Symmetry-adapted Cluster-configuration Interaction Research Articles

Theoretical study of the singlet and triplet vertical electronic transitions of styrene by the symmetry adapted cluster-configuration interaction method

Abstract The ground state, singlet → singlet and singlet → triplet vertical excited states of styrene have been studied by using the symmetry adapted cluster-configuration interaction (SAC-CI) method with aug-cc-pVDZ basis sets supplemented with molecule-centered Rydberg functions. The characteristic structures of the bands observed in the vacuum ultraviolet (VUV) and electron energy loss (EEL) spectra have been theoretically clarified by calculating the excitation energies, oscillator strengths, and second moments for all the excited states in the energy region 2.6–7.0 eV. The present SAC-CI theoretical results, including both the singlet → singlet and singlet → triplet vertical electronic transitions, have well reproduced the profile of the electronic spectra of styrene. Higher-energy singlet → triplet excited states and Rydberg states were extensively addressed. The valence and Rydberg configurations were found strongly mix with each other in the 6 1 A ′ and 8 1 A ′ excited states at the SAC-CI/aug-cc-pVDZ(R) level. Three main differences were found comparing with the previous CASPT2 study. (1) The 3s ′ - and 3p-series of Rydberg states were predicted lower than the 5 1 A ′ and 6 1 A ′ valence π–π * excited states in the SAC-CI study, whereas higher than the 5 1 A ′ and 6 1 A ′ excited states in the CASPT2 study. (2) The valence excited state (4 1 A ′ ) involving doubly excited configurations (4a″,4a″) → (5a″,5a″) computed at 6.08 eV at the CASPT2 level was not found in the SAC-CI calculation. (3) The characterizations (main configurations) of the 5 1 A ′ and 6 1 A ′ excited states have been found to exchange their components in the SAC-CI and CASPT2 calculations.

Magnetic Circular Dichroism of Nonaromatic Cyclic π-Electron Systems. 5. Biphenylene and Its Aza Analogues

The algebraic form of the perimeter model for nonaromatic cyclic π-electron systems developed in parts 1−4 of this series is used to analyze the previously reported magnetic circular dichroism (MCD) of biphenylene (1) and its aza analogues, to classify its excited states, and to relate them to those of other nonaromatic cyclic π systems. The observed MCD signs are interpreted in terms of relative sizes of orbital energy differences and the resulting configuration energy ordering. These require deviations from the alternant pairing associated with the simplest classical description, which are attributed to the increased negative magnitude of the diagonal resonance integrals in the four-membered ring. The interpretation of the UV and MCD spectra of 1 is confirmed by the observed effects of aza substitution, and predictions for other types of substitution follow. The magnetic field induced state mixing deduced from the perimeter model is supported by computations by the linear combination of orthogonalized atomic orbitals (LCOAO), time-dependent density functional theory (TD DFT), and symmetry-adapted cluster configuration interaction (SAC-CI) methods.

Vibrationally resolved O 1s photoelectron spectrum of water

The O 1s photoelectron spectrum of water was recorded with the resolution high enough to resolve the vibrational structure of the O 1s −1 state and the lifetime width and the Franck-Condon (FC) factors were extracted. The experimental spectrum was reproduced well by the molecular ab initio calculations based on the symmetry adapted cluster-configuration interaction (SAC-CI) method. The vibrational structure was attributed mostly to the bending mode of the core-ionized molecule.

157-nm Resist Material Design for Improvement of Its Transparency Using Highly Precise Theoretical Calculation

Vacuum ultraviolet (VUV) absorption spectra of resist materials for 157 nm lithography were calculated theoretically by the symmetry adapted cluster configuration interaction (SAC-CI) method. In this study, we investigated the excited states of several alkanes and fluorinated alkanes in the VUV region, and found that most of the transitions of the evaluated alkanes are Rydberg-like transitions. Furthermore, we found a good linear correlation between the lowest absorption energy of alkane and its highest occupied orbital (HOMO) energy. This suggests that consideration of these HOMO energies could be an effective way to explain the change in VUV spectra by fluorination. We also investigated the molecular structures of fluorinated norbornanes to improve their transparency at the VUV region. Through our SAC-CI spectroscopic calculations and evaluation of the HOMO energies for the norbornane derivatives, it was found that fluorination at positions 1, 2, 4 and 5 of norbornane is an efficient molecular method for improving transparency in the VUV region.

Theoretical investigation on the valence ionization spectra of Cl2O, ClOOCl, and F2O by correlation-based configuration interaction methods

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 Cl2O and F2O 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 Cl2O starting already in the outer-valence region because of strong correlation effects; the (2b1−1), (8a1−1), and (6b2−1) 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 F2O and no prominent satellites with strong intensity were found in the outer-valence region. The (4b2−1), (6a1−1), and (1a2−1) were attributed to the second band of F2O, 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 Cl2O and F2O 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 ClOOCl, 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 ClO radical.

Fine Theoretical Spectroscopy Using SAC-CI General-R Method: Outer- and Inner-Valence Ionization Spectra of N2O and HN3

Abstract Fine theoretical spectroscopy for the outer- and inner-valence ionization spectra has been presented by using the SAC-CI (symmetry adapted cluster-configuration interaction) general-R method applied to N2O and HN3. The SAC-CI general-R method accurately simulated the experimental spectra and the detailed assignments of the satellite peaks were proposed. The continuous peaks I ∼ V of N2O observed by the dipole (e,2e) spectroscopy were finely reproduced. In particular, the low-lying satellites were calculated in good agreement with the experiment; two 2Π shake-up states at the foot of the C state, 2Σ and 2Π states for the peak I. For HN3, new interpretation was proposed for the outer-valence region, namely, peaks 3 ∼ 5 are composed of the mixture of the single-electron main peaks and the two-electron shake-up peaks. Inner-valence ionization spectrum of HN3 was theoretically predicted for which no experimental spectrum has been reported.

Ground and excited states of linked and fused zinc porphyrin dimers: Symmetry adapted cluster (SAC)—configuration interaction (CI) study

The symmetry adapted cluster (SAC)/SAC-configuration interaction method was applied to calculate the ground and excited states of zinc porphyrin monomers (without and with phenyl groups, ZnP and ZnPPh, respectively) and meso–meso linked (Zn2PMM) and doubly fused (Zn2PDF) zinc porphyrin dimers. Various features of the absorption spectra are studied, clarified, and assigned theoretically. The calculated electronic spectrum of ZnPPh, in comparison with that of ZnP, showed that the phenyl groups affect the spectrum in both the peak positions and intensities. In the dimers, Zn2PMM and Zn2PDF, the interactions of the monomer’s four-orbitals result in an eight-orbital model of the dimers, which plays an important role in the interpretation of the excited states observed in the spectra. In Zn2PMM, the interaction is smaller and each peak in the split Soret (BI and BII) bands consists of two peaks, in contrast to the prediction based on Kasha’s exciton rule. In Zn2PDF, the interaction between the two monomer units is so strong that the small highest occupied molecular orbital–lowest unoccupied molecular orbital gap causes the red-shifted Q (1.16 eV) and BI (2.13 eV) bands. In addition, the excitations out of the eight orbitals appear in the low-energy region of the spectrum, which is very different from the case of the monomer. A comprehensive and pictorial analysis is given for the excited states of the dimers in comparison with those of the monomer.

Ionized and excited states of ferrocene: Symmetry adapted cluster–configuration–interaction study

The ground state, singlet, and triplet excited states, and ionized states of ferrocene Fe(C5H5)2 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 (2E2′ and A1′2) were assigned to the ionizations from the occupied 3d 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 3E1″, 1 3E2″, 2 3E1″) differs from that of singlet states (1 1E2″, 1 1E1″, 2 1E1″).

Fine theoretical spectroscopy using symmetry adapted cluster-configuration interaction general-R method: Outer- and inner-valence ionization spectra of CS2 and OCS

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 CS2 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 CS2, four outer-valence satellites Πu2 states were calculated, one of which was attributed to the recently observed peak (1′). Numerous Σu+2 and Σg+2 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 Σ+2 satellites were obtained, which reproduced the feature of the photoelectron spectrum.

Excited and ionized states of aniline: Symmetry adapted cluster configuration interaction theoretical study

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* nature are assigned as A″1 (∼1B2), A′1 (∼1A1), A″1 (∼1B2), A′1 (∼1A1), A″1 (∼1B2) 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 NH2→C6H5); 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 A′2 (∼2B1), A″2 (∼2A2), A′2 (∼2B1) in increasing-energy order, all being π-ionizations. The sixth one is also due to π-ionization (∼2B1) and the others are σ-ionizations. Ordering was the same as Koopmans’ case.

Development of 157 nm Resist Using Highly Exact Theoretical Calculation of Absorption Spectra

Vacuum ultraviolet (VUV) absorption spectra of organic materials were calculated theoretically by the symmetry-adapted cluster-configuration interaction (SAC-CI) method [rf1,rf2,rf3,rf4] to establish a molecular design for high-transparency resist materials to be used in 157 nm lithography. We investigated several saturated hydrocarbons and fluorinated compounds, and obtained low prediction error of absorption peaks (< 0.25 eV, in the case of formaldehyde). High-precision prediction enables exact assignment of an absorption spectrum. The theoretical SAC-CI spectra obtained were very close to the experimentally measured spectra. In addition, we investigated the reasons for changes occurring in VUV-absorption spectra when C–H bonds of alkane are substituted with C–F bonds, and found that major changes in electronic structure occur with fluorination.

Molecular structures and excited states of CpM(CO)(2) (Cp = eta(5)-C(5)H(5); M = Rh, Ir) and [Cl(2)Rh(CO)(2)](-). Theoretical evidence for a competitive charge transfer mechanism.

Molecular structures and excited states of CpM(CO)(2) (Cp = eta(5)-C(5)H(5); M = Rh, Ir) and [Cl(2)Rh(CO)(2)](-) complexes have been investigated using the B3LYP and the symmetry-adapted cluster (SAC)/SAC-configuration interaction (SAC-CI) theoretical methods. All the dicarbonyl complexes have singlet ground electronic states with large singlet-triplet separations. Thermal dissociations of CO from the parent dicarbonyls are energetically unfavorable. CO thermal dissociation is an activation process for [Cl(2)Rh(CO)(2)](-) while it is a repulsive potential for CpM(CO)(2). The natures of the main excited states of CpM(CO)(2) and [Cl(2)Rh(CO)(2)](-) are found to be quite different. For [Cl(2)Rh(CO)(2)](-), all the strong transitions are identified to be metal to ligand CO charge transfer (MLCT) excitations. A significant feature of the excited states of CpM(CO)(2) is that both MLCT excitation and a ligand Cp to metal and CO charge transfer excitation are strongly mixed in the higher energy states with the latter having the largest oscillator strength. A competitive charge transfer excited state has therefore been identified theoretically for CpRh(CO)(2) and CpIr(CO)(2). The wavelength dependence of the quantum efficiencies for the photoreactions of CpM(CO)(2) reported by Lees et al. can be explained by the existence of two different types of excited states. The origin of the low quantum efficiencies for the C-H/S-H bond activations of CpM(CO)(2) can be attributed to the smaller proportion of the MLCT excitation in the higher energy states.

Outer- and inner-valence ionization spectra of NH3, PH3, and AsH3: symmetry-adapted cluster configuration interaction general-R study

Outer- and inner-valence ionization spectra of group V hydrides, NH3, PH3, and AsH3 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 NH3, we interpreted the spectrum using the relative intensity and proposed some unresolved bands. For PH3, bands 2 and 3, for which different assignments have been proposed, were attributed to the A12 inner-valence satellites. A detailed inner-valence satellite spectrum of AsH3 is theoretically proposed.

Analytical energy gradient of high-spin multiplet state calculated by the SAC-CI method

A method of calculating analytical energy gradient of high-spin multiplet state by the SAC-CI (symmetry-adapted-cluster configuration-interaction) method is developed and implemented. This method is expected to be a powerful tool in studying the dynamics and properties of molecules having high spin-multiplicities. Good performance of this method is shown for the quartet states of BH + and C 2 + and for the quintet states of C 2. The SAC-CI general- R method is also extended to the high-spin states, and proved to be useful especially for calculating accurate adiabatic excitation energies of the systems having quasi-degenerate orbital structure.

Excited states of Na and Al iso‐electronic ions: Symmetry adapted cluster–configuration interaction study

AbstractThe Rydberg excited levels of s, p, d, and f symmetries are studied up to principal quantum number n=5 for the first eight members of the Na iso‐electronic sequence (Na to Ar7+) and for the first six members of the Al iso‐electronic sequence (Al to Ar5+) by the symmetry adapted cluster–configuration interaction (SAC–CI) method. The valence Slater‐type orbital (STO) basis sets of Clementi et al. and the optimized Rydberg STO functions are used by the STO‐6G expansion method. The calculated transition energies agree well with the experimental values wherever available. The results for the 4f level of S3+ and for the 5s, 4p, 5p, and 4f levels of Cl4+ and Ar5+ are predicted for the first time. © 2001 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2001

Analytical energy gradients of the excited, ionized and electron-attached states calculated by the SAC-CI general- R method

A method of calculating analytical energy gradients of the excited, ionized and electron-attached states calculated by the symmetry-adapted-cluster configuration-interaction (SAC-CI) general- R method is formulated and implemented. This method is expected to be a powerful tool in the studies of dynamics and properties of molecules in which two- and multi-electron processes are involved. Good performance of this method is shown for the singlet and triplet excited states of BH and for the doublet ground and excited states of CH.

Theoretical study on the outer- and inner-valence ionization spectra of H2O, H2S and H2Se using the SAC-CI general-R method

The outer- and inner-valence ionization spectra of the Group VI hydrides H2O, H2S and H2Se below the double-ionization threshold were studied by the SAC-CI (symmetry-adapted-cluster configuration-interaction) general-R method. The SAC-CI method quite accurately reproduced the experimental spectra of these hydrides and gave detailed characterizations of the shake-up states. Several unknown satellite peaks were predicted. The shake-up state which includes excitations to the Rydberg orbitals was found to be very important for describing the satellite peaks of these hydrides. A detailed inner-valence satellite spectrum of H2Se is theoretically proposed prior to any experimental observation.

Electronic excitation and ionization spectra of azabenzenes: Pyridine revisited by the symmetry-adapted cluster configuration interaction method

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* and π→π* 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.

Electronic excitation spectrum of thiophene studied by symmetry-adapted cluster configuration interaction method

Electronic excitation spectrum of thiophene was investigated by the symmetry-adapted cluster (SAC)/SAC configuration interaction method. Seventy singlet and four lowest triplet electronic states of thiophene were computed to give a detailed satisfactory theoretical interpretation of the vacuum ultraviolet (VUV) spectrum and the electron energy loss spectrum of thiophene. The present calculations gave the 2 1A1 valence state at 5.41 eV and the 1 1B2 valence state at 5.72 eV with oscillator strengths 0.0911 and 0.1131, respectively, and the 5 1A1 valence state at 7.32 eV and the 4 1B2 valence state at 7.40 eV with oscillator strengths 0.3614 and 0.1204, respectively. These valence-excited states were assigned to the two strong absorption bands of the VUV spectrum centered around 5.5 and 7.05 eV, respectively. A number of Rydberg transitions were obtained and assigned to the 6.0, 6.6, and 7.5–8.7 eV, etc. energy regions. The similarities and differences in the electronic excitations between thiophene and other five-membered ring compounds were discussed. The accuracy and assignment of the present results are compared with those of the recent theoretical studies by CASPT2 and multireference double configuration interaction methods.

Excited states of Ne isoelectronic ions: SAC-CI study

Excited states of the s, p, and d symmetries up to principal quantum number n = 4 are studied for the first eight members of Ne isoelectronic sequence (Ne to Cl7+) by the SAC-CI (symmetry-adapted-cluster configuration-interaction) method. The valence STO basis sets of Clementi et al. and the optimized excited STO are used by the STO-6G expansion method. The calculated transition energies agree well with the experimental values wherever available.