Symmetry-adapted Cluster-configuration Interaction Method Research Articles

Photophysical properties and vibrational structure of ladder-type penta p-phenylene and carbazole derivatives based on SAC-CI calculations

The π-conjugated ladder-type molecules constitute an attractive field of organic photoactive materials. In this work, the photophysical properties of ladder-type penta-p-phenylene (LPP) and carbazole derivatives (bisindenocarbazole and diindolocarbazole) have been investigated theoretically using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The equilibrium geometries in the ground (S 0) and first excited (S 1) states were calculated to be planar, and the excitation is delocalized over the molecules. SAC-CI/DZP calculations have been applied to the absorption and emission spectra of these molecules. The absorption spectra were well reproduced in both peak positions and the shape of the absorption bands. The strong absorption is attributed to the highest occupied molecular orbital to the lowest unoccupied molecular orbital (H–L) transition; however, in carbazoles, the H–1→L transition is located below the H–L transition. The vibrational structure in the S 0–S 1 absorption band of LPP was analyzed by calculating the Franck–Condon (FC) factors based on the potential energy surfaces (PESs) along the normal coordinates that are relevant to the geometry change. The vibrational structure was well reproduced by the theoretical simulation. The C–C stretching mode dominantly contributes to the vibrational structure, while the breathing motion of the molecular frame does not influence the structure. The emission energies calculated by the SAC-CI method also agree well with the experimental values. The vibrational structure in the fluorescence band was also examined by the FC analysis; the theoretical spectrum is satisfactory for the two carbazoles, while the 0–0 transition is overestimated in LPP. In diindolocarbazole, the S 2 state has a large oscillator strength, while the S 1 state has a small oscillator strength.

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

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.

The SAC/SAC-CI studies of ground and low-lying electronic excited states of OClO, OClO + and OClO −

The properties of the ground and low-lying electronic excited states of OClO, OClO + and OClO − are studied employing symmetry-adapted-cluster (SAC)/symmetry-adapted-cluster configuration interaction (SAC-CI) method. The geometry of the ground state of OClO is optimized by SAC method using different basis sets and the reasonable geometry of the ground state of OClO is obtained by SAC/6-311++G (2d, 2p) level. The properties of nine low-lying electronic excited states of OClO, such as geometries, vertical excitation energies, adiabatic excitation energies, transition dipole moments and oscillation strengths, are studied at SAC-CI method. By SAC-CI/6-311++G (2d, 2p) level, the geometries of ten electronic states of OClO + are optimized and the adiabatic ionization potentials (AIP) and the vertical ionization potentials (VIP) of OClO + are calculated. The geometries of six electronic states of OClO − are optimized and the vertical detachment energies (VDE) and adiabatic detachment energies (ADE) of OClO − are obtained. Comparing with the available experimental and previous theoretical data, the SAC/SAC-CI/6-311++G (2d, 2p) results are reliable.

Absorption spectra of nucleic acid bases studied by the symmetry-adapted-cluster configuration-interaction (SAC-CI) method

The ground and excited states of five nucleic acid bases (adenine, guanine, cytosine, uracil and thymine) were calculated by employing the SAC/SAC-CI (symmetry adapted cluster/SAC configuration-interaction) method. The absorption spectra with the SAC-CI method were compared with the experimental spectra. The spectra obtained with the SAC-CI method were in good agreement with the experimental spectra in gas phase. Comparisons with the calculations with other methods were made.

Electronic excited states of macrocyclic compounds: direct SAC-CI study

Abstract We developed the direct SAC-CI (symmetry-adapted cluster-configuration interaction) method for accurate calculations of electronic excited states of large molecules. The direct SAC-CI method uses an efficient MO (molecular orbital) direct scheme that is compatible with the perturbation-selection technique with using sparse linear algebra techniques. The direct SAC-CI can calculate large molecules with moderate computational cost. Using the direct SAC-CI method, excited states of free-base tetraazaporphyrin, phthalocyanine, naphthalocyanine, and anthracocyanine were studied. An interesting feature of the observed spectra is that the splitting of the Q-bands decreases with increasing molecular size. The SAC-CI calculation well reproduced the observed trend of excitation energies and showed the importance of electron correlation effects in the excited states.

Excited states and electronic spectra of extended tetraazaporphyrins

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 B(2u) and B(3u) states of free-base porphyrins.

Symmetry-adapted cluster and symmetry-adapted cluster-configuration interaction method in the polarizable continuum model: Theory of the solvent effect on the electronic excitation of molecules in solution

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.

Quantum Chemistry of the Color Tuning Mechanism in the Photobiological System

In visual systems and fluorescent proteins, controlling the photo-absorption/emission energy (color tuning) of the chromophore is the essentials to furnish a protein with the photo-functionality. Depending on the protein environment, the chromophores show a variety of colors, which are relevant to the character of the excited states and to the interactions between the chromophore and the environment. Here we summarize our recent studies on the spectral tuning mechanism of the human visual cone pigments and the fluorescent proteins. These studies elucidated a common feature in the color tuning, which also suggests a strategy to artificially control the color of proteins. We also explain our recent progress in developing the symmetry-adapted cluster-configuration interaction (SAC-CI) method and hybrid quantum mechanical/molecular mechanical (QM/MM) method particularly for studying the photo-functional proteins.

Absorption and emission spectra of ultraviolet B blocking methoxy substituted cinnamates investigated using the symmetry-adapted cluster configuration interaction method

The absorption and emission spectra of ultraviolet B (UVB) blocking cinnamate derivatives with five different substituted positions were investigated using the symmetry-adapted cluster configuration interaction (SAC-CI) method. This series included cis- and trans-isomers of ortho-, meta-, and para-monomethoxy substituted compounds and 2,4,5-(ortho-, meta-, para-) and 2,4,6-(ortho-, para-) trimethoxy substituted compounds. The ground and excited state geometries were obtained at the B3LYP/6-311G(d) and CIS/D95(d) levels of theory. All the compounds were stable as cis- and trans-isomers in the planar structure in both the S(0) and S(1) states, except the 2,4,6-trimethoxy substituted compound. The SAC-CI/D95(d) calculations reproduced the recently observed absorption and emission spectra satisfactorily. Three low-lying excited states were found to be relevant for the absorption in the UV blocking energy region. The calculated oscillator strengths of the trans-isomers were larger than the respective cis-isomers, which is in good agreement with the experimental data. In the ortho- and meta-monomethoxy compounds, the most intense peak was assigned as the transition from next highest occupied molecular orbital (next HOMO) to lowest unoccupied molecular orbital (LUMO), whereas in the para-monomethoxy compound, it was assigned to the HOMO to LUMO transition. This feature was interpreted as being from the variation of the molecular orbitals (MOs) due to the different substituted positions, and was used to explain the behavior of the excited states of the trimethoxy compounds. The emission from the local minimum in the planar structure was calculated for the cis- and trans-isomers of the five compounds. The relaxation paths which lead to the nonradiative decay were also investigated briefly. Our SAC-CI calculations provide reliable results and a useful insight into the optical properties of these molecules, and therefore, provide a useful tool for developing UVB blocking compounds with regard to the tuning of the photoabsorption.

Valence ionization spectra of group six metal hexacarbonyls studied by the symmetry-adapted cluster-configuration interaction method

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.

Circular Dichroism and Absorption Spectroscopy for Three-Membered Ring Compounds Using Symmetry-Adapted Cluster-Configuration Interaction (SAC-CI) Method

Abstract The singlet excited states of oxirane and thiirane derivatives, ethylene oxide, (R)-methyloxirane, (2S,3S)-dimethyloxirane, ethylene sulfide, (R)-methylthiirane, and (2S,3S)-dimethylthiirane, were calculated employing the symmetry-adapted cluster (SAC)/SAC-configuration interaction (CI) method. The rotatory strengths of the CD spectra were calculated in the velocity form, which is gauge-origin independent. Both the ultraviolet (UV) spectra and the circular dichroism (CD) spectra obtained with the SAC-CI method were in good agreement with the experimental spectra. In oxirane derivatives, the low-lying excited states were composed of excitations from n and σ orbitals to s, p, and d Rydberg orbitals. The excitation from the σ orbital was especially important in (2S,3S)-dimethyloxirane because of the steric effect of the methyl substitutions. However, in thiirane derivatives, the excitations to the low-lying excited states were only from the n orbital.

Critical Role of External Axial Ligands in Chirality Amplification of trans-Cyclohexane-1,2-diamine in Salen Complexes

A series of Mn(IV)(salen)(L)(2) complexes bearing different external axial ligands (L = Cl, NO(3), N(3), and OCH(2)CF(3)) from chiral salen ligands with trans-cyclohexane-1,2-diamine as a chiral scaffold are synthesized, to gain insight into conformational properties of metal salen complexes. X-ray crystal structures show that Mn(IV)(salen)(OCH(2)CF(3))(2) and Mn(IV)(salen)(N(3))(2) adopt a stepped conformation with one of two salicylidene rings pointing upward and the other pointing downward due to the bias from the trans-cyclohexane-1,2-diamine moiety, which is in clear contrast to a relatively planar solid-state conformation for Mn(IV)(salen)(Cl)(2). The CH(2)Cl(2) solution of Mn(IV)(salen)(L)(2) shows circular dichroism of increasing intensity in the order L = Cl < NO(3) << N(3) < OCH(2)CF(3), which indicates Mn(IV)(salen)(L)(2) adopts a solution conformation of an increasing chiral distortion in this order. Quantum-chemical calculations with a symmetry adapted cluster-configuration interaction method indicate that a stepped conformation exhibits more intense circular dichroism than a planar conformation. The present study clarifies an unexpected new finding that the external axial ligands (L) play a critical role in amplifying the chirality in trans-cyclohexane-1,2-diamine in Mn(IV)(salen)(L)(2) to facilitate the formation of a chirally distorted conformation, possibly a stepped conformation.

Artificial color tuning of firefly luminescence: Theoretical mutation by tuning electrostatic interactions between protein and luciferin

Electrostatic interactions between firefly oxyluciferin and the surrounding proteins were analyzed, and the amino acids important for controlling emission energy were identified. We propose Arg223Ala, Glu344Ala, and Asp422Ala mutations in firefly oxyluciferase of Photinuspyralis, which artificially change the luminescence color by tuning the electrostatic effect from the luciferase proteins. In the theoretical mutation simulation, the emission energy of the triple mutant was estimated to be 2.05eV (602nm, reddish-orange), which is 0.18eV lower than that of the wild type (2.23eV, 557nm, yellow–green). For calculating the emission energies, we used the symmetry-adapted cluster-configuration interaction (SAC-CI) method.

Excited electronic and ionized states of the nitramide molecule, H2NNO2, studied by the symmetry-adapted-cluster configuration interaction method

Symmetry-adapted-cluster configuration interaction (SAC-CI) wave functions were employed to compute 16 singlet and 13 triplet vertical transitions, and 14 ionized states including relative intensities of the nitramide molecule, H2NNO2. This molecule is the simplest neutral closed-shell molecule which has an N–NO2 bond and is a member of the nitramine family, R,R′N(NO2), an important class of energetic materials with practical applications. The present nitramide results showed strong similarities with the ones of the N, N-dimethylnitramine molecule, which has also an N–NO2 bond and was previously studied using the SAC-CI method. Experimental ultraviolet and photoelectron band spectra of the nitramide molecule could be successfully assigned. All the singlet transitions have valence character. The computed singlet and triplet transitions, excepting a singlet one, result from excitation originating in the four highest occupied molecular orbitals, which have close energies. Most of the singlet and triplet transitions involved mixing of singly excited configurations. The strongest computed transition, at 6.8 eV, is a mixture of two nπNO2 → π* configurations corresponding to excitations from the highest occupied molecular orbital (HOMO) to the first two virtual orbitals and has an optical oscillator strength value of 0.2665. The computed ionized states described the whole measured spectrum, have excellent agreement when compared with the measured ionization potentials and revealed an inversion of the ordering of the first states not expected according to Koopmanns’ theorem, thereby showing the limitations of the latter.

Formulation and implementation of direct algorithm for the symmetry-adapted cluster and symmetry-adapted cluster–configuration interaction method

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(N(2)xM) 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.

Ground and low-lying excited states of SO 2 studied by the SAC/SAC-CI method

The SAC (Symmetry-adapted-cluster)/SAC-CI (Symmetry-adapted-cluster configuration interaction) method is applied for studying the properties of the ground and eight low-lying excited states of SO 2. Firstly, the geometry of the ground state of SO 2 is optimized by SAC method using many different basis sets. The calculated results are in agreement with the experiments, and the conclusion suggests that the basis sets 6-311+G (2df) and cc-pVTZ are the better suitable ones for the calculation of SO 2 in the SAC method and the 3 d function plays an important role in SO 2. Then eight low-lying excited states of SO 2 are optimized at SAC-CI/cc-pVTZ level and the adiabatic excitation energies of the low-lying excited states are also got based on the energy of ground state. Comparing with the available data, the equilibrium geometries and adiabatic excitation energies are in well agreement with the experimental values. Finally, based on the equilibrium geometry of the ground state X ˜ 1 A 1 , the vertical excitation energies, transition dipole moments and oscillation strengths of the eight excited states are also got at SAC-CI/cc-pVTZ level.

Excited states of GFP chromophore and active site studied by the SAC‐CI method: Effect of protein‐environment and mutations

Excited states of fluorescent proteins were studied using symmetry-adapted cluster-configuration interaction (SAC-CI) method. Protein-environmental effect on the excitation and fluorescence energies was investigated. In green fluorescent protein (GFP), the overall protein-environmental effect on the first excitation energy is not significant. However, glutamine (Glu) 94 and arginine (Arg96) have the red-shift contribution as reported in a previous study (Laino et al., Chem Phys 2004, 298, 17). The excited states of GFP active site (GFP-W22-Ser205-Glu222-Ser65) were also calculated. Such large-scale SAC-CI calculations were performed with an improved code containing a new algorithm for the perturbation selection. The SAC-CI results indicate that a charge-transfer state locates at 4.19 eV, which could be related to the channel of the photochemistry as indicated in a previous experimental study. We also studied the excitation and fluorescence energies of blue fluorescent protein, cyan fluorescent protein, and Y66F. The SAC-CI results are very close to the experimental ones. The protonation state of blue fluorescent protein was determined. Conformation of cyan fluorescent protein indicated by the present calculation agrees to the experimentally observed structure.

Coupling between Substituents as a Function of Cage Structure: Synthesis and Valence Ionized States of Bridgehead Disubstituted Parent and Hexafluorinated Bicyclo[1.1.1]pentane Derivatives C5X6Y2

He(I) photoelectron spectroscopy was used to examine the valence-shell electronic structure of three new and seven previously known bicyclo[1.1.1]pentane derivatives, 1,3-Y2-C5X6 (for X = H, Y = H, Cl, Br, I, CN; for X = F, Y = H, Br, I, CN). A larger series (X = H or F, Y = H, F, Cl, Br, I, At, CN) has been studied computationally with the SAC-CI (symmetry-adapted cluster configuration interaction) method. The outer-valence ionization spectra calculated by the SAC-CI method, including spin-orbit interaction, reproduced the experimental photoelectron spectra well, and quantitative assignments are given. When the extent of effective through-cage interaction between the bridgehead halogen lone-pair orbitals was defined in the usual way by orbital-energy splitting, it was found to be larger than that mediated by other cages such as cubane, and was further enhanced by hexafluorination. The origin of the orbital-energy splitting is analyzed in terms of cage structure, and it is pointed out that its relation to the degree of interaction between the bridgehead substituents is not as simple as is often assumed.

Investigation of the Electronic Spectra and Excited-State Geometries of Poly(para-phenylene vinylene) (PPV) and Poly(para-phenylene) (PP) by the Symmetry-Adapted Cluster Configuration Interaction (SAC-CI) Method

The symmetry-adapted cluster-configuration interaction (SAC-CI) method has been used to investigate the optical and geometric properties of the oligomers of poly(para-phenylene vinylene) (PPV) and poly(para-phenylene) (PP). Vertical singlet and triplet absorption spectra and emission spectra have been calculated accurately; the mean average deviation from available experimental results lies within 0.2 eV. The chain length dependence of the transition energies has been improved in comparison to earlier TDDFT and MRSDCI calculations. The present analysis suggests that conventional TDDFT with the B3LYP functional should be used carefully, as it can provide inaccurate estimates of the chain length dependence of the excitation energies of these molecules with long pi conjugation. The T1 state was predicted to be at a lower energy, by 1.0-1.5 eV for PPV and by 0.9-1.7 eV for PP, than the S1 state, which indicates a localized T1 state with large exchange energy. By calculating the SAC-CI electron density difference between the ground and excited states, the geometry relaxations due to excitations can be analyzed in detail using electrostatic force theory. For trans-stilbene, the doubly excited 21Ag state was studied, and the calculated transition energy of 4.99 eV agrees very well with the experimental value of 4.84 eV. In contrast to previous ab initio calculations, we predict this doubly excited 21Ag state to lie above the 11Bu state.

Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals

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.