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We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzc exp(−αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry. Actually, the rG functions drastically improve the wave function near the cusp region. This was shown by the applications of the present theory to the hydrogen and helium atoms. When we use the FC-sij theory, in which the inter-electron function rij is replaced with its square s i j = r i j 2 that is integrable, we need only one- and two-electron integrals for the G and rG functions. The one-center one- and two-electron integrals of the rG functions are always available in a closed form. To calculate the integrals of the multi-centered rG functions, we proposed the rG-NG expansion method, in which an rG function is expanded by a linear combination of the G functions. The optimal exponents and coefficients of this expansion were given for N = 2, 3, 4, 5, 6, and 9. To show the accuracy and the usefulness of the rG-NG method, we applied the FC-sij theory to the hydrogen molecule. [ABSTRACT FROM AUTHOR]

The free-complement (FC) theory proposed for solving the Schrödinger equation of atoms and molecules highly accurately was applied to the calculations of the potential curves of the lower nine states of the Li2 molecule. The results were compared with the accurate experimental Rydberg–Klein–Rees potential curves available. They overlap completely with each other without any shift everywhere for all the states of Li2. At all the calculated points on the seven potential curves ranging between −14.83 and −15.00 hartree, the average difference was only 0.0583 kcal/mol and the maximum difference was only +0.165 kcal/mol. For the vertical excitation energies from the ground state curve to the seven excited states, the differences between theory and experiment were 0.000 645 eV in average and their maximum difference was −0.007 20 eV. The potential properties calculated with the FC theory also agreed well with the experimental values. These results show a high potentiality of the FC theory as a highly predictive quantum chemistry theory. For comparison, as an example of the Hartree–Fock based theory popular in modern quantum chemistry, we adopted the symmetry-adapted-cluster (SAC)-configuration-interaction (CI) theory using a highly flexible basis set. While the FC theory gave the absolute agreements with experiments, the SAC-CI potential curves compare reasonably well with experiments only after shifting-down of the SAC-CI curves by 5.727 kcal/mol. The differences in the excitation energies between SAC-CI and experiments were 0.004 28 eV on average, and the maximum difference was +0.109 67 eV. The SAC-CI results reported in 1985 were less accurate but still reasonable. [ABSTRACT FROM AUTHOR]

The scaling function g of the scaled Schrödinger equation (SSE) is generalized to obtain accurate solutions of the Schrödinger equation (SE) with the free complement (FC) theory. The electron–nuclear and electron–electron scaling functions, giA and gij, respectively, are generalized. From the relations between SE and SSE at the inter-particle distances being zero and infinity, the scaling function must satisfy the collisional (or coalescent) condition and the asymptotic condition, respectively. Based on these conditions, general scaling functions are classified into "correct" (satisfying both conditions), "reasonable" (satisfying only collisional condition), and "approximate but still useful" (not satisfying collisional condition) classes. Several analytical scaling functions are listed for each class. Popular functions riA and rij belong to the reasonable class. The qualities of many electron–electron scaling functions are examined variationally for the helium atom using the FC theory. Although the complement functions of FC theory are produced generally from both the potential and kinetic operators in the Hamiltonian, those produced from the kinetic operator were shown to be less important than those produced from the potential operator. Hence, we used only the complement functions produced from the potential operator and showed that the correct-class gij functions gave most accurate results and the reasonable-class functions were less accurate. Among the examined correct and reasonable functions, the conventional function rij was worst in accuracy, although it was still very accurate. Thus, we have many potentially accurate "correct" scaling functions for use in FC theory to solve the SEs of atoms and molecules. [ABSTRACT FROM AUTHOR]

The chemical formula theory (CFT) proposed in Paper I of this series [H. Nakatsuji et al., J. Chem. Phys. 149, 114105 (2018)] is a simple variational electronic structure theory for atoms and molecules. The CFT constructs simple, conceptually useful wave functions for the ground and excited states, simultaneously, from the ground and excited states of the constituent atoms, reflecting the spirits of the chemical formulas. The CFT wave functions are also designed to be used as the initial wave functions of the free complement (FC) theory, that is, the exact theory producing the exact wave functions of the Schrödinger accuracy. This combined theory is referred to as the FC-CFT. We aim to construct an exact wave function theory that is useful not only quantitatively but also conceptually. This paper shows the atomic applications of the CFT and the FC-CFT. For simplicity, we choose the small atoms, Be and Li, and perform variational calculations to essentially exact levels. For these elements, a simple Hylleraas CI type formulation is known to be potentially highly accurate: we realize it with the CFT and the FC-CFT. Even from the CFT levels, the excitation energies to the Rydberg excited states were calculated satisfactorily. Then, with increasing the order of the FC theory in the FC-CFT, all the absolute energies and the excitation energies of the Be and Li atoms were improved uniformly and reached rapidly to the essentially exact levels in order 3 or 4 with moderately small calculational labors. [ABSTRACT FROM AUTHOR]

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states of the hydrogen molecule (H2) with the 1Σg+, 1Σu+, 3Σg+, 3Σu+, 1Πg, 1Πu, 3Πg, 3Πu, 1Δg, 1Δu, 3Δg, 3Δu, 1Φg, 1Φu, 3Φg, and 3Φu symmetries (in total, 54 states). The initial functions of the FC theory were formulated based on the atomic states of the hydrogen atom and its positive and negative ions at the dissociation limits. The local Schrödinger equation (LSE) method, which is a simple sampling-type integral-free methodology, was employed instead of the ordinary variational method and highly accurate results were obtained stably and smoothly along the potential energy curves. Thus, with the FC-LSE method, we succeeded to perform the comprehensive studies of the H2 molecule from the ground to excited states belonging up to higher angular momentum symmetries and from equilibriums to dissociation limits with almost satisfying spectroscopic accuracy, i.e., 10−6 hartree order around 1 cm−1, as absolute solutions of the SE by moderately small calculations. [ABSTRACT FROM AUTHOR]

The free-complement chemical-formula theory (FC-CFT) for solving the Schrödinger equation (SE) was applied to the first-row atoms and several small molecules, limiting only to the ground state of a spin symmetry. Highly accurate results, satisfying chemical accuracy (kcal/mol accuracy for the absolute total energy), were obtained for all the cases. The local Schrö dinger equation (LSE) method was applied for obtaining the solutions accurately and stably. For adapting the sampling method to quantum mechanical calculations, we developed a combined method of local sampling and Metropolis sampling. We also reported the method that leads the calculations to the accurate energies and wave functions as definite converged results with minimum ambiguities. We have also examined the possibility of the stationarity principle in the sampling method: it certainly works, though more extensive applications are necessary. From the high accuracy and the constant stability of the results, the present methodology seems to provide a useful tool for solving the SE of atoms and molecules. [ABSTRACT FROM AUTHOR]

Chemistry is governed by the principle of quantum mechanics as expressed by the Schrödinger equation (SE) and Dirac equation (DE). The exact general theory for solving these fundamental equations is therefore a key for formulating accurately predictive theory in chemical science. The free-complement (FC) theory for solving the SE of atoms and molecules proposed by one of the authors is such a general theory. On the other hand, the working theory most widely used in chemistry is the chemical formula that refers to the molecular structural formula and chemical reaction formula, collectively. There, the central concepts are the local atomic concept, transferability, and from-atoms- to-molecule concept. Since the chemical formula is the most successful working theory in chemistry ever existed, we formulate our FC theory to have the structure reflecting the chemical formula. Our basic postulate is that as far as the SE is the principle of chemistry, its solutions for chemistry should have the structure that can be related to the chemical formulas. So, in this paper, we first formulate a theory that designs the wave function to reflect the structure of the chemical formula. We call this theory chemical formula theory (CFT). In the CFT, we place the valence ground and excited states of each atom at each position of the chemical formula of the molecule and let them interact using their free valences to form the ground and excited states of the molecule. The principle there is the variational principle so that the ground and excited states obtained satisfy the orthogonality and Hamiltonian-orthogonality relations. Then, we formulate the exact FC theory starting from the initial functions produced by the CFT. This FC theory is referred to as free-complement chemical- formula theory (FC-CFT), which is expected to describe efficiently the solution of the SE by the above reason. The FC-CFT wave function is modified from that of CFT. Since this modification is done by the exact SE, its analysis may give some insights to chemists that assist their chemistry. Thus, this theory would be not only exact but also conceptually useful. Furthermore, the intermediate theory between CFT and FC-CFT would also be useful. There, we use only integratable functions and apply the variational principle so that we refer to this theory as FC-CFT-variational (FC-CFT-V). It is an advanced theory of CFT. Since the variational method is straightforward and powerful, we can do extensive chemical studies in a reasonable accuracy. After finishing such studies, if we still need an exact level of solutions, we add the remaining functions of the FC-CFT and perform the exact calculations. Furthermore, when we deal with large and even giant molecules, the inter-exchange (iExg) theory for the antisymmetry rule introduced previously leads to a large simplification. There, the inter-exchanges between distant electron pairs fade away so that only Coulombic interactions survive. Further in giant systems, even an electrostatic description becomes possible. Then, the FC-CFT for exactly solving the SE would behave essentially to order N for large and giant molecular systems, though the pre-factor should be very large and must be minimized. [ABSTRACT FROM AUTHOR]

Electronic excitation spectra of the radical anions of cyanoethylenes (trans-dicyanoethylene and tetracyanoethylene) and cyanobenzenes (1,2-dicyanobenzene: o-DCNB, 1,3-dicyanobenzene: m-DCNB, and 1,4-dicyanobenzene: p-DCNB) were studied by the symmetry adapted cluster-configuration interaction (SAC-CI) method. Theoretical calculations predicted positive electron affinities for all the molecules in good agreement with the experimental observations. Electronic excitation spectra of open-shell radicals is a topic that has not been studied as much as such spectra of closed-shell molecules, but this can be easily addressed using SAC-CI theory. The present paper systematically describes the calculation procedures for radical anions by investigating several basis sets, including anion diffuse and Rydberg functions. The calculated excitation energies were in good agreement with the experimental UV/NIR (near infrared region) spectra, which had been observed by one of the present authors in 2-methyltetrahydrofuran matrix frozen to transparent glassy solids at 77 K. For p-DCNB, the SAC-CI theoretical spectrum agreed particularly well with the experimental spectrum. An extremely weak π*(SOMO) - π* excitation at 1.41 eV predicted in the present work, but had been overlooked in the previous experimental spectrum published in 1988, was confirmed to be real by a careful re-examination of the old spectrum. [ABSTRACT FROM AUTHOR]

In this series of studies, we systematically apply the analytical energy gradients of the direct symmetry-adapted cluster-configuration interaction singles and doubles nonvariational method to calculate the equilibrium geometries and vibrational frequencies of excited and ionized states of molecules. The harmonic vibrational frequencies were calculated using the second derivatives numerically computed from the analytical first derivatives and the anharmonicity was evaluated from the three-dimensional potential energy surfaces around the local minima. In this paper, the method is applied to the low-lying valence singlet and triplet excited states of HAX-type molecules, HCF, HCCl, HSiF, HSiCl, HNO, HPO, and their deuterium isotopomers. The vibrational level emission spectra of HSiF and DSiF and absorption spectra of HSiCl and DSiCl were also simulated within the Franck-Condon approximation and agree well with the experimental spectra. The results show that the present method is useful and reliable for calculating these quantities and spectra. The change in geometry in the excited states was qualitatively interpreted in the light of the electrostatic force theory. The effect of perturbation selection with the localized molecular orbitals on the geometrical parameters and harmonic vibrational frequencies is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent. [ABSTRACT FROM AUTHOR]

Electronic excited states, electronic absorption, and magnetic circular dichroism (MCD) spectra of free-base tetraazaporphyrin (TAP), phthalocyanine (Pc), naphthalocyanine (Nc), and anthracocyanine (Ac) were studied by quantum chemical calculations using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. Not only optically allowed states including the Q- and B-bands but also optically forbidden states were calculated for transitions whose excitation energies were lower than 4.5 eV. The present SAC-CI calculations consistently assigned the absorption and MCD peaks as optically allowed π→π* excitations, although these calculations using double-zeta basis limit quantitative agreement and discussion. For Nc and Ac, excited states beyond the four-orbital model appeared in the low-energy region. The low-energy shifts of the Q-bands with the extension of molecular size were explained by the orbital energies. The splitting of the Q-bands decreases with extension of the molecular size. This feature was reproduced by the SAC-CI calculations but the configuration interaction with single excitations and time-dependent density functional theory calculations failed to reproduce this trend. Electron correlation in the excited states is important in reproducing this splitting of the Q-bands and in describing the energy difference between the B2u and B3u states of free-base porphyrins. [ABSTRACT FROM AUTHOR]

In this paper we present the theory and implementation of the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method, including the solvent effect, using the polarizable continuum model (PCM). The PCM and SAC/SAC-CI were consistently combined in terms of the energy functional formalism. The excitation energies were calculated by means of the state-specific approach, the advantage of which over the linear-response approach has been shown. The single-point energy calculation and its analytical energy derivatives are presented and implemented, where the free-energy and its derivatives are evaluated because of the presence of solute-solvent interactions. We have applied this method to s-trans-acrolein and metylenecyclopropene of their electronic excitation in solution. The molecular geometries in the ground and excited states were optimized in vacuum and in solution, and both the vertical and adiabatic excitations were studied. The PCM-SAC/SAC-CI reproduced the known trend of the solvent effect on the vertical excitation energies but the shift values were underestimated. The excited state geometry in planar and nonplanar conformations was investigated. The importance of using state-specific methods was shown for the solvent effect on the optimized geometry in the excited state. The mechanism of the solvent effect is discussed in terms of the Mulliken charges and electronic dipole moment. [ABSTRACT FROM AUTHOR]

Valence ionized states of iron pentacarbonyl Fe(CO)5 and η5-cyclopentadienyl cobalt dicarbonyl Co(η5-C5H5)(CO)2 have been studied by ultraviolet photoelectron spectroscopy, two-dimensional Penning ionization electron spectroscopy (2D-PIES), and symmetry-adapted cluster-configuration interaction calculations. Theory provided reliable assignments for the complex ionization spectra of these molecules, which have metal-carbonyl bonds. Theoretical ionization energies agreed well with experimental observations and the calculated wave functions could explain the relative intensities of PIES spectra. The collision-energy dependence of partial ionization cross sections (CEDPICS) was obtained by 2D-PIES. To interpret these CEDPICS, the interaction potentials between the molecules and a Li atom were examined in several coordinates by calculations. The relation between the slope of the CEDPICS and the electronic structure of the ionized states, such as molecular symmetry and the spatial distribution of ionizing orbitals, was analyzed. In Fe(CO)5, an attractive interaction was obtained for the equatorial CO, while the interaction for the axial CO direction was repulsive. For Co(η5-C5H5)(CO)2, the interaction potential in the direction of both Co–C–O and Co–Cp ring was attractive. These anisotropic interactions and ionizing orbital distributions consistently explain the relative slopes of the CEDPICS. [ABSTRACT FROM AUTHOR]

The valence ionization spectra up to 20 eV of group six metal carbonyls, chromium hexacarbonyl, molybdenum hexacarbonyl, and tungsten hexacarbonyl were studied by the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The assignments of the spectra are given based on reliable SAC-CI calculations. The relativistic effects including the spin-orbit effects are important for the ionization spectrum of W(CO)6. The relation between the metal-CO distance and ionization energies was examined. The lowest ionization energies of the three metal carbonyls are approximately the same because of the energy dependence of the metal-CO length and relativistic effects. In Cr(CO)6, the Cr–CO interaction significantly increases the lowest ionization energy in comparison with Mo(CO)6 and W(CO)6 because of the relatively short metal-CO bond length. The relativistic effect reduces the lowest ionization energy of W(CO)6 because the effective core potential of 5d electrons is more efficiently screened as a result of the relativistic contraction of the inner electrons. [ABSTRACT FROM AUTHOR]

The Schrödinger equations for the hydrogen molecular ion (H2+) and its isotopomers (D2+, T2+, HD+, HT+, and DT+) were solved very accurately using the free iterative complement interaction method, which is referred to in short as the free complement (FC) method, in the non-Born–Oppenheimer (non-BO) level, i.e., in the nonrelativistic limit. Appropriate complement functions for both electron and nuclei were generated automatically by the FC procedure with the use of the non-BO Hamiltonian, which contains both electron and nuclear operators on an equal footing. Quite accurate results were obtained not only for the ground state but also for the vibronic excited states. For example, we obtained the ground-state energy of H2+ as -0.597 139 063 123 405 074 834 134 096 025 974 142 a.u., which is variationally the best in literature. The difference in the nuclear spin states of 1S (para) and 3P (ortho) of H2+ and some physical expectation values for several of the isotopomers shown above were also examined. The present study is the first application of the FC method to molecular systems with the non-BO Hamiltonian. [ABSTRACT FROM AUTHOR]

Electronic structures of trans- and cis-dichloroethylenes and tetrachloroethylene were studied using symmetry-adapted cluster configuration interaction theory. Basis sets up to the aug-cc-pVTZ of Dunning, Jr., augmented with appropriate Rydberg functions were used for the calculations. The results derived in the present study show good agreement with the available experimental values. In all cases, the main bright excitation was the π→π* transition. The other vertical excitations, π→σ*, n→σ*, and n→π*, which have not been studied before, were also investigated. First Rydberg series involving transitions from the π orbitals to one 3s, three 3p, and five 3d orbitals were identified clearly. Several new assignments and reassignments of features in the experimental spectra were suggested. Contrary to earlier prediction, two n-σ* states, along with a π-σ* state in the dichloroethylenes, were calculated to be located above the main π-π* state. Accordingly, crossing between both the n-σ* states with the bright π-π* state is highly likely, unlike conclusions made in the earlier studies. This indicates that the photodissociation mechanism proposed by the earlier calculations warrants revision. Several low-lying triplet excited states were also studied. Electronic spectra of trans-1-chloro-2-fluoroethylene and cis-1-chloro-2-fluoroethylene were also calculated. The π→π* transitions of these haloethylenes are compared and interpreted in terms of the inductive and resonance effects. [ABSTRACT FROM AUTHOR]

Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrödinger equation in the fixed-nucleus approximation could be very accurately solved for helium atom and its isoelectronic ions (Z=1–10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained -2.903 304 557 729 580 294 733 816 943 892 697 752 659 273 965 a.u. for helium atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary atom called “eneon,” [e-e10+e-]8+, in which both of the quantum effect of nuclear motion and the three-particle collisions are differently important from the helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism. [ABSTRACT FROM AUTHOR]

Very accurate variational calculations with the free iterative-complement-interaction (ICI) method for solving the Schrödinger equation were performed for the 1sNs singlet and triplet excited states of helium atom up to N=24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schrödinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry. [ABSTRACT FROM AUTHOR]

The nonrelativistic Schrödinger equation and the relativistic four-component Dirac equation of H2+ were solved accurately in an analytical expansion form by the free iterative complement interaction (ICI) method combined with the variational principle. In the nonrelativistic case, we compared the free ICI wave function with the so-called “exact” wave function as two different expansions converging to the unique exact wave function and found that the free ICI method is much more efficient than the exact method. In the relativistic case, we first used the inverse Hamiltonian to guarantee Ritz-type variational principle and obtained accurate result. We also showed that the ordinary variational calculation also gives a nice convergence when the g function is appropriately chosen, since then the free ICI calculation guarantees a correct relationship between the large and small components of each adjacent order, which we call ICI balance. This is the first application of the relativistic free ICI method to molecule. We calculated both ground and excited states in good convergence, and not only the upper bound but also the lower bound of the ground-state energy. The error bound analysis has assured that the present result is highly accurate. [ABSTRACT FROM AUTHOR]

We present a new computational algorithm, called direct algorithm, for the symmetry-adapted cluster (SAC) and SAC–configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states. The perturbation-selection technique and the molecular orbital index based direct sigma-vector algorithm were combined efficiently with the use of the sparse nature of the matrices involved. The formal computational cost was reduced to O(N2×M) for a system with N-active orbitals and M-selected excitation operators. The new direct SAC-CI program has been applied to several small molecules and free-base porphin and has been shown to be more efficient than the conventional nondirect SAC-CI program for almost all cases. Particularly, the acceleration was significant for large dimensional computations. The direct SAC-CI algorithm has achieved an improvement in both accuracy and efficiency. It would open a new possibility in the SAC/SAC-CI methodology for studying various kinds of ground, excited, and ionized states of molecules. [ABSTRACT FROM AUTHOR]

The Schrödinger equation was solved very accurately for helium atom and its isoelectronic ions (Z=1–10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions. For helium, the calculated energy was -2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 a.u., correct over 40 digit accuracy, and for H-, it was -0.527 751 016 544 377 196 590 814 566 747 511 383 045 02 a.u. These results prove numerically that with the free ICI method, we can calculate the solutions of the Schrödinger equation as accurately as one desires. We examined several types of scaling function g and initial function ψ0 of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r1 and r2 but also r12 in the same logarithm function. [ABSTRACT FROM AUTHOR]

The electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) methods and their equation-of-motion coupled-cluster (EOMCC) analogs provide an elegant framework for studying open-shell systems. As shown in this study, these schemes require the presence of higher-order excitations, such as the four-particle-three-hole (4p-3h) or four-hole–three-particle (4h-3p) terms, in the electron attaching or ionizing operator R in order to produce accurate ground- and excited-state potential energy surfaces of radicals along bond breaking coordinates. The full inclusion of the 4p-3h/4h-3p excitations in the EA/IP SAC-CI and EOMCC methods leads to schemes which are far too expensive for calculations involving larger radicals and realistic basis sets. In order to reduce the large costs of such schemes without sacrificing accuracy, the active-space EA/IP EOMCC methodology [J. R. Gour et al., J. Chem. Phys. 123, 134113 (2005)] is extended to the EA/IP SAC-CI approaches with 4p-3h/4h-3p excitations. The resulting methods, which use a physically motivated set of active orbitals to pick out the most important 3p-2h/3h-2p and 4p-3h/4h-3p excitations, represent practical computational approaches for high-accuracy calculations of potential energy surfaces of radicals. To illustrate the potential offered by the active-space EA/IP SAC-CI approaches with up to 4p-3h/4h-3p excitations, the results of benchmark calculations for the potential energy surfaces of the low-lying doublet states of CH and OH are presented and compared with other SAC-CI and EOMCC methods, and full CI results. [ABSTRACT FROM AUTHOR]

The symmetry adapted cluster (SAC)/symmetry adapted cluster configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states of molecules was extended to giant molecular systems. The size extensivity of energy and the size intensivity of excitation energy are very important for doing quantitative chemical studies of giant molecular systems and are designed to be satisfied in the present giant SAC/SAC-CI method. The first extension was made to giant molecular crystals composed of the same molecular species. The reference wave function was defined by introducing monomer-localized canonical molecular orbitals (ml-CMO’s), which were obtained from the Hartree-Fock orbitals of a tetramer or a larger oligomer within the electrostatic field of the other part of the crystal. In the SAC/SAC-CI calculations, all the necessary integrals were obtained after the integral transformation with the ml-CMO’s of the neighboring dimer. Only singles and doubles excitations within each neighboring dimer were considered as linked operators, and perturbation selection was done to choose only important operators. Almost all the important unlinked terms generated from the selected linked operators were included: the unlinked terms are important for keeping size extensivity and size intensivity. Some test calculations were carried out for the ring crystals of up to 10 000-mer, confirming the size extensivity and size intensivity of the calculated results and the efficiency of the giant method in comparison with the standard method available in GAUSSIAN 03. Then, the method was applied to the ring crystals of ethylene and water 50-mers, and formaldehyde 50-, 100-, and 500-mers. The potential energy curves of the ground state and the polarization and electron-transfer-type excited states were calculated for the intermonomer distances of 2.8–100 Å. Several interesting behaviors were reported, showing the potentiality of the present giant SAC/SAC-CI method for molecular engineering. [ABSTRACT FROM AUTHOR]

Several lowest-lying singlet electronic states of vinyl fluoride, trans-, cis-, and 1,1-difluoroethylene, trifluoroethylene, and tetrafluoroethylene were investigated by using symmetry-adapted cluster configuration interaction theory. Basis sets up to Dunning’s aug-cc-pVTZ augmented with appropriate Rydberg functions were utilized for the calculations. Calculated excitation energies show a good agreement with the available experimental values. Even in the troublesome π→π* transitions, the excitation energies obtained in the present study agree well with the experimental values except in one or two fluoroethylenes. Strong mixing between different states was noticed in a few fluoroethylenes; especially the mixing is very strong between π-π* and π-3pπ states in trifluoroethylene. No pure π-σ* excited state was found in almost all the fluoroethylenes. Several assignments and reassignments of features in the experimental spectra were suggested. The present study does not support the existing argument that the interaction between the π-π* and σ-σ* states is the reason behind the blueshift of around 1.25 eV in the π-π* excitation energy of tetrafluoroethylene. Possible reasons, including structural changes, for this shift are discussed in detail. Several low-lying triplet excited states were also studied. [ABSTRACT FROM AUTHOR]

The ground state structure for the CCCCCl radical was computed by using symmetry-adapted cluster configuration-interaction (SAC-CI) theory along with density functional theory to overcome the differences raised in the recently published paper [Y. Sumiyoshi et al., Chem. Phys. Lett. 414, 82 (2005)] between the theory and the experiment. SAC-CI results clearly support the earlier experimental conclusion that the radical has the bent ground state structure corresponding to 2Π symmetry. Contrarily, probably due to spin contamination, mixing of a bent doublet ground state with the quartet components of a linear structure, coupled-cluster singles and doubles (CCSD) calculations were unable to provide reliable results. Results obtained using density functional theory also show that the radical has a bent structure. Some low-lying doublet excited states were also studied using the SAC-CI theory. The energy difference between the ground Π state and the nearby Σ state is around 0.2 eV. The excitation energy for the transition with the largest oscillator strength agrees with the strongest absorption peak. [ABSTRACT FROM AUTHOR]

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 Å and 0.7° for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 1Ag states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states. [ABSTRACT FROM AUTHOR]

Open-shell reference version of the symmetry-adapted cluster (SAC) and SAC-configuration-interaction (CI) methods, termed open-shell reference (OR)-SAC and OR-SAC-CI methods, are developed and applied to inner-shell ionizations of CH4, NH3, H2O, and HF. The inner-shell ionization potentials and spectra calculated by the OR-SAC and OR-SAC-CI methods are in excellent agreement with the experimental data. Including both of the electron correlation and orbital relaxation is important for quantitative agreements. Timing comparisons with the SAC-CI general-R calculations that give similar high accuracies show an efficiency of the present OR-SAC and OR-SAC-CI methods. [ABSTRACT FROM AUTHOR]

The vertical absorption spectrum and photodissociation mechanism of vinyl chloride (VC) were studied by using symmetry-adapted cluster configuration interaction theory. The important vertical π→π* excitation was intensively examined with various basis sets up to aug-cc-pVTZ augmented with appropriate Rydberg functions. The excitation energy for π→π* transition obtained in the present study, 6.96 eV, agrees well with the experimental value, 6.7–6.9 eV. Calculated excitation energies along with the oscillator strengths clarify that the main excitation in VC is the π→π* excitation. Contrary to the earlier theoretical reports, the results obtained here support that the C–Cl bond dissociation takes place through the nCl-σC–Cl* state. [ABSTRACT FROM AUTHOR]

The quasirelativistic (QR) generalized unrestricted Hartree–Fock method for the magnetic shielding constant [R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys. 118, 1015 (2003); R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys.118, 1027 (2003)] has been extended to include the electron correlation effect in the level of the second-order Mo\ller–Plesset perturbation theory (MP2). We have implemented the energy gradient and finite-perturbation methods to calculate the magnetic shielding constant at the QR MP2 level and applied to the magnetic shielding constants and the NMR chemical shifts of 125Te nucleus in various tellurium compounds. The calculated magnetic shielding constants and NMR chemical shifts well reproduced the experimental values. The relations of the chemical shifts with the natures of ligands, and the tellurium oxidation states were investigated. The chemical shifts in different valence states were explained by the paramagnetic shielding and spin-orbit terms. The tellurium 5p electrons are the dominant origin of the chemical shifts in the Te I and Te II compounds and the chemical shifts were explained by the p-hole mechanism. The tellurium d electrons also play an important role in the chemical shifts of the hypervalent compounds. [ABSTRACT FROM AUTHOR]

Theoretical fine spectroscopy has been performed for the valence ionization spectra of furan, pyrrole, and thiophene with the symmetry-adapted-cluster configuration-interaction general-R method. The present method described that the π1 state interacts with the π3-2π*, π2-2π*, and π2-1π3-1π* shake-up states providing the split peaks and the outer-valence satellites, both of which are in agreement with the experiments. The intensity distributions were analyzed in detail for the inner-valence region. In particular, for furan, theoretical intensities were successfully compared with the intensity measured by the electron momentum spectroscopy. The interactions of the 3b2 and 5a1 states with the shake-up states were remarkable for furan and pyrrole, while the 4b2 state of thiophene had relatively large intensity. [ABSTRACT FROM AUTHOR]

The iterative configuration-interaction general singles and doubles (ICIGSD) method was applied to various closed- and open-shell electronic states of molecules within finite basis sets and was shown to give the exact results that are identical to the full CI ones. The structure of the ICIGSD is unique among the ICI formalisms, that is, the singularity problem intrinsic to atomic and molecular Hamiltonians can be avoided. The convergence of the ICIGSD method was fairly good regardless of the characters of the electronic states and the qualities of the basis sets; only several iterations were enough for obtaining microhartree accuracy. These favorable properties are attributed to the unique GSD structure. The present method was shown to be applicable to various spin states and to quasidegenerate states appearing in bond dissociation process. We have also applied the ICIGSD-CI method to calculate the excited states simultaneously. We have confirmed that the ICIGSD-CI method is accurate for calculating the excited states the symmetries of which are not only similar to but also different from that of the ground state. [ABSTRACT FROM AUTHOR]

Molecular core ionization spectra and their satellites were studied by the symmetry adapted cluster–configuration interaction (SAC-CI) general-R method. The core-electron binding energies of C, N, O, and F atoms of 22 molecules were calculated with an average deviation of 0.11 eV from the experimental values. The energy splittings between K-shell gerade and ungerade states were calculated and discussed in relation to the bond length. The satellite spectra of the C 1s and N 1s core ionizations of methane and ammonia were investigated. The SAC-CI general-R method gave many shake-up states with moderate intensities, reproducing the general feature of the experimental spectra, and thus enabling the detailed understanding and assignments of the core-electron ionization spectra. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A method of calculating analytical energy gradients of the singlet and triplet excited states, ionized states, electron-attached states, and high-spin states from quartet to septet states by the symmetry-adapted-cluster configuration-interaction general-R method is developed and implemented. This method is a powerful tool in the studies of geometries, dynamics, and properties of the states of molecules in which not only one-electron processes but also two- and multielectron processes are involved. The performance of the present method was confirmed by calculating the geometries and the spectroscopic constants of the diatomic and polyatomic molecules in various electronic states involving the ground state and the one- to three-electron excited states. The accurate descriptions were obtained for the equilibrium geometries, vibrational frequencies, and adiabatic excitation energies, which show the potential usefulness of the present method. The particularly interesting applications were to the C[sup ′] [sup 1]A[sub g] state of acetylene, the A [sup 2]Δ[sub u] and B [sup 2]Σ[sub u][sup +] states of CNC and the [sup 4]B[sub 1] and a [sup 4]Π[sub u] states of N[sub 3] radical. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report on theoretical valence ionization spectra of molecules relevant in the stratosphere photochemistry obtained by all-electron SAC-CI (symmetry-adapted-cluster-configuration-interaction) calculations. Vertical ionization energies and pole strengths of the one- and two-electron processes of C1[sub 2]O and F[sub 2]O were calculated beyond the energy region so far explored in the few other available theoretical and experimental studies to interpret the electronic structure of these molecules. Early and recently proposed incomplete assignments of the available He I photoelectron spectra are discussed and completed at least up to 20-21 eV binding energy on firmer grounds relying on valuable and accurate results based on different basis sets and an adequate treatment of electron correlations. Our theoretical data predict satellite states of C1[sub 2]O starting already in the outer-valence region because of strong correlation effects; the (2b[sup -1, sub 1]), (8a[sup -1, sub 1]), and (6b[sup -1, sub 2]) states interact with the two-electron processes and they split into more-than-two peaks. On the other hand, Koopmans' picture is valid for the main peaks of F[sub 2]O and no prominent satellites with strong intensity were found in the outer-valence region. The (4b[sup -1, sub 2]), (6a[sup -1, sub 1]), and ( 1a[sup -1, sub 2]) were attributed to the second band of F[sub 2]O, for which different assignments or orderings of the states have previously been proposed in some experimental and theoretical works. Differences of the valence-ionization spectra of C1[sub 2]O and F[sub 2]O for the appearance of the satellites in the intermediate energy region have been discussed with the aid of the calculated ionization potentials and excitation energies. For C1OOC1, we have presented the first theoretical low-energy ionization spectrum and discussed the character of the calculated states referring to the available ionization spectra of C1O radical. [ABSTRACT FROM AUTHOR]

A two-component quasirelativistic theory based on the Douglas-Kroll-Hess (DKH) transformation has been developed to study magnetic properties of molecules. The proposed Hamiltonian includes the relativistic magnetic vector potential in the framework of the DKH theory, and is applicable to the calculations of magnetic properties without further expansion in powers of c[sup -1]. By combining with the finite-perturbation theory and the generalized-UHF method, new pictures of the magnetic shielding constant are derived. We apply the theory to calculations of the magnetic shielding constants of He isoelectronic systems, Ne isoelectronic systems, and noble gas atoms. The results of the present theory compare well with those of the four-component Dirac-Hartree-Fock calculations; the differences were within 3%. We note that the quasirelativistic theory that handles the magnetic vector potential at a nonrelativistic level greatly underestimates the relativistic effect. The so-called "picture change" effect is quite important for the magnetic shielding constant of heavy elements. The change in the orbital picture plays a significant role in the valence-orbital magnetic response as well as the core-orbital one. The effect of the finite nucleus is also studied using Gaussian nucleus model. The present theory reproduces the correct behavior of the finite-nucleus effect that has been reported with the Dirac theory. In contrast, the nonrelativistic theory and the quasirelativistic theory with the nonrelativistic vector potential underestimate the finite-nucleus effect. [ABSTRACT FROM AUTHOR]

Quasirelativistic theory of magnetic shielding constants based on the Douglas-Kroll-Hess transformation of the magnetic potential presented in a previous paper is extended to molecular systems that contain heavy elements. The gauge-including atomic orbital method is adapted to the quasirelativistic Hamiltonian to allow origin-independent calculations. The present theory is applied to the proton and halogen magnetic shielding constants of hydrogen halides and the [sup 199]Hg magnetic shielding constants and chemical shifts of mercury dihalides and methyl mercury halides. While the relativistic correction to the magnetic interaction term has little effect on the proton magnetic shielding constants, this correction is a dominant origin of the heavy atom shifts of the magnetic shielding constants of heavy halogens and mercury. The basis set-dependence of mercury shielding constants is quite large in the relativistic calculation; it is important to use the basis functions that are optimized by the relativistic method to properly describe the relativistic effect. The relativistic correction to the magnetic interaction term is quite important for mercury dihalides in which the relativistic effects from mercury and halogen are strongly coupled. Without this correction, we obtain quite incorrect results. The origin of the [sup 199]Hg chemical shifts in mercury dihalides is the spin-orbit interaction from heavy halogens. In methyl mercury halides, the paramagnetic shielding term as well as the spin-orbit interaction from heavy halogens dominates the [sup 199]Hg chemical shifts. [ABSTRACT FROM AUTHOR]

The ground state, singlet, and triplet excited states, and ionized states of ferrocene Fe(C[SUB5]H[SUB5])[SUB2] were studied by the symmetry adapted cluster (SAC)/SAC-configuration-interaction method. The calculated ionization energies and intensities fairly well reproduced the observed photoelectron spectrum in the wide region of 6-14 eV. In particular, the first two peaks ([SUP2]E′[SUB2] and [SUP2]A′[SUB1]) were assigned to the ionizations from the occupied 3 d orbitals of Fe, mixed already with the two-electron shake-up processes. This is the first ab initio quantitative assignment that is consistent with the experimental data. For the singlet states, three d-d transitions were calculated at 2.12, 2.26, and 4.02 eV, which correspond to the experimental peaks observed at 2.69, 2.97, and 3.82 eV. We propose possible assignments for other absorption bands in the range of 2.12-6.57 eV. In another three triplet d-d transition states we calculated, we found that the energy order of these states (1 [SUP3]E″[SUB1], 1 [SUP3]E″[SUB2], 2 [SUP3]E″[SUB1]) differs from that of singlet states (1 [SUP1]E″[SUB2], 1 [SUP1]E″[SUB1], 2 [SUP1]E″[SUB1]). [ABSTRACT FROM AUTHOR]

Fine theoretical spectroscopy has been presented by the SAC-CI (symmetry adapted cluster-configuration interaction) general-R method for the outer- and inner-valence ionization spectra of CS[sub 2] and OCS. The SAC-CI general-R method simulated the experimental spectra quite accurately and the detailed assignments of the satellite peaks were given. For CS[sub 2], four outer-valence satellites ²Π[sub u] states were calculated, one of which was attributed to the recently observed peak (1'). Numerous ²Σ[sub +][sub u] ' and ²Σ[sup +][sub g] satellite peaks were obtained in the inner-valence region and some of them were dominantly described by triple electron processes; the quadruple R-operators were found to be important for describing these states in the general-R method. For OCS, the relative position of the main peaks was correctly reproduced and the higher R-operators were found to be important for the ordering of A and B states. In the energy region of 24-36 eV, continuous spectra of numerous ²Σ[sup +] satellites were obtained, which reproduced the feature of the photoelectron spectrum. [ABSTRACT FROM AUTHOR]

Singlet excited states and ionized states of aniline are studied by the symmetry adapted cluster/ configuration interaction method. Absorption bands of states that have mainly π - π[sup *] nature are assigned as ¹ A' (∼ &supl;B[sub 2]), ¹A' (∼¹A[sub 1]), 1A' (∼ ¹B[sub 2]), ¹A' (∼ ¹A[sub 1]), ¹A' (∼ ¹B[sub 2]) in increasing-energy order. An s-Rydberg state is predicted to lie between the first and second valence states, in agreement with recent experimental results. The lowest band has a charge-resonance character with a slight charge-transfer (CT) character (CT is defined as NH[sub 2] → C[sub 6]H[sub 5] ); third and fifth valence bands have back-CT (BCT) nature, and second and fourth are local excitations within the benzene ring. The extent of CT of excited states depends on amino group conformation. In the planar form, CT characters of several states were altered; however, spectral shapes are very similar to that of the equilibrium form. On the other hand, amino group twisting altered both the spectrum and nature of excited states. Third and fourth lowest valence states exhibited strong CT character, while fifth to eighth states are of the strong BCT type, implying that the CT nature of excited states of aniline can be changed by amino group twisting. For ionized states, the lowest three states are assigned to ²A' (∼²B[sub 1]), 2A' (∼²A[sub 2]), 2A' (∼²B[sub 1]) in increasing-energy order, all being π-ionizations. The sixth one is also due to π-ionization (∼ ²B[sub 1]) and the others are σ-ionizations. Ordering was the same as Koopmans' case. [ABSTRACT FROM AUTHOR]

The iterative configuration interaction (ICI) method is applied to molecular systems within finite basis using only few (1-3) variables and shown to give the exact results that are identical to the full CI (FCI) ones. Since each iteration step of ICI is variational, the ICI converges monotonically to the exact solution from above. The diagonalization in ICI is so slight as the number of variables is so small, in contrast to the huge number of variables of FCI. We calculated the molecular ground states of various spin-space symmetries using minimal basis and double zeta basis. The number of iterations for convergence was small for minimal basis but moderate for double zeta basis, considering that only 1-3 variables are optimized in each iteration step. [ABSTRACT FROM AUTHOR]

The density matrix variational theory (DMVT) algorithm developed previously [J. Chem. Phys. 114, 8282 (2001)] was utilized for calculations of the potential energy surfaces of molecules, H[sub 4], H[sub 2]O, NH[sub 3], BH[sub 3], CO, N[sub 2], C[sub 2], and Be[sub 2]. The DMVT(PQG), using the P, Q, and G conditions as subsidiary condition, reproduced the full-CI curves very accurately even up to the dissociation limit. The method described well the quasidegenerate states and the strongly correlated systems. On the other hand, the DMVT(PQ) was not satisfactory especially in the dissociation limit and its potential curves were always repulsive. The size consistency of the method was discussed and the G condition was found to be essential for the correct behavior of the potential curve. Further, we also examined the Weinhold-Wilson inequalities for the resultant 2-RDM of DMVT(PQG) calculations. Two linear inequalities were violated when the results were less accurate, suggesting that this inequality may provide a useful N-representability condition for the DMVT. [ABSTRACT FROM AUTHOR]

In a previous paper of this series [Paper III: Nakatsuji, J. Chem. Phys. 105, 2465 (2001)], the author showed a high potentiality of the extended coupled cluster (ECC) method to calculate the exact wave function of the ground state. In this paper, we propose ECC-configuration interaction (CI) method, which is an accurate useful method to calculate the excited states from the ECC wave function of the ground state. In contrast to the ECC method, the standard ECC-CI method is approximate, but we can make it exact by generalizing its excitation operator (ECC-CI general). The ECC-CI method is applicable not only to the excited states having the same spin-space symmetry as the ground state, but also to those having different spin-space symmetries and to the ionized and electron-attached states. The theoretical framework of the ECC-CI method is similar to that of the symmetry-adapted-cluster (SAC)-CI method proposed in 1978 by the present author. Next in this paper, we examine the performance of the methods proposed in this series of papers for a simple one-dimensional harmonic oscillator. The iterative configuration interaction (ICI) and ECC methods are examined for the ground state and the ICI-CI and ECC-CI methods for the excited states. The ICI method converges well to the exact ground state and the excited states are calculated nicely by the ICI-CI method in both the standard and general active spaces. In contrast to the simplest (S)ECC examined in Paper III, the ECC2 method shows quite a rapid convergence to the exact ground state, which enables us to calculate the true exact wave function in the ECC form. The ECC-CI methods in both the standard and general active spaces also work well to calculate the excited states. Thus, we conclude that the ICI and ECC approaches have a potentiality to provide useful method to calculate accurate wave functions of the ground and excited states. A merit of ECC is that it provides the exact wave function in a simple explic... [ABSTRACT FROM AUTHOR]

Outer- and inner-valence ionization spectra of group V hydrides, NH[sub 3], PH[sub 3], and AsH[sub 3] were studied by the symmetry-adapted-cluster configuration-interaction (SAC-CI) general-R method. Fine details of the experimental spectra of these hydrides were reproduced and the quantitative assignments of the peaks were proposed. The inner-valence satellites were classified into those including the valence or Rydberg excitations. For NH[sub 3], we interpreted the spectrum using the relative intensity and proposed some unresolved bands. For PH[sub 3], bands 2 and 3, for which different assignments have been proposed, were attributed to the [sup 2]A[sub 1] inner-valence satellites. A detailed inner-valence satellite spectrum of AsH[sub 3] is theoretically proposed. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This is the second progress report on the study of the structure of the exact wave function. First, Theorem II of Paper I (H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000)) is generalized: when we divide the Hamiltonian of our system into N[sub D] (number of division) parts, we correspondingly have a set of N[sub D] equations that is equivalent to the Schro¨dinger equation in the necessary and sufficient sense. Based on this theorem, the iterative configuration interaction (ICI) method is generalized so that it gives the exact wave function with the N[sub D] number of variables in each iteration step. We call this the ICIND method. The ICIGSD (general singles and doubles) method is an important special case in which the GSD number of variables is involved. The ICI methods involving only one variable [ICION(one) or S(simplest)ICI] and only general singles (GS) number of variables (ICIGS) are also interesting. ICIGS may be related to the basis of the density functional theory. The convergence rate of the ICI calculations would be faster when N[sub D] is larger and when the quality of the initial guess function is better. We then study the structure of the ICI method by expanding its variable space. We also consider how to calculate the excited state by the ICIGSD method. One method is an ICI method aiming at only one exact excited state. The other is to use the higher solutions of the ICIGSD eigenvalues and vectors to compute approximate excited states. The latter method can be improved by extending the variable space outside of GSD. The underlying concept is similar to that of the symmetry-adapted-cluster configuration-interaction (SAC-CI) theory. A similar method of calculating the excited state is also described based on the ICIND method. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Electronic excited and ionized states of pyridine were reinvestigated by the symmetry-adapted cluster configuration interaction (SAC-CI) method using an extended basis set and a wide active space. The present SAC-CI results for the singlet and triplet excited states are greatly improved and agree well with the experimental observations, providing a firm assignment of all low-lying n→π[sup *] and π→π[sup *] valence excited states observed in the vacuum ultraviolet spectrum and electron energy-loss spectrum. The ionization potentials were reexamined by the SAC-CI general-R (R represents excitation operator) method. The first four ionization potentials are greatly improved compared with our previous results obtained by the SAC-CI single- and double-R (SD-R) method. The present theoretical ionization potentials are in good agreement with the experimental values in high-resolution synchrotron photoelectron spectrum for energy regions up to 25 eV (which contain outer- and inner-valence regions), and give a detailed theoretical assignment for the photoelectron spectra. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The SAC(symmetry adapted cluster)/SAC-CI method is applied to the calculations of the ground, excited, and ionized states of the free base porphin. The electronic spectrum of porphin is well reproduced and new assignments for the B (Soret), N, L, and M bands are proposed. The present result shows that the four-orbital model is strongly perturbed for the B and N bands by the excitations from the lower 4b1u MO and that the σ electron correlations are important for the description of the excited states. The absorption peaks in the ionization spectrum are assigned and the reorganization effect is found to be large especially for the n and σ electron ionizations. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Electronic mechanism of the surface enhanced Raman scattering (SERS) is investigated by an ab initio molecular orbital theory. The time-dependent Hartree–Fock method is used to calculate the polarizability of the surface–molecule interacting system. For representing the surface effect, we use small solid clusters Ag2, Ag10, K2, Pd2, and MgO. The present method succeeds in describing the enhancement of the Raman intensity for the adsorbed CO molecule. The maximum intensity of the Ag10CO system is calculated to be seven orders of magnitude larger than that of the free CO molecule. Furthermore, the wavelength dependence of the Raman intensity calculated by the Ag10CO system agrees with the experimental spectrum. The electronic mechanism of the SERS is due to the resonance transitions, in which the surface polarization and the surface–molecule interaction are very important. This mechanism explains the orientation- and distance-dependencies in the surface–adsorbate interacting systems. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The collisionally induced absorption process and the broadening of the 6P resonance line of the Cs–Rg system (Rg=Xe, Kr, Ar, and Ne) are studied theoretically by the symmetry adapted cluster-configuration interaction (SAC-CI) method. The potential energy curves and the transition moments of the CsRg system correlating to the 6S, 6P, 5D, and 7S states of the Cs atom are investigated. The reduced absorption coefficients are calculated using the quasistatic approximation and the results agree well with the experimental data. The monotonic dependence of the spectral peaks on the rare gas species is due to the similar monotonic dependence of the avoided crossing point between the 7sΣ and 5dΣ states. The absorption intensities decrease as the rare gas atom is substituted from Xe to Ne in agreement with the experimental observation. The intensities of the 6sΣ–5dΣ transitions are calculated to be larger than those of the 6sΣ–7sΣ ones, since the former transitions are induced at larger internuclear distances than the latter. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The use of augmented basis sets of the form, {χ, rtχ, rtruχ, ...} (rt, ru=x, y, z), is proposed for calculating magnetic properties which are almost gauge-origin independent. It is derived from Epstein’s theorem which states the sufficient condition for unitary invariance. Test calculations using the coupled-Hartree–Fock/finite perturbation method show that the augmented sets correctly reduce the origin dependence of magnetic shielding constants, and that the results agree well with the experiment. Through systematic modifications of the basis set, a practical procedure in choosing basis functions to be added is suggested. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]