Symmetry-adapted Cluster-configuration Interaction Research Articles

On the performance of time-dependent double-hybrid density functionals for description of absorption and emission spectra of heteroaromatic compounds

Theoretical chemistry provides a panel of powerful tools to investigate the geometries and electronic properties of excited states. However, it is necessary to benchmark the accuracy of existing models to determine the range of their applicability and accountability. In the present work, the performance of two related methodologies in this context, symmetry-adapted cluster-configuration interaction (SAC-CI) and time-dependent double-hybrid density functional theory (TD-DHDFT), is compared in detail for the calculation of absorption and fluorescence energies of small organic molecules and π-conjugated heteroaromatic compounds. Pragmatically, for the SAC-CI calculations the singles and doubles linked excitation operators are considered in the wave functions. On the other hand, for the TD-DHDFT calculations the linear-response Tamm–Dancoff formalism has been imposed. The considered DH density functionals include the approximations from both families of adjusted and non-adjusted models. Our numerical data reveal that of the tested adjusted DHs, B2-PLYP performs the best, while among the category of non-adjusted approximations the PBE0-DH functional outperforms others. Furthermore, the DH density functionals show deviations less than those obtained from SAC-CI method. Putting all the results together, the B2-PLYP and B2GP-PLYP functionals are found to be superior for overall performance. Altogether, the present contribution and recent efforts in this arena point out that besides the ground-state properties the DH approximations have also unquestionably entered into the field of excited-state calculations, where the DHDFT again comes into play and further evidence on the quality of the corresponding models is pronounced.

Low-Lying π* Resonances of Standard and Rare DNA and RNA Bases Studied by the Projected CAP/SAC-CI Method.

Low-lying π* resonance states of DNA and RNA bases have been investigated by the recently developed projected complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction (SAC-CI) method using a smooth Voronoi potential as CAP. In spite of the challenging CAP applications to higher resonance states of molecules of this size, the present calculations reproduce resonance positions observed by electron transmission spectra (ETS) provided the anticipated deviations due to vibronic effects and limited basis sets are taken into account. Moreover, for the standard nucleobases, the calculated positions and widths qualitatively agree with those obtained in previous electron scattering calculations. For guanine, both keto and enol forms were examined, and the calculated values of the keto form agree clearly better with the experimental findings. In addition to these standard bases, three modified forms of cytosine, which serve as epigenetic or biomarkers, were investigated: formylcytosine, methylcytosine, and chlorocytosine. Last, a strong correlation between the computed positions and the observed ETS values is demonstrated, clearly suggesting that the present computational protocol should be useful for predicting the π* resonances of congeners of DNA and RNA bases.

Corrigendum to: Quantum-chemical Ab Initio Calculations on the Donor–Acceptor Complex Pyridine–Borabenzene (C5H5N–BC5H5)

The adduct of borabenzene (C5H5B) and pyridine (C5H5N) was studied by means of quantum-chemical ab initio and time-dependent density functional theory calculations at different levels of theory. In the fully optimized structure (MP2/6-311++G**) of the free donor–acceptor complex (C2), the C–B–C angle amounts to 120.6°. The planes of the two aromatic rings enclose a torsion angle of ~40° with a barrier to rotation about the B–N bond of less than 3kcalmol–1 (1kcalmol–1=4.186kJmol–1). The highest computational level applied in this study (complete basis set limit, coupled cluster with single and double excitations (CCSD)) results in an energy associated with the reaction of borabenzene with pyridine of –52.2kcalmol–1. Natural bond orbital analyses were performed to study the bond between the borabenzene and the pyridine unit of the adduct. The UV-vis spectrum of the adduct was calculated employing time-dependent density functional theory methods and the symmetry-adapted cluster-configuration interaction method. Our calculated electronic excitation spectrum of the pyridine adduct as well as its spectrum of the normal modes qualitatively reproduce the characteristic features of the IR and the UV-vis spectra described by experimentalists and thus allows assignment of the observed absorption bands, which in part agree with those by other authors.

Coumarin-based donor–π–acceptor organic dyes for a dye-sensitized solar cell: photophysical properties and electron injection mechanism

The electronic structure and photophysical properties of five coumarin-based donor–π–acceptor (D–π–A)-type organic dyes for a dye-sensitized solar cell (DSSC) which were recently developed have been investigated using the time-dependent density functional theory and the symmetry-adapted cluster configuration interaction method. Theoretical calculations including the solvent effect in state-specific and linear-response scheme reproduced the experimental UV–Vis absorption spectra of these dyes satisfactorily. The π-spacers, thiophene and thiophene–phenylene mixed units, affect the planarity of the molecular structures which is relevant to the photophysical properties and charge polarization. Energy levels of the frontier orbitals and charge separation were analyzed, and the thiophene linker was found to be effective for the electron injection in DSSC. The adsorption of these dyes on the TiO2 anatase (101) surface and the electron injection mechanism were also investigated using a dye–(TiO2)38 cluster model employing PBE and TD-CAM-B3LYP calculations, respectively. The adsorption energies of these dyes were estimated to be ~14 kcal/mol, indicating strong adsorption of dye to a TiO2 surface by carboxylate group. The possible direct electron injection mechanism was suggested in the present coumarin-based D–π–A dyes in a dye–TiO2 interacting system.

Electronic spectra of azaindole and its excited state mixing: A symmetry-adapted cluster configuration interaction study.

Electronic structures of azaindole were studied using symmetry-adapted cluster configuration interaction theory utilizing Dunning's cc-pVTZ basis set augmented with appropriate Rydberg spd functions on carbon and nitrogen atoms. The results obtained in the present study show good agreement with the available experimental values. Importantly, and contrary to previous theoretical studies, the excitation energy calculated for the important n-π(∗) state agrees well with the experimental value. A recent study by Pratt and co-workers concluded that significant mixing of π-π(∗) and n-π(∗) states leads to major change in the magnitude and direction of the dipole moment of the upper state vibrational level in the 0,0 + 280 cm(-1) band in the S1←S0 transition when compared to that of the zero-point level of the S1 state. The present study, however, shows that all the four lowest lying excited states, (1)Lb π-π(∗), (1)La π-π(∗), n-π(∗), and π-σ(∗), cross each other in one way or another, and hence, significant state mixing between them is likely. The upper state vibrational level in the 0,0 + 280 cm(-1) band in the S1←S0 transition benefits from this four-state mixing and this can explain the change in magnitude and direction of the dipole moment of the S1 excited vibrational level. This multistate mixing, and especially the involvement of π-σ(∗) state in mixing, could also provide a route for hydrogen atom detachment reactions. The electronic spectra of benzimidazole, a closely related system, were also investigated in the present study.

Electronic spectra of oxygen containing polycyclic hydrocarbon cations and the protonated analogues.

The electronic transitions of 9-fluorenone FL(+) and 2,3,6,7-dibenzotropone DBT(+) cations were detected in 6 K neon matrices following a mass-selective deposition. The absorptions at 649.2 and 472.2 nm are assigned to the 2 (2)B1←X̃(2)A2 FL(+) and 2(2)A(')←X̃(2)A(') DBT(+) transitions. Absorption spectra of protonated 9-fluorenone H(+)-FL and 2,3,6,7-dibenzotropone H(+)-DBT have also been measured. Protonation of the oxygenated polycyclic aromatic hydrocarbons is carried out in a hot cathode source via in situ produced protonated ethanol. Vibrationally resolved absorptions commencing at 423.3 nm of H-FL(+) and two band systems of H-DBT(+) with origins at 502.4 and 371.5 nm are assigned to the 2(1)A(')←X̃(1)A(') electronic transition of 9-hydroxy-fluorenyl cation and 1 (1)A←X̃(1)A, 2 (1)A←X̃(1)A of 2,3,6,7-dibenzocycloheptenol cation. The assignments are based on vertical excitation energy calculations with time dependent density functional theory, symmetry adapted cluster configuration interaction, and MS-CASPT2 methods.

Structures and Photoelectron Spectra of Helium Nano Clusters

The ionization energies and photoelectron spectra of van der Waals (vdW) helium nano clusters (Hen) were studied in this work. Clusters with different numbers of helium atoms, in the range from n = 2 to n = 100, and belonging to different symmetry point groups were selected. Density functional theory (DFT) employing the CAM-B3LYP functional and the 6-31+G(d) basis set was used for optimizing the structures. Symmetry adapted cluster-configuration interaction (SAC-CI) methodology and the 6-31+G(3df) basis set were also used to calculate the ionization energies and their intensities. The calculated ionization energies and their intensities were used to simulate the photoelectron spectrum of each structure. It was found that the clustering of He atoms decreases the first ionization energy of the cluster compared to the isolated helium atom in the gas phase. The variation of the first ionization energies of the nanostructures were plotted versus their sizes and fitted into a mathematical equation. The simulated photoelectron spectra of the nano clusters were compared with each other comprehensively to investigate the change in the shape of the spectrum with the size of the cluster. The calculated ionization bands of each cluster were assigned using natural bonding orbital (NBO) analysis, and their changes with the size were studied. Also, it was studied how much the ionization processes are governed by the electron correlation, and the effect of the size on the electron correlation was examined.

Photo-assisted intersystem crossing: The predominant triplet formation mechanism in some isolated polycyclic aromatic molecules excited with pulsed lasers.

Naphthalene, anthracene, and phenanthrene are shown to have very long-lived triplet lifetimes when the isolated molecules are excited with nanosecond pulsed lasers resonant with the lowest singlet state. For naphthalene, triplet state populations are created only during the laser pulse, excluding the possibility of normal intersystem crossing at the one photon level, and all molecules have triplet lifetimes greater than hundreds of microseconds, similar to the behavior previously reported for phenylacetylene. Although containing 7-12 thousand cm(-1) of vibrational energy, the triplet molecules have ionization thresholds appropriate to vibrationless T1 states. The laser power dependences (slopes of log-log power plots) of the excited singlet and triplet populations are about 0.7 for naphthalene and about 0.5 for anthracene. Kinetic modeling of the power dependences successfully reproduces the experimental results and suggests that the triplet formation mechanism involves an enhanced spin orbit coupling caused by sigma character in states at the 2-photon level. Symmetry adapted cluster-configuration interaction calculations produced excited state absorption spectra to provide guidance for estimating kinetic rates and the sigma character present in higher electronic states. It is concluded that higher excited state populations are significant when larger molecules are excited with pulsed lasers and need to be taken into account whenever discussing the molecular photodynamics.

The low-lying singlet electronic excited states of ZrO2: A symmetry adapted cluster–configuration interaction (SAC–CI) study

The ground electronic state [X1A1(S0)] and nine low-lying singlet excited states [21A1(S2), 11A2(S3), 21A2(S6), 11B1(S4), 21B1(S7), 31B1(S11), 11B2(S1), 21B2(S5), and 31B2(S8) states] of ZrO2 were studied using SAC–CI theory. The geometries of the nine electronic excited states were optimized at the SAC–CI/def2-SVP, SAC–CI/def2-SVPD, and SAC–CI/LANL2TZ(f) levels. The vertical excitation energies and adiabatic excitation energies of the selected electronic excited states were calculated by single-point calculations at the SAC–CI/def2-TZVPPD and SAC–CI/LANL2TZ(f) levels. Stable C2v structures for the 11B2, 21B2, 31B2, and 11A2 states and stable Cs structures for the 11B1(A″), 31B1(A″), and 21A1(A′) states were determined. For comparison, the unrestricted density functional theory (UBPW91) was also applied to study the X1A1, 11A2, 11B1, and 11B2 states.

Projected CAP/SAC‐CI method with smooth Voronoi potential for calculating resonance states

The complex absorbing potential (CAP)/symmetry-adapted cluster-configuration interaction (SAC-CI) method has been combined with a smooth Voronoi potential, which was recently introduced in the extrapolation procedure, to locate π* resonance states of small- to medium-size molecules. Here, the projected CAP/SAC-CI method is combined with this potential and used to calculate the double-bond and heteroaromatic π* resonances of acetaldehyde, butadiene, glyoxal, pyridine, pyrazine, and furan. As observed in the pilot applications, the corrected η-trajectories provide a stable resonance energy and width or lifetime regardless of the size parameter (rcut ) of the smooth Voronoi potential. However, in general, the stabilization behavior of the trajectories is clearer for larger rcut values, which implies that the interaction of the CAP with the valence electrons is more advantageously addressed by a larger "cavity" size.

Photoelectron Spectroscopy and Ionic Fragmentation of OSeCl2 and Its Analogue OSCl2 under VUV Irradiation.

The electronic structure and the dissociative ionization of selenium oxychloride, OSeCl2, have been investigated in the valence region by using results from both photoelectron spectroscopy (PES) and synchrotron-based photoelectron photoion coincidence (PEPICO) spectra. The PES is assigned with the help of quantum chemical calculations at the outer-valence Green's function (OVGF) and symmetry adapted cluster/configuration interaction (SAC-CI) levels. The first energy ionization is observed at 11.47 eV assigned to the ionization of electrons formally delocalized over the Se, Cl, and O lone pair orbitals. Irradiation of OSeCl2 with photons in the valence region leads to the formation of OSeCl2(•+), OSeCl(+), SeCl2(•+), SeCl(+), and SeO(•+) ions. Furthermore, the inner shell Se 3p, Cl 2p, and Se 3s electronic regions of OSeCl2 together with S 2p, Cl 2p, and S 2s electronic regions of thionyl chloride, OSCl2, have been studied by using tunable synchrotron radiation. Thus, total ion yield spectra and the fragmentation patterns deduced from PEPICO spectra at the various excitation energies have been studied. Cl(+), O(•+), and Se(•+) ions appear as the most intense fragments in the OSeCl2 PEPICO spectra, like in the sulfur analogue OSCl2, whose photofragmentation is dominated by the Cl(+), O(•+), and S(•+) ions. Fragmentation processes in OSCl2 leading to the formation of the double coincidences involving atomic ions appear as the most intense in the PEPIPICO spectra.

Synthesis and Optical Properties of Imidazole- and Benzimidazole-Based Fused π-Conjugated Compounds: Influence of Substituent, Counteranion, and π-Conjugated System.

Fused π-conjugated imidazolium chlorides having hydrogen (1-Cl), octyloxy (2-Cl), N,N-dibutylamino (3-Cl), trifluoromethyl (4-Cl), and cyano (5-Cl) groups substituted on the benzene ring at the 2-position of imidazole were prepared. Counteranion exchanges from chloride to bis(trifluoromethanesulfonyl)imidate (2-TFSI) and tetrafluoroborate (2-BF4) were performed. The optical properties of these compounds (absorption and emission wavelengths, fluorescence quantum yield, and solvatochromism) were influenced by both the substituent and anion character, which was investigated by theoretical calculations using the density functional theory (DFT) and symmetry-adapted cluster-configuration interaction (SAC-CI) methods. Fused π-conjugated benzimidazolium chlorides having N,N-dibutylamino (6-Cl) and cyano (7-Cl) groups were also prepared to observe the different solvatochromic shifts.

Comparison between hybrid functionals free of adjustable parameters and symmetry-adapted cluster–configuration interaction for electronically excited states of organic compounds: TD-PBE0-1/3 is better than expected

Developing and benchmarking methodological approaches able to accurately predict the electronically excited states are major challenges for theoretical chemists. In this work, we analyze the performances of the hybrid density functionals based on Perdew, Burke, and Ernzerhof (PBE) with a single non-fitted parameter for Hartree–Fock (HF) exchange and without invoking to any fitting process for predicting the valence and Rydberg excitation energies of organic compounds in the framework of time-dependent density functional theory (TD-DFT). As a wave function theory-based approach in the context of excite states calculations, symmetry-adapted cluster–configuration interaction (SAC–CI) method including single- and double-linked excitation operators has been considered. Our test calculations show that the SAC–CI gives the best performance for Rydberg excited states, while for valence excited states the PBE hybrid functional with parameter 1/3 for HF exchange (PBE0-1/3) outperforms other methods. Overall, of the several combinations of functionals and parameters, the TD-PBE0-1/3 is found to offer the best performance with respect to others and its validity compared to SAC–CI has also been verified by computing low-lying excited states of a few molecules. From the viewpoint of compromising between accuracy and computational cost, these findings reveal that how nonempirical hybrid functionals are economical to model electronic excitation energies of various systems and still much better achievements can be obtained in this respect.

Modeling Molecular Systems at Extreme Pressure by an Extension of the Polarizable Continuum Model (PCM) Based on the Symmetry-Adapted Cluster-Configuration Interaction (SAC-CI) Method: Confined Electronic Excited States of Furan as a Test Case.

Novel molecular photochemistry can be developed by combining high pressure and laser irradiation. For studying such high-pressure effects on the confined electronic ground and excited states, we extend the PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (SAC-configuration interaction) methods to the PCM-XP (extreme pressure) framework. By using the PCM-XP SAC/SAC-CI method, molecular systems in various electronic states can be confined by polarizable media in a smooth and flexible way. The PCM-XP SAC/SAC-CI method is applied to a furan (C4H4O) molecule in cyclohexane at high pressure (1-60 GPa). The relationship between the calculated free-energy and cavity volume can be approximately represented with the Murnaghan equation of state. The excitation energies of furan in cyclohexane show blueshifts with increasing pressure, and the extents of the blueshifts significantly depend on the character of the excitations. Particularly large confinement effects are found in the Rydberg states. The energy ordering of the lowest Rydberg and valence states alters under high-pressure. The pressure effects on the electronic structure may be classified into two contributions: a confinement of the molecular orbital and a suppression of the mixing between the valence and Rydberg configurations. The valence or Rydberg character in an excited state is, therefore, enhanced under high pressure.

Dissociation, absorption and ionization of some important sulfur oxoanions (S2On2−n = 2, 3, 4, 6, 7 and 8)

In this work, a systematic theoretical study was performed on the dissociation, absorption and ionization of several important sulfur oxoanions (S2On2− (n=2, 3, 4, 6, 7 and 8)). ΔEelec (thermal corrected energy), ΔH° and ΔG° of the dissociation reactions of the oxoanions to their radical monoanions were calculated using combined computational levels of theories such as Gaussian-3 (G3) and a new version of complete basis set method (CBS-4M) in different environments including gas phase, microhydrated in gas phase and different solvents. Calculations showed S2O72− is the most stable anion against the dissociation to its radical monoanions (SO4−+SO3−). It was also found that S2O42− has more tendency to dissociate to its radical anions (SO2−+SO2−) compared to the other anions. The absorption spectra of the anions were also calculated using the time-dependent density functional theory (TD-DFT) employing M062X functional. The effect of microhydration and electrostatic field of solvent on the different aspects (intensity, energy shift and assignment) of the absorption spectra of these anions were also discussed. It was observed that both hydrogen bonding and electrostatic effect of water increases the intensity of the absorption spectrum compared to the gas phase. Effect of microhydration in shifting the spectra to the shorter wavelength is considerably higher than the effect of electrostatic field of water. Finally, several gas phase ionization energies of the anions were calculated using the symmetry-adapted cluster–configuration interaction methodology (SAC–CI) and found that the first electron detachment energies of S2O22−, S2O32− and S2O42− are negative. Natural bonding orbital (NBO) calculations were also performed to assign the electron detachment bands of the anions.

The low-lying singlet electronic excited states of TiO2: A symmetry adapted cluster-configuration interaction (SAC-CI) study

The ground electronic state (X1A1) and nine low-lying singlet electronic excited states (21A1, 31A1, 11A2, 21A2, 11B1, 21B1, 31B1, 11B2, and 21B2) of TiO2 were studied using SAC-CI theory. The geometries of the nine electronic excited states were optimized at the SAC-CI/def2-SVP and SAC-CI/def2-SVPD levels. The adiabatic excitation energies of the nine electronic excited states were obtained from single-point calculations at the SAC-CI/def2-TZVPD//SAC-CI/def2-SVPD and SAC-CI/def2-TZVPPD//SAC-CI/def2-SVPD levels. Stable Cs structures for the 11B1 (A″) and 31B1 (A″) states were determined in this study. For comparison, the X1A1, 11A2, 11B1, and 11B2 states were also studied using the unrestricted DFT theory (UBPW91) with the def2-SVP, def2-SVPD, def2-TZVPD, def2-TZVPPD, and aug-cc-pVTZ basis sets.

Electronic excitation spectra of doublet anion radicals of cyanobenzene and nitrobenzene derivatives: SAC-CI theoretical studies

Electronic ground and excited states of anion radicals of cyanobenzene derivatives: 1,3,5-tricyanobenzene, 1,2,4,5-tetracyanobenzene, and tetracyanoquinodimethane (TCNQ) and nitrobenzene derivatives: nitrobenzene, p-nitroaniline, m-nitroaniline, and o-nitroaniline were theoretically investigated by the symmetry adapted cluster-configuration interaction (SAC-CI) method, which is able to produce accurate theoretical electronic excitation spectra even for radical doublet states. For all the target molecules, the present calculations reproduced the positive electron affinities, which were mostly in good agreement with the experimental values, and their features, especially for TCNQ, were characterised by singly occupied molecular orbitals as well as the number of the electron-withdrawing terminal groups. The excitation energies and their oscillator strengths by the SAC-CI method were also in good agreement with the corresponding experimental UV/VIS/NIR spectra observed by one of the authors and other experimental evidences. Except for TCNQ, the present theoretical calculations were successful to first predict the existences of the forbidden (or very low intense) pure valence excited states in near-infrared region. The physical natures of the observed intense spectral bands were clarified and some new assignments to their electronic states were provided. By extending the present work, photo-related molecular designs of new functional electron acceptors may be challenged.

One-photon mass-analyzed threshold ionization (MATI) spectroscopy of pyridine: determination of accurate ionization energy and cationic structure.

Ionization energies and cationic structures of pyridine were intensively investigated utilizing one-photon mass-analyzed threshold ionization (MATI) spectroscopy with vacuum ultraviolet radiation generated by four-wave difference frequency mixing in Kr. The present one-photon high-resolution MATI spectrum of pyridine demonstrated a much finer and richer vibrational structure than that of the previously reported two-photon MATI spectrum. From the MATI spectrum and photoionization efficiency curve, the accurate ionization energy of the ionic ground state of pyridine was confidently determined to be 73,570 ± 6 cm(-1) (9.1215 ± 0.0007 eV). The observed spectrum was almost completely assigned by utilizing Franck-Condon factors and vibrational frequencies calculated through adjustments of the geometrical parameters of cationic pyridine at the B3LYP/cc-pVTZ level. A unique feature unveiled through rigorous analysis was the prominent progression of the 10 vibrational mode, which corresponds to in-plane ring bending, and the combination of other totally symmetric fundamentals with the ring bending overtones, which contribute to the geometrical change upon ionization. Notably, the remaining peaks originate from the upper electronic state ((2)A2), as predicted by high-resolution photoelectron spectroscopy studies and symmetry-adapted cluster configuration interaction calculations. Based on the quantitatively good agreement between the experimental and calculated results, it was concluded that upon ionization the pyridine cation in the ground electronic state should have a planar structure of C(2v) symmetry through the C-N axis.

An efficient computational scheme for electronic excitation spectra of molecules in solution using the symmetry-adapted cluster-configuration interaction method: the accuracy of excitation energies and intuitive charge-transfer indices.

Solvent effects on electronic excitation spectra are considerable in many situations; therefore, we propose an efficient and reliable computational scheme that is based on the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the polarizable continuum model (PCM) for describing electronic excitations in solution. The new scheme combines the recently proposed first-order PCM SAC-CI method with the PTE (perturbation theory at the energy level) PCM SAC scheme. This is essentially equivalent to the usual SAC and SAC-CI computations with using the PCM Hartree-Fock orbital and integrals, except for the additional correction terms that represent solute-solvent interactions. The test calculations demonstrate that the present method is a very good approximation of the more costly iterative PCM SAC-CI method for excitation energies of closed-shell molecules in their equilibrium geometry. This method provides very accurate values of electric dipole moments but is insufficient for describing the charge-transfer (CT) indices in polar solvent. The present method accurately reproduces the absorption spectra and their solvatochromism of push-pull type 2,2'-bithiophene molecules. Significant solvent and substituent effects on these molecules are intuitively visualized using the CT indices. The present method is the simplest and theoretically consistent extension of SAC-CI method for including PCM environment, and therefore, it is useful for theoretical and computational spectroscopy.

Electron momentum spectroscopy of NF3

The electronic structure of nitrogen trifluoride was investigated by combining the high-resolution electron momentum spectroscopy with the high-level calculations. The experimental binding energy spectra and the momentum distributions of each orbital were compared with the results of Hartree—Fock, density functional theory (DFT), and symmetry-adapted-cluster configuration-interaction (SAC-CI) methods. SAC-CI and DFT-B3LYP with the aug-cc-pVTZ basis set can well reproduce the binding energy spectra and the observed momentum distributions of the valence orbitals except 1a2 and 4e orbitals. It was found that the calculated momentum distributions using DFT-B3LYP are even better than those using the high-level SAC-CI method.