Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Ab initio study of the spectroscopy of (CH3)(3)CN and (CH3)(2)CHN

Using the complete active space self-consistent field (CASSCF) method with 6-311++g(3df,3pd) basis sets, a few electronic states of nitrenes (CH3)3CN and (CH3)2CHN and their positive ions are calculated. All calculated states are valence states, and their characteristics are discussed in detail. In order to investigate the Jahn-Teller effect on (CH3)3CN radical, Cs symmetry was used for (CH3)3CN and (CH3)2CHN in the calculations. The results of our calculations (CASPT2 adiabatic excitation energies and RASSI oscillator strengths) suggest that the calculated transitions of (CH3)3CN at 27,710 cm(-1) and (CH3)2CHN at 28,110 cm(-1) are attributed to 23A' --> 13A', while those of (CH3)3CN at 28,916 cm(-1) and (CH3)2CHN at 29,316 cm(-1) are attributed to 13A' --> 13A'. The vertical and adiabatic ionization energies were obtained to compare with the photoelectron spectroscopic data. These results are in agreement with previous experimental data. Also, we present a comprehensive review on the CAS calculation results for (CH3)nCH(3-n)N (n = 0-3) presented in our previous and present papers.     

UV-vis spectra of <Emphasis Type="Italic">p</Emphasis>-benzoquinone anion radical in solution by a TD-DFT/PCM approach

Excited electronic states of the anion radical of para-benzoquinone were studied by time dependent density functional theory (TD-DFT) including bulk solvent effects by the polarizable continuum model (PCM). The computed vertical excitation energies for the first four low-lying doublet states are in good agreement with previous post-Hartree–Fock computations. Geometry optimization of excited states and inclusion of solvent effects lead to a remarkable agreement between computed adiabatic transition energies and experimental band maxima. Together with their specific interest, the results point out the reliability of TD-DFT/PCM approach for valence excitations and the need to take geometry relaxation and solvent effects into the proper account for a meaningful comparison between computed and experimental absorption spectra.     

Ab initio study of the spectroscopy of CH3N and CH3CH2N

Complete active space (CAS) calculations with 6-311++g(3df,3pd) basis sets were performed for a large number of electronic states of the nitrate free radical (CH3N/CH3CH2N) and their positive and negative ions. All calculated states are valence states, and their characters are discussed in detail. To investigate the Jahn-Teller effect on the CH3N radical, Cs symmetry was used for both CH3N and CH3CH2N in calculations. The results (CASPT2 adiabatic excitation energies and CASSI oscillator strengths) suggest that the calculated transitions of CH3N at 32172 and 32139 cm(-1) are attributed to the 2(3)A' ' --> 1(3)A' ' and 1(3)A' --> 1(3)A' ', respectively, which is in accordance with the A3E --> X3A2 emission spectrum at T0 = 31 817 cm(-1). The calculated transitions of CH3CH2N at 334 nm are attributed to the 1(3)A' ' --> 2(3)A' ' and 1(3)A' ' --> 1(3)A', respectively, which is in accordance with the UV absorption spectrum of a series of 11 bands beginning at 335 nm. The vertical and adiabatic ionization energies were obtained to compare with the PES data. These results are in agreement with previous experimental data, which is discussed in detail.     

Structures of small Li(NH3)n and Li(NH3)n+ clusters (n = 1-5): evidence from combined photoionization efficiency measurements and ab initio calculations

Photoionization threshold measurements have been carried out for small Li(NH3)n clusters (n = 1-5) and have been combined with ab initio calculations to determine structural information. The calculated adiabatic ionization energy for the lowest-energy isomer of each cluster is found to be in excellent agreement with the corresponding experimental photoionization threshold, providing evidence that the calculated structures are correct. The combination of the photoionization efficiency curve and the calculated adiabatic ionization energies also confirms the tentative assignment of the infrared spectrum of Li(NH3)4 reported by Salter and co-workers (J. Chem. Phys. 2006, 125, 34302); i.e., the 3 + 1 isomer does not contribute and the spectrum is due solely to the 4 + 0 isomer. The findings are consistent with an inner solvation shell that can hold a maximum of four ammonia molecules around the central lithium atom.     

Interpretation of the electronic spectra of four disilanes

Time-dependent density functional theory (TD-DFT/B3LYP(AC)/cc-pVTZ/cc-pVTZ/6-311G//MP2/cc-pVTZ/cc-pVTZ/6-31G**) has been used to compute vertical excitation energies and oscillator strengths of the six low-lying excited states of four peralkylated disilanes, hexamethyldisilane (1), hexa-tert-butyldisilane (2), 1,6-disila[4.4.4]propellane (3), and 1,7-disila[5.5.5]propellane (4). The results provide an accurate interpretation of the reported UV absorption spectra of 1-4 in solution, and for 1 also in the gas phase up to 62,000 cm(-1). The excellent agreement of the calculated with the available experimental energies and oscillator strengths, and with magnetic circular (MCD) and linear (LD) dichroism, gives us confidence that the method will be useful for dependable interpretation of the electronic spectra of longer oligosilanes. Although the disilane chromophore finds itself in quite different environments in 1-4, its fundamental characteristics remain the same, with one important exception. In all four compounds, the first valence excited state is due to an electron promotion from the sigma(1) HOMO to the pi(1)* orbital, and the second valence excited state to a promotion from the sigma(1) HOMO to the sigma(1)* orbital. Surprisingly, however, it is only in 2, which has an extraordinarily long SiSi bond, that the terminating sigma(1)* orbital is the sigma*(SiSi) antibond, as anticipated, and the sigma sigma* transition has the expected very high oscillator strength. In 1, 3, and 4, the sigma*(SiSi) antibonding orbital is high in energy and does not play any role in low-energy excitations. Instead, the terminating orbital of the sigma(1)sigma(1)* excitation is represented by Si-alkyl antibonds, combined symmetrically with respect to rotation around the SiSi axis and antisymmetrically with respect to operations that interchange the two Si atoms. The common assumption that the characteristic intense sigma sigma* transitions of longer peralkylated oligosilanes extrapolate to the lowest sigma sigma* transition in common peralkylated disilanes is incorrect, and only the weak sigma pi* transitions extrapolate simply.     

Electronic spectrum of UO2(2+) and [UO2Cl4]2- calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.     

Theoretical Study of Haloacetonitrile Anions: CH2XCN- (X=F,Cl)

Haloacetonitrile anions CH2XCN- (X=F, Cl) were studied by HF-SCF, Becke3-LYP, and MP2 methods together with the Dunning's basis set aug-cc-PVTZ. The vertical electron attachments to the neutral are endothermic. The geometrically optimized CH2FCN- is mainly a valence-bounded anion and CH2FCN-→CH2CN+F- is a nonadiabatic dissociation. This theoretical study in good agreement with the experimental results shows that the Becke3-LYP method is reasonable in describing the electronic structures of anions and dissociative attachment dynamics, while significant differences between MP2 and Becke3-LYP results are shown for the dissociation potential curves of CH2ClCN-→CH2CN+Cl-.2,70-(Ethylene)-bis-8-hydroxyquinoline was optimized with DFT/B3LYP and ab initio HF methods, so ionization potential and electron affinity could be determined. Absorption spectrum was calculated by ZINDO and TD-DFT. CIS method was used to calculate the S1 excited states of the compound and afterwards the emission spectrum was computed. When the solvent effect was taken into account, the computed results show encouraging agreement with known experimental data. The results of analyzing the relationship between the energies and absorption spectra indicate that the ability to transporting electrons is strengthened compared with 8-hydroxyquinoline and that absorption and emission spectra are red-shifted. The intramolecular reorganization energy of tris(2,70-(ethylene)-bis-8-hydroxyquinoline)-aluminum implies its electron transporting property is worse than tris(8-hydroxyquinoline)-aluminum. The predicted maximum emission wavelength is red-shifted compared with tris(8-hydroxyquinoline)-aluminum.     

Computational Investigation of Neutral and Anionic AlnCom Clusters by Density-functional Theory

Structural and electronic properties of bimetallic clusters AlnCom with n=1～7 and m=1～2 have been investigated using the B3LYP-DFT method.Structural optimization and frequency analysis were performed at the CEP-121G level.The charge-induced structural changes in these anions were discussed.In addition,the corresponding total energies,binding energies,adiabatic electron affinities and vertical electron affinity were also presented and discussed.Our predicted vertical ionization potentials are in reasonable agreement with the experimental ionization potentials.Among different AlnCom and AlnCom-anions (n=1～7,m=1～2),Al4Co,Al6Co,Al4Co-,Al6Co-and Al4Co2-are predicted to be species with high stabilities.     

Optical excitations of defects in realistic nanoscale silica clusters: comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

Substituent effects on the energies of the electronic transitions of geminally diphenyl-substituted trimethylenemethane (TMM) radical cations. Experimental and theoretical evidence for a twisted molecular and localized electronic structure

Substituent effects on the energies (Eob) of electronic transitions of geminally diphenyl-substituted trimethylenemethane (TMM) radical cations 5a-k*+ and those of structurally related 1,1-diarylethyl cations 7a-k+ were determined experimentally by using electronic transition spectroscopy. In addition, transition energies of these radical cations were determined by using density functional theory (DFT) and time-dependent (TD)-DFT calculations. The electronic transition bands of 5a-k*+ and 7a-k+ have maxima (lambdaob) that appear at 500-432 and 472-422 nm, respectively. A Hammett treatment made by plotting the Eob values relative to that of the diphenyl-TMM radical cation 5d*+ (DeltaEob) vs the cationic substituent parameter sigma+ give a favorable correlation with a boundary point at sigma+ = 0.00 and a positive rho for sigma+ < 0 and a negative rho for sigma+ > 0. A comparison of the lambdaob and rho values for 5a-k*+ and 7a-k+ suggests that the chromophore of 5*+ is substantially the same as that of 7+. The results of TD-DFT calculations, which reproduce the experimental electronic transition spectra and relationships between DeltaEob and sigma+, and suggest that the absorption band of 5*+ is associated with the SOMO-X --> SOMO transition, while that of 7+ is due to the HOMO --> LUMO transition. Another interesting observation is that Cl and Br substituents in the diphenyl-substituted TMM radical cations and 1,1-diarylethyl cations 7a-k+ act as electron-donating groups in terms of their effect on the corresponding electronic transitions. The results show that the molecular structure of 5*+ is a considerably twisted and that 5*+ has a substantially localized electronic state in which the positive charge and odd electron are localized in the respective diarylmethyl and the allyl moieties.     

H atom transfer along an ammonia chain: tunneling and mode selectivity in 7-hydroxyquinoline.(NH3)3

Excitation of the 7-hydroxyquinoline(NH(3))(3) [7HQ(NH(3))(3)] cluster to the S(1) (1)pi pi(*) state results in an O-H-->NH(3) hydrogen atom transfer (HAT) reaction. In order to investigate the entrance channel, the vibronic S(1)<-->S(0) spectra of the 7HQ.(NH(3))(3) and the d(2)-7DQ.(ND(3))(3) clusters have been studied by resonant two-photon ionization, UV-UV depletion and fluorescence techniques, and by ab initio calculations for the ground and excited states. For both isotopomers, the low-frequency part of the S(1)<--S(0) spectra is dominated by ammonia-wire deformation and stretching vibrations. Excitation of overtones or combinations of these modes above a threshold of 200-250 cm(-1) for 7HQ.(NH(3))(3) accelerates the HAT reaction by an order of magnitude or more. The d(2)-7DQ.(ND(3))(3) cluster exhibits a more gradual threshold from 300 to 650 cm(-1). For both isotopomers, intermolecular vibrational states above the threshold exhibit faster HAT rates than the intramolecular vibrations. The reactivity, isotope effects, and mode selectivity are interpreted in terms of H atom tunneling through a barrier along the O-H-->NH(3) coordinate. The barrier results from a conical intersection of the optically excited (1)pi pi(*) state with an optically dark (1)pi sigma(*) state. Excitation of the ammonia-wire stretching modes decreases both the quinoline-O-H...NH(3) distance and the energetic separation between the (1)pi pi(*) and (1)pi sigma(*) states, thereby increasing the H atom tunneling rate. The intramolecular vibrations change the H bond distance and modulate the (1)pi pi(*)<-->(1)pi sigma(*) interaction to a much smaller extent.     

Computations on the A-X transition of isoprene-OH-O2 peroxy radicals

Calculations are carried out on the A state of HO2, CH3O2, and CH3CH2O2 and 10 isomers and conformers of the isoprene-OH-O2 peroxy radicals derived from OH addition to isoprene (2-methyl-1,3-butadiene). In addition to calculating vertical and adiabatic excitation energies, we consider the effect of excitation on molecular structure, and examine the OO stretching frequencies, which are known to be major features in the absorption spectra of the A states of the smaller radicals. The two methods used are the configuration interaction with single excitations (CIS) method and time-dependent density functional theory (TD-DFT), both with a range of basis sets up to 6-311++G(2df,2pd). TD-DFT overestimates excitation energies considerably, while CIS tends to underestimate them slightly. TD-DFT does seem to capture the trend in excitation energy vs. size for the smaller peroxy radicals. Conformation and configuration strongly affect the excitation energies of the peroxy radicals from isoprene. CIS calculations indicate that the intramolecular OH--O hydrogen bonds, present in the ground state of some peroxy radicals from isoprene, are weakened or broken in the excited state, while TD-DFT calculations suggest they are retained.     

Steric asymmetry and lambda-doublet propensities in state-to-state rotationally inelastic scattering of NO(2Pi(1/2)) with He

Relative integrated cross sections are measured for rotationally inelastic scattering of NO(2Pi(1/2)),hexapole selected in the upper lambda-doublet level of the ground rotational state (j = 0.5), in collisions with He at a nominal energy of 514 cm(-1). Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, [formula: see text], which is equal to within a factor of (- 1) to the molecular steric effect, S(i-->f) is identical with (sigma(He-->NO) - (sigma(He-->ON))/(sigma(He-->NO) + sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming lambda-doublet component is also observed as a function of the final rotational (j'), spin-orbit (omega'), and lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of omega'. However, the lambda-doublet propensities are very different for [omega=0.5(F1)-->omega'= 1.5(F2)] and [omega=0.5(F1)-->omega'=0.5(F1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO(2Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R.Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry S(i-->f) of the inelastic cross sections at Etr= 514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F1-->Fl) and spin-manifold changing (F1 --F2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at Etr = 508 cm(-1) are compared to the experimental data of Joswig et al. [J. Chem. Phys.85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy Etr= 491 cm(-1) is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F1 (j = 0.5) -F1f (j' = 3.5).     

线性BC2nB (n＝1～12)的结构特征和电子光谱的理论研究

应用密度泛函理论, 在B3LYP/6-31G^*水平上优化得到了线性簇合物BC_2nB (n＝1～12, D_(h)的平衡几何构型, 并计算了它们的谐振动频率. 在优化平衡几何构型下, 通过TD-B3LYP/cc-pvDZ和TD-B3LYP/cc-pvTZ计算, 分别得到了n＝1～12和n＝1～7的电子跃迁的垂直激发能和对应的振子强度. 在B3LYP/6-311＋G^*水平上计算得到了簇合物BC_2nB (n＝1～12, D_(h)的电离能. 基于计算结果, 导出了BC_2nB体系电子跃迁能以及第一电离能与体系大小n的解析表达式.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.