific models. The careful attention devoted to the structural details rewards the theory with an extended understanding of various bonding regimes and at the same time enriches the experimentalists’ perspectives beyond the geometric description and taxonomic systematization of X-ray molecular structure and crystal packing data.

Today it is common knowledge that relativistic effects are important in the heavy-element chemistry. The continuing development of the relativistic molecular theory is opening up rows of the periodic table that are impossible to treat with the non-relativistic approach. The most straightforward way to treat relativistic effects on heavy-element systems is to use the four-component Dirac-Hartree-Fockapproach and its electron-correlation methods based on the Dirac-Coulomb(-Breit)Hamiltonian. The Dirac-Hartree-Fock(DHF) or Dirac-Kohn-Sham(DKS) equation with the four-component spinors composed of the large- and small-components demands severe computational efforts to solve, and its applications to molecules including heavy elements have been limited to small- to medium-size systems. Recently, we have developed a very efficient algorithm for the four-component DHFand DKSapproaches. As an alternative approach, several quasi-relativistic approximations have also been proposed instead of explicitly solving the four-component relativistic equation. We have developed the relativistic elimination of small components (RESC) and higher-order Douglas-Kroll(DK) Hamiltonians within the framework of the two-component quasi-relativistic approach. The developing four-component relativistic and approximate quasi-relativistic methods have been implemented into a program suite named REL4D.Today it is common knowledge that relativistic effects are important in the heavy-element chemistry. The continuing development of the relativistic molecular theory is opening up rows of the periodic table that are impossible to treat with the non-relativistic approach. The most straightforward way to treat relativistic effects on heavy-element systems is to use the four-component Dirac-Hartree-Fockapproach and its electron-correlation methods based on the Dirac-Coulomb(-Breit)Hamiltonian. The Dirac-Hartree-Fock(DHF) or Dirac-Kohn-Sham(DKS) equation with the four-component spinors composed of the large- and small-components demands severe computational efforts to solve, and its applications to molecules including heavy elements have been limited to small- to medium-size systems. Recently, we have developed a very efficient algorithm for the four-component DHFand DKSapproaches. As an alternative approach, several quasi-relativistic approximations have also been proposed instead of explicitly solving the four-component relativistic equation. We have developed the relativistic elimination of small components (RESC) and higher-order Douglas-Kroll(DK) Hamiltonians within the framework of the two-component quasi-relativistic approach. The developing four-component relativistic and approximate quasi-relativistic methods have been implemented into a program suite named REL4D.

We propose a new simple scheme for self‐interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self‐interactions for exchange functionals in regions of self‐interaction. To classify the regions of self‐interaction, we take advantage of the property of the total kinetic energy density approaching the Weizsäcker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional “pure” functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1592–1598, 2003

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizsäcker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional “pure” functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1592–1598, 2003

The second‐order multireference perturbation theory using an optimized partitioning, denoted as MROPT(2), is applied to calculations of various molecular properties—excitation energies, spectroscopic parameters, and potential energy curves—for five molecules: ethylene, butadiene, benzene, N2, and O2. The calculated results are compared with those obtained with second‐ and third‐order multireference perturbation theory using the traditional partitioning techniques. We also give results from computations using the multireference configuration interaction (MRCI) method. The presented results show very close resemblance between the new method and MRCI with renormalized Davidson correction. The accuracy of the new method is good and is comparable to that of second‐order multireference perturbation theory using Møller‐Plesset partitioning. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1390–1400, 2003

The quasi‐degenerate perturbation theory (QDPT) with complete active space (CAS) self‐consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum‐over‐states approaches is presented. The second‐order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix‐based sum‐over‐states approach. The method is tested on the calculations of excitation energies of H2O, potential energy curves of LiF, and valence excitation energies of H2CO. The results show that the present method yields very close results to the corresponding CAS‐SCF reference QDPT results and the available experimental values. The deviations from CAS‐SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H2O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H2CO, the maximum deviation from available experimental values is 0.28 eV. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1166–1175, 2002

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H2O, potential energy curves of LiF, and valence excitation energies of H2CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H2O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H2CO, the maximum deviation from available experimental values is 0.28 eV. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1166–1175, 2002

A new perturbation approach is proposed that enhances the low‐order, perturbative convergence by modifying the zeroth‐order Hamiltonian in a manner that enlarges any small‐energy denominators that may otherwise appear in the perturbative expansion. This intruder state avoidance (ISA) method can be used in conjunction with any perturbative approach, but is most applicable to cases where small energy denominators arise from orthogonal‐space states—so‐called intruder states—that should, under normal circumstances, make a negligible contribution to the target state of interests. This ISA method is used with multireference Møller–Plesset (MRMP) perturbation theory on potential energy curves that are otherwise plagued by singularities when treated with (conventional) MRMP; calculation are performed on the 13Σ−ustate of O2; and the 21Δ, 31Δ, 23Δ, and 33Δ states of AgH. This approach is also applied to other calculations where MRMP is influenced by intruder states; calculations are performed on the 3Πustate of N2, the 3Π state of CO, and the 21A′state of formamide. A number of calculations are also performed to illustrate that this approach has little or no effect on MRMP when intruder states are not present in perturbative calculations; vertical excitation energies are computed for the low‐lying states of N2, C2, CO, formamide, and benzene; the adiabatic 1A1–3B1energy separation in CH2, and the spectroscopic parameters of O2are also calculated. Vertical excitation energies are also performed on the Q and B bands states of free‐base, chlorin, and zinc–chlorin porphyrin, where somewhat larger couplings exists, and—as anticipated—a larger deviation is found between MRMP and ISA‐MRMP. © 2002 Wiley Periodicals, Inc. J Comput Chem 10: 957–965, 2002

The theoretical and technical foundations are presented for the efficient relativistic electronic structure theories to treat heavy‐atomic molecular systems. This review contains two surveys of four‐component and two‐component quasi‐relativistic approaches. First, we review our highly efficient computational scheme for four‐component relativistic ab initiomolecular orbital (MO) methods over generally contracted spherical harmonic Gaussian‐type spinors (GTSs). Illustrative calculations, which are performed with a new four‐component relativistic ab initiomolecular orbital program package REL4D, clearly show the efficiency of our computational scheme by the Dirac–Hartree–Fock (DHF) and Dirac–Hartree–Fock (DKS) methods. Next, in the two‐component quasi‐relativistic framework, two relativistic Hamiltonians, RESC and higher order Douglas–Kroll (DK) Hamiltonians, are introduced, and several illustrative calculations are shown. Numerical results for several systems show that good accuracy can be obtained with our third‐order DK (DK3) Hamiltonian. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 847–860, 2002

We explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–dinterconfigurational energies (ICEs) and the outermost sand dionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–dICEs and the sand dIPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost sand dorbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001

The hydration reaction of ethylene, C2H4+H2O → C2H5OH, catalyzed by oxoacids (H3PO4, H2SO4, and HClO4) and metal cations (B3+, Al3+, Sc3+, Ga3+, La3+, Be2+, Mg2+, Ca2+, Zn2+, and Sr2+) are studied systematically by density functional theory with a BLYP functional. The reaction profiles of the main reaction and some side reactions, such as ester formation, dimerization of ethylene, and dehydrogenation of ethanol, have been determined with a variety of catalysts. In each case, the intermediate states, the transition states, and their energetics are calculated. Metal cations react more efficiently for the main reaction than oxoacids, but they also make the dehydrogenation reaction active. While the dimerization reaction is strongly affected by the acidity of the catalyst, both the acidity and basicity of the catalyst are important for the dehydrogenation reaction. Efficient formation of ethanol from ethylene over a catalyst is suggested. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1292–1304, 2000

An algorithm for computing electron repulsion integrals (ERIs) oriented to the general contraction scheme is presented. The accompanying coordinate expansion (ACE) method of Ishida is utilized to derive an efficient algorithm. The performance estimated with the floating-point operation (FLOP) count is about N² times and more as efficient as the conventional algorithm for the segmented contraction scheme, where N indicates the number of contracted Gaussian-type orbitals (GTOs) contained in a set of generally contracted GTOs. The efficiency is also confirmed by using a realistic molecular system, the benzene molecule, with C:14s9p/3s2p, H:8s4p/2s1p, and C:14s9p/6s5p, H:8s4p/4s3p basis sets. The measured central processing unit (CPU) time is in good agreement with the FLOP count estimation. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 396–406, 2000

The effects of relativity on the bond lengths, vibrational frequencies, dissociation energies, and dipole moments of the ground states of the group IB hydrides MH, chlorides MCl, and dimers M2 (M=Cu, Ag, and Au) have been studied by relativistic density functional theory (DFT) with the B88 plus one-parameter progressive (BOP) exchange–correlation functional. The relativistic effects were included through a scalar relativistic scheme by the elimination of the small components (RESC) of the four-component Dirac spinors. Comparisons were made between all-electron results using the nonrelativistic Hamiltonian, results with quasi-relativistic effective core potentials (ECP), and results with a spin-free RESC scheme. The RESC approach clearly works very well. The bond distances, vibrational frequencies, and dissociation energies show a good agreement with the experiment. The expected trends of bond length decrease, harmonic vibrational frequency increase, and dipole moment decrease with relativity are found. Although the dissociation energy increases with the relativity for hydrides and dimers, the reverse trend is observed for chlorides. A quasi-relativistic ECP also works well for hydrides. However, ECP gives rather poor description for chlorides and dimers. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 757–766, 1999

The catalysis of Cu-exchanged zeolite for the direct decomposition of nitric oxide was investigated by hybrid density functional theory (B3LYP) using a molecular model of the active site. For reactions of two NO molecules over a Cu ion bound to the zeolite model (ZCu), the structures and energies of adsorption complexes and transition states were examined and compared with those of the corresponding reactions over an isolated Cu+ and Cu atom and also reactions of free NO. The ZCu shows an enhanced catalytic activity compared with the isolated Cu+. The ZCu and adsorbed molecules interact strongly in the transition state structures through π(d–p) bonding. Theory also suggests that the Cu atom has the potential to be a highly active catalyst for the NO decomposition reaction.

Abstract.: The valence π → π * excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π * excited states of anthracene and naphthacene. The present theory predicts the valence π → π * excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes.

The simple energy relation between the RHF and UHF methods are obtained by expanding these orbital sets by the closed-shell orbital with the same geometry of the open-shell systems. The results are also applied to higher spin states.

The geometries and the energies of the reactants, transition state, and products for the gas phase reaction: Cl− + CH3Br = ClCH3 + Br−, were obtained from abinitiocalculations using a closed shell SCF method with a MINI basis set developed by Huzinaga etal. The energy changes predicted by the calculations are found in good agreement with the experimental data. The energies and geometries of the reactants and the transition state for the gas phase reactions: Cl− + RBr = ClR + Br−, where R = C2H5and iso-C3H7, were also obtained. The resulting activation energies follow the same trend as the experimental data: Me < Et < iso-Pr; however, the predicted increase of activation energy is considerably larger. The energies and geometries for the reactants, transition state, and products of the gas phase ion-dihydrate reaction: Cl−(H2O)2 + CH3Br → H2O(ClCH3Br)−H2O → Br−(H2O)2 + CH3Cl were obtained as well. These data provide an interesting comparison with experimental results in aqueous solution. The reaction coordinate of the ion-dihydrate reaction is very much closer to that for aqueous solution than to that for the gas phase. Keywords: nucleophilic substitution reactions, ion–molecule reactions, activation energy.

Abstract.: Using optimal exponents for B through Ne given by Dunning and those for Al through Ar by Woon and Dunning, d-type contracted polarization functions (2d/1d), (3d/1d), and (3d/2d) are generated from natural orbitals of atomic single and double excitation configuration interaction (SDCI) calculations, where the numbers before and after the slash are those of the primitive and contracted Gaussian type functions. The resulting contracted functions are tested on N2 and P2 molecules by self-consistent field and SDCI calculations, which clarify characteristics of the present polarization functions.

An abinitioMO calculation is made on the H3S+(H2S)ncluster (n = 0–5). For n = 1, full thermodynamic data are reproduced theoretically, and for n = 1, 2, and 3 the effect of dfunctions on the structure and energies is investigated. On the basis of the present results, the accuracy of two conflicting experimental data is examined.

The optimized configurations of Be18(D3d) and Be20(D3h) clusters which are considered as the smallest subunits of Be crystal are calculated by the ab initio STO-3G SCF energy gradient method. The characteristics of these optimized geometries are discussed. The impurity effect caused by a He atom in the center of these clusters is also discussed.

Multireference perturbation theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the valence π→π* excited states of 1,3-butadiene, 1,3,5-hexatriene, 1,3,5,7-octatetraene, and 1,3,5,7,9-decapentaene. Our focus was put on determining the nature of the two lowest-lying singlet excited states, 1¹Bu⁺ and 2¹Ag⁻, and their ordering. The 1¹Bu⁺ state is a singly excited state with an ionic nature originating from the HOMO→LUMO one-electron transition while the covalent 2¹Ag⁻ state is the doubly excited state which comes mainly from the (HOMO)²→(LUMO)² transition. The active-space and basis-set effects are taken into account to estimate the excitation energies of larger polyenes. For butadiene, the 1¹Bu⁺ state is calculated to be slightly lower by 0.1 eV than the doubly excited 2¹Ag⁻ state at the ground-state equilibrium geometry. For hexatriene, our calculations predict the two states to be virtually degenerate. Octatetraene is the first polyene for which we predict that the 2¹Ag⁻ state is the lowest excited singlet state at the ground-state geometry. The present theory also indicates that the 2¹Ag⁻ state lies clearly below the 1¹Bu⁺ state in decapentaene with the energy gap of 0.4 eV. The 0–0 transition and the emission energies are also calculated using the planar C2h relaxed excited-state geometries. The covalent 2¹Ag⁻ state is much more sensitive to the geometry variation than is the ionic 1¹Bu⁺ state, which places the 2¹Ag⁻ state significantly below the 1¹Bu⁺ state at the relaxed geometry. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 157–175, 1998

The orbital ambiguity in the Hartree-Fock theory is removed in such a way as to improve the convergence property of the configuration interaction calculation. A practical proposal is made to obtain efficient orbitals for use in construction of wavefunctions. These orbitals are called the zeroth-order natural orbitals and their partner orbitals. It is also demonstrated by an illustrative calculation that use of partner orbitals rather than SCF orbitals gives much more rapid convergence and greater physical insight.

Localized MO calculations have been carried out by the “energy localization” method of Edmiston and Ruedenberg, based upon the INDO MO’s, for 3-, 4-, and 5-membered cycloalkanes and their heterocycles containing one oxygen or nitrogen atom. Furthermore, LMO calculations were performed for the protonated three-membered heterocyclic compounds. The s-nature of the LMO’s is discussed and correlated with the bond angle, the bond moment, the bond energy, and the bond polarity. Some LMO density maps are shown.

The stability and vibrational frequencies of protonated ethane, C2H7+, have been studied by ab initiomolecular orbital theory. The IR spectra for C2H7+recorded by Y. T. Lee’s group were interpreted from a theoretical point of view. Ab initiocomputations predict the existence of two isomers, a bridged structure, and a tight and loose open form. The loose open form is represented as an H2molecule attached loosely to a classical open C2H5+ion. The different behavior observed in the IR spectra can be attributed to the changing ratio of the bridged C2H7+to the open C2H5+isomers. The final interpretation of these data is that the spectrum at 150 Torr (1 Torr = 133.322 Pa) arises from the bridged structure which is the most stable form of C2H7+. The additional band in the spectrum observed at 60 Torr originates form the weakly bound complex which dissociates upon absorbing a single IR photon.

An equation has been derived for a correlated electronic wave function satisfying the two-particle correlation cusp condition. Molecular integrals of spatial operators in the equation have been formulated based on the recursive formulations of general molecular integrals given by Honda, Sato, and Obara. An efficient scheme of computing them is proposed by taking advantage of the recursive and translational relations of the integrals.

We tried to explain the electrophilicity of radical reagents such as H and OH radicals in the aromatic substitution reaction by using the molecular orbital theory. The delocalization energy of π electrons was decomposed into two parts: one is the energy due to the delocalization from a substrate to a reagent and another is that from a reagent to a substrate. The former was considered to be a measure of the electrophilicity and the latter of the nucleophilicity. The decomposition of the delocalization energy into two parts was carried out by modifying the relevant core resonance integrals as appropriate. The result indicated that the delocalization energy for the electrophilicity was much larger than that for the nucleophilicity for both radicals. Thus, H and OH radicals should be electrophilic in nature, in good agreement with the experimental facts. Finally, the origin of the electrophilicity was discussed in connection with the height of the relevant energy levels by following a perturbational approach.

The CNDO/2 and INDO calculations were performed on three azines: pyridazine, pyrimidine, and pyrazine. In order to check the validity of the lone-pair orbital energies, the calculated orbital energies were compared with those obtained by ab initiocalculations. These molecules have two lone-pairs, which can be transformed into symmetric and antisymmetric combinations. In pyridazine and pyrimidine, the symmetric one is lower than the antisymmetric one in energy, while in pyrazine the reverse is true. These results were subjected to an analysis from the standpoint of the through-bond interaction. That is, we transformed the canonical molecular orbitals obtained by the CNDO/2 method into localized molecular orbitals. By the use of the localized molecular orbitals thus obtained, the variation in the lone-pair orbital energies of these molecules was estimated in terms of the through-bond (and/or the through space) interaction according to a method which selectively considered the particular interaction between the specified localized molecular orbitals in a molecule. As a result of this analysis, it was found that the relative order of the lone-pair orbital energies was determined by the different types of interactions from molecule to molecule, and the energy variation in the lone-pair orbitals was elucidated in terms of the specified through-bond and through-space interactions.

By using the closed-shell SCF MO method with the zero-differential overlap approximation for all valence electron systems previously presented by us, the electronic structures of trans- and cis- substituted ethylenes (treated substituent=CH3, Cl, Br, and I) are studied. The calculated values of the p and valence electron charges, and the total energies of these isomers are presented. The natures of the higher occupied MO’s, especially the lonepair MO’s, of chlorinated ethylenes are discussed in connection with the photoelectron observation. The calculated lowest p–p*singlet transition energies accord well with the observed values. As to the rotational energy changes, the calculated results show that, at the perpendicular configurations, the triplet states for all the treated compounds are lowest, while the intermediate states for the cis-transisomerizations of these compounds may be common to both the isomers.

We theoretically evaluated the stability, UV-Vis spectra and possibility of stacking of [S-M(II)-S] (M=Ni, Pd, Pt, S: hydroxypyridonethione) by means of the density functional theory (DFT). From the view of the free energy, we assessed formation energy of possible combinations of chalcogen atoms and metal cations. The results confirmed that [H-Ni(II)-H] and [S-Cu(II)-S] would form stable metal-base pairing, on the other hand [H-Pt(II)-H] would not, which have been experimentally proven. Moreover, by use of time-dependent density functional theory (TDDFT), we observed d-* transition accompanied with -* transition in [S-M(II)-S]. These results reveal that metal-to-ligand charge transfer (MLCT) shifts the peak of -* transition in [S-2H+-S] (without metal cations).

We investigated the proton-transfer reactions in guanine-cytosine (GC) pairs with density functional theories. In the GC pair bound to cis-platin, the barrier height of proton-transfer reaction dramatically decreases in comparison with the GC pair without the cis-platin. This is because (a) successive processes of charge transfer from G to cisplatin thereby stabilizing both the GC and G*C pairs and (b) an additional hydrogen bond between G and the ligand of Pt atom. In two GC pairs bound to the cis-platin, the single protontransfer reaction occurs in one of the two GC pairs. No simultaneous single proton-transfer reaction can occur in both base pairs. From the geometry optimization, two different single proton-transferred structures (cis-(CG*)d-Pt-(GC)p and cis-(CG)d-Pt-(G*C)p, where * means a proton donor of G) are as stable as the original structures (CG)d-Pt-(GC)p.

The relativistic effects for static polarizabilities α and hyperpolarizabilities γ of rare gas atoms (Ne through Rn) are investigated theoretically with the third-order Douglas–Kroll method. The results yield interesting trends of relativity in going from Ne to Rn: The relativistic effect decreases α values of Ne and Ar and increases the values of Kr, Xe, and Rn, and it decreases γ values of Rn slightly and increases the values of other rare gas atoms, while the electron correlation effect increases α and γ of all rare gas atoms.

An abinitioMO calculation is made for the H+(acetone)nand H+(DMSO)ngas-phase clusters. In the "shells" of n = 2, the cationic nature for the attack of the third solvent molecule is dispersed to the methyl hydrogens and the S atom (in DMSO) as well as to the proton. This leads to the small difference of stability for several geometries of n = 3. A noticeable disagreement between experimental and calculated energies for n = 1 → 2 in H+(DMSO)nis discussed.

The directly-bonded nuclear spin-spin coupling constants were calculated by a perturbation method involving the summing over singly-excited states using localized orbitals. It is shown that a localized representation of orbitals in the perturbation expansion can be of considerable value both for interpretative purposes and for assessing the rate at which the pertubation expansion converges.