Theoretical Molecular Double-Core-Hole Spectroscopy of

ARTICLE pubs.acs.org/JPCA

Theoretical Molecular Double-Core-Hole Spectroscopy of Nucleobases Osamu Takahashi,*,† Motomichi Tashiro,‡,§ Masahiro Ehara,‡,§,|| Katsuyoshi Yamasaki,† and Kiyoshi Ueda^ †

Department of Chemistry, Hiroshima University, Higashi-Hiroshima 739-8526, Japan Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki 444-8585, Japan § Research Center for Computational Science, Okazaki 444-8585, Japan JST, CREST, Sanboncho-5, Chiyoda-ku, Tokyo 102-0075, Japan ^ Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

)

‡

bS Supporting Information ABSTRACT: Double-core-hole (DCH) spectra have been investigated for pyrimidine, purine, the RNA/DNA nucleobases, and formamide, using the density functional theory (DFT) method. DCH spectra of formamide were also examined by the complete-active-space self-consistent-field (CASSCF) method. All possible single- and two-site DCH (ssDCH and tsDCH) states of the nucleobases were calculated. The generalized relaxation energy and interatomic generalized relaxation energy were evaluated from the energy differences between ssDCH and single-core-hole (SCH) states and between tsDCH and SCH states, respectively. The generalized relaxation energy is correlated to natural bond orbital charge, whereas the interatomic generalized relaxation energy is correlated to the interatomic distance between the core holes at two sites. The present analysis using DCH spectroscopy demonstrates that the method is useful for the chemical analysis of large molecular systems.

1. INTRODUCTION The environmental dependence of the core electron binding energy is known as a chemical shift. Measurement of this chemical shift by X-ray photoelectron spectroscopy (XPS) is a well-established method for chemical analysis.1 There are two main effects that can cause a change in the core-electron binding energy. The first effect is a so-called initial-state-bonding shift. Charge polarization due to a change in the bonding interaction of a given molecule in the ground state can lead to a shift in the core-level binding energy. This shift is included in the HartreeFock (HF) core orbital energy. The second effect is a final-state-relaxation shift, in which the polarizability of external ligands can lead to different shielding or screening contributions of the core hole. It can be related to the difference between the ionization potential (IP) and the HF core orbital energy.2 Hereafter, we call the final-staterelaxation shift the “relaxation energy”. About 25 years ago, the double-core-hole (DCH) states were theoretically investigated by Cederbaum et al.35 They analyzed double ionization potentials (DIPs) of DCH states and demonstrated that DIPs of DCH states are more sensitive to the chemical environment around atoms with core holes than IPs of single-core-hole (SCH) states. These theoretical works on DCH states were followed by that of Ågren et al.6 Although DCH spectroscopy was shown theoretically to be powerful for chemical analysis, experimental detection of DCH states is extremely difficult because of their small cross sections with single-photon r 2011 American Chemical Society

spectroscopy. Therefore, few observations have been reported until recently.7 Studies of DCH states have been revived by the appearance of new light sources, namely, intense free-electron lasers (FELs)8,9 in the X-ray spectral region. This new trend was invoked by Santra et al.,10 who proposed that DCH states can be formed and identified by X-ray two-photon photoelectron spectroscopy (XTPPS) with FELs. Following this theoretical proposal, Cryan et al.,11 Fang et al.,12 and Berrah et al.13 demonstrated the feasibility of XTPPS with a Linac coherent light source,9 an FEL facility in the United States, using the simplest molecules N2 and CO. In parallel, Eland et al.14 and Lablanquie et al.15 extensively investigated the DCH states of many small molecules, using multielectron coincidence detection combined with conventional synchrotron radiation as the light source. The DCH states in a molecule can be classified into two groups; the first group includes the DCH states at a single site (ssDCH), and the second one includes the DCH states at two sites (tsDCH). Most of the observations described above are on ssDCH states, except for the latest work by Berrah et al.,13 who clearly identified the tsDCH state on CO. According to the seminal works by Cederbaum et al.,3,4 probing tsDCH states is Received: June 23, 2011 Revised: September 25, 2011 Published: September 26, 2011 12070

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The Journal of Physical Chemistry A

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Figure 1. Optimized structures obtained at the MP2/cc-pVTZ level of theory: (a) pyrimidine, (b) uracil, (c) cytosine, (d) thymine, (e) purine, (f) adenine, and (g) guanine. The numbering of atoms is defined.

the key to enhanced sensitivity for chemical analysis by DCH spectroscopy. On the theoretical side, Tashiro et al. extensively investigated the DCH states of many small closed-shell16 and open-shell17 molecules by the complete-active-space self-consistent-field (CASSCF) method. They also proposed that the interatomic relaxation energy, which is a key parameter for sensing the chemical environment, can be obtained by the measurement of SCH IPs and tsDCH DIPs. More recently, Kryzhevoi et al. investigated SCH and DCH states of para-, meta-, and ortho-aminophenol molecules, using fourth-order and second-order algebraic diagrammatic construction [ADC(4) and ADC(2)] methods and demonstrated that these isomers might be distinguishable by DCH spectroscopy.18 The DCH spectroscopy described above has so far been limited to K-shell DCH states of molecules that include firstrow elements. For molecules including the second-row elements, Ohrendorf et al.19 investigated DCH states K2, K1L1, and L2 of SiH4 and SiF4 using the ADC(2) method, and the present authors extended their study to include four molecules of the form SiX4 (X = H, F, Cl, and CH3),20 using both CASSCF and density functional theory (DFT) methods. An L-shell DCH spectroscopy study was also demonstrated for H2S, SO2, and CS2 using multielectron coincidence detection with a synchrotron radiation source.21

It should be noted that L-shell or any other inner-shell double holes, except for K-shell DCHs, can be produced by core corecore-type Auger processes such as KLL of the second-row elements, and indeed, a significant number of works on such Auger final DCH states have been reported for molecules that include heavy elements.2227 In this sense, DCH spectroscopy by Auger spectroscopy, which attracted a great deal of attention during the 1970s and 1980s, is now enjoying a renaissance thanks to the development of new experimental facilities and techniques for investigating the energetics of double core holes. These earlier investigations during the 1970s and 1980s were, however, limited to the creation of double holes at a single site except for the K-shell core. The addition of another dimension to these measurements in the form of the energies of tsDCH states opens up new possibilities, as discussed by Cederbaum et al.35 and Tashiro et al.16 In our previous theoretical DCH spectroscopy of small molecules,14,16,17 we used the CASSCF method to calculate the DIPs of DCH states. The computational cost, however, increases dramatically for large systems, so that, in practice, CASSCF calculations of the DCH states of large molecules are very difficult. In our latest article,20 we thus demonstrated that the DFT method can be used for investigating the DCH states for large systems under some restrictions. DFT calculations have been widely applied to estimate the SCH IPs for various systems.2830 12071

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The Journal of Physical Chemistry A In the present study, we extend our theoretical studies of DCH spectroscopy14,16,17,20,21 to seven nucleobases as one an application for larger molecular systems, namely, pyrimidine, uracil, cytosine, thymine, purine, adenine, and guanine. Cytosine, thymine, and uracil are pyrimidine derivatives, whereas adenine and guanine are purine derivatives. In DNA, the purines adenine and guanine form base pairs with the pyrimidines thymine and cytosine, through hydrogen bonds. In RNA, the complement of adenine is uracil instead of thymine. These pairs are used to store genetic information and play significant roles in molecular biology. Despite the experimental difficulty of handling these molecules because of their low vapor pressures at room temperature, the SCH states of these molecules have been studied extensively both experimentally and theoretically because of their general interest and importance.3138 To the best of our knowledge, however, their DCH states have not been investigated so far. Noting a nice demonstration by Kryzhevoi et al. of the structure sensitivity of DCH spectroscopy on aminophoenol isomers,18 it is of particular interest to explore the structure and chemical sensitivity of DCH spectroscopy for the present nucleobases. As a benchmark small compound for biomolecules, we first investigated the K-shell DCH states of formamide using the CASSCF and DFT methods. Formamide is the simplest molecule containing a peptide bond, a key functional group in peptides and proteins. We then extended the DFT calculations to the Kshell DCH state of the nucleobases. We performed chemical analysis with DCH spectroscopy by calculating the SCH IPs, ssDCH DIPs, tsDCH DIPs, generalized relaxation energies, and generalized interatomic relaxation energies.

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(PD91)46 functionals of Perdew and Wang were used for the correlation-exchange functional in the DFT calculations. The generalized gradient approximation (GGA) exchange and correlation functionals of Perdew, Burke, and Ernzerhof (PBE)47 were also used. For example, the functional combination PD86 PD91 means the use of PD86 as the exchange functional and PD91 as the correlation functional. The PD86PD91, PD91 PD91, and PBEPBE functionals were examined in the calculation of formamide. All DFT calculations were conducted using the StoBe-deMon program.48

3. DCH SPECTROSCOPY FOR CHEMICAL ANALYSIS We first briefly review DCH spectroscopy for the ssDCH and tsDCH states following refs 33 and 16. The SCH IP is given by IP ¼ εa RCða1 Þ

ð1Þ

where εa is the HartreeFock energy of orbital a (a is a 1s core orbital) and RC(a1) is the generalized relaxation energy, which includes orbital relaxation and electron correlation. For the Kshell IPs discussed here, the effect of orbital relaxation is much larger than that of electron correlation. Analogously, the DIP of a state with two core vacancies, a1b1, is given by DIP ¼ εa εb RCða1 b1 Þ þ REða1 b1 Þ

ð2Þ

1 1

where RC(a b ) is the generalized relaxation energy of the DCH state and RE(a1b1) is the repulsion-exchange energy of the two core holes. The DCH generalized relaxation energy can be decomposed into three terms, RCða1 b1 Þ ¼ RCða1 Þ þ RCðb1 Þ þ ERCða1 b1 Þ

2. COMPUTATIONAL DETAILS The vertical SCH and DCH ionizations were considered in the present work, and the molecular geometries of the target molecules were calculated by geometry optimization at the MP2/ccpVTZ level of theory using the Gaussian 03 suite of programs.39 The target molecules in the present study, except for formamide, are illustrated in Figure 1, along with the corresponding atom numbering definitions. For cytosine and guanine, some tautomers and rotamers coexist in the gas phase.35,36 In the present work, only the most stable rotamer was studied for each molecule. The optimized structures of our target molecules are listed with the Cartesian coordinates in the Supporting Information. Ab initio calculations of the SCH and DCH states of the formamide molecule were performed using the CASSCF method.40 Computational details were described in ref 16. We used the active space comprising all occupied molecular orbitals (except for the 1s orbitals of atoms other than H) and all valence unoccupied orbitals containing large contributions from different atomic p orbitals with core occupancy being fixed. More explicitly, sizes of the active space in the present study consist of 18 electrons distributed in 15 orbitals (12 a0 and 3 a00 orbitals in the Cs point group). The correlation-consistent polarized valence triple-ζ (cc-pVTZ) basis sets of Dunning41,42 were employed in all CASSCF calculations. The CASSCF calculations were performed with the Molpro 2008 quantum chemistry package.43 DFT calculations of the SCH and DCH states were performed by the ΔKS method,28 that is, allowing full relaxation of the corehole states to compute the relaxed IPs and DIPs. The basis set dependence of the DFT calculations was examined for the K-shell DCH states with the IGLO-III44 and cc-pCVTZ basis sets. The gradient-corrected exchange (PD86)45 and correlation

ð3Þ 1 1

where ERC(a b ) is the generalized excess relaxation energy, representing a nonadditive contribution to the DCH relaxation energy. In the case where two core holes are created on the same atomic site, ERC(a2) measures local properties of a core ionized atom. In the case where two core holes are created on different atomic sites, ERC(a1b1) can be called an interatomic generalized relaxation energy IRC(a1b1) and can measure the environment around the atoms involved. In experiments, IP in eq 1 and DIP in eq 2 can be measured. We thus introduce the measurable quantity ΔEða1 b1 Þ ¼ DIPða1 b1 Þ IPða1 Þ IPðb1 Þ

ð4Þ

Note that this energy difference is essentially the same as a quantity called the Auger parameter for the Auger final doublehole states,24 which are identical to ssDCH states in our definition. From eqs 14, we have the excess generalized relaxation energy in the case of ssDCH states as ERCða2 Þ ¼ REða2 Þ ΔE1 ða2 Þ

ð5Þ

and the interatomic generalized relaxation energy in the case of tsDCH states as IRCða1 b1 Þ ¼ REða1 b1 Þ ΔE2 ða1 b1 Þ

ð6Þ

To avoid confusion, the symbol ΔE is written as ΔE1 for ssDCH states and ΔE2 for tsDCH states, following Tashiro et al.16 An equation similar to eq 5 was used for the Auger final DCH states (e.g., in Cavell and Sodhi26), whereas eq 6 was introduced by Tashiro et al.16 as a key equation of tsDCH spectroscopy. These 12072



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equations mean that one can experimentally evaluate ERC(a2) and IRC(a1b1) from the energy difference between the DIP and IPs if one knows the holehole repulsion energy, RE. The repulsion energy RE can be calculated straightforwardly. If the two holes are in the same nondegenerate orbital a2, which corresponds to the ssDCH states, then the repulsion energy RE(a2) is given by the Coulomb repulsion integral Vaaaa ¼ hað1Þ að2Þjað1Þ að2Þi Z 1 ¼ að1Þ að2Þ að1Þ að2Þ dτ1 dτ2 r12

Table 1. SCH IPs and Their Constituent Parts (in eV) for Formamide As Calculated with the CASSCF/cc-pVTZ and DFT/IGLO-III Methodsa

ð7Þ

In particular, if a is a 1s orbital, the analytical formula is given by 2

REða Þ ¼ ð2

5=2

=3πÞðZ 2

3=2

Þ

ð8Þ

where Z is the atomic number of the atom with the core holes.3 If Z in eq 8 is substituted with 1.037Z, the agreement between the Coulomb repulsion integral Vaaaa from ab initio calculations and that from eq 8 is improved.16 This was confirmed also for the present target molecules. If the two holes are in different 1s core orbitals, which corresponds to tsDCH states, then the analytical formula for the holehole repulsion energy, RE(a1b1), is approximated as REða1 b1 Þ ¼ 1=r

ð9Þ 3

where r is the holehole distance in atomic units. We briefly note the interrelation between the excess generalized relaxation energy, ERC(a2), for ssDCH creation and the generalized relaxation energy, RC(a1), for SCH creation. Within second-order perturbation theory,3,2527 assuming that the relaxation energy is much larger than the correlation energy, for the double vacancy creation on the same orbital, we have RCða2 Þ ¼ 4RCða1 Þ,

ERCða2 Þ ¼ 2RCða1 Þ

ð10Þ

This gives RCða1 Þ ¼ ERCða2 Þ=2 ¼ ½REða2 Þ ΔEða2 Þ=2

CASSCF

DFT1b

DFT2b

DFT3b

MP2c

experimentd

ε(C)

309.23

309.35

309.35

309.35

IP

294.71

294.93

294.24

RC(C)

14.52

14.42

15.11

293.91

294.03

294.44

15.44

15.20e

ε(N)

423.83

423.94

423.94

423.94

IP RC(N)

406.47 17.36

406.33 17.60

405.51 18.43

405.17 18.77

ε(O)

559.60

559.69

559.69

559.69

IP

537.67

539.16

538.23

RC(O)

21.93

20.53

21.45

406.87 16.96e

406.36

537.85

537.85

537.6

21.84

21.75e

a

Atom with a core hole indicated in parentheses. Calculations by the MP2/TZP method from a previous work are also listed. b Different functional combinations: DFT1, PD86PD91; DFT2, PD91PD91; DFT3, PBEPBE. c Reference 6. d Reference 49. e To estimate RC, orbital energies at the CASSCF/cc-pVTZ level were used.

can happen when DCHs are created at adjacent two atoms.16,18 The amplitude of the IRC in this case includes the information about the environment of these two atoms, such as the electrondonating character of the attached atoms and/or functional groups. On the other hand, a negative IRC means that the creation of core hole a1 suppresses the relaxation of the creation of core hole b1 and vice versa. This usually happens when two core holes are created at distant atoms.16,18 The amplitude of the IRC in this case depends on both the distance between the two holes and atoms and any functional groups between them. In the next section, we explore how the observables ΔE1 and ΔE2 and the extractable generalized relaxation parameters RC and IRC can be correlated to the chemical and structural information of the target molecules. For simplicity, the term “generalized” is suppressed in the rest of the article.

4. RESULTS AND DISCUSSION ð11Þ

This means that one can estimate the generalized relaxation energy RC(a1) from the experimentally accessible energy difference ΔE1(a2), if the holehole repulsion energy RE(a2) is known, and thus, one can evaluate the final-state relaxation energy separately from the initial-state bonding shift. Such separation is useful for understanding the chemical implications of the shifts. It should be noted that sorting out the initial-state effect from the final-state relaxation based on the comparison of the SCH ionization energies and double ionization energies was discussed previously for Auger final DCH states.2227 The present discussion on ssDCH states overlaps significantly with that given for Auger final DCH states in the 1970s and 1980s. Despite the extensive works on ssDCH states, studies on tsDCH states are still limited. The creation of DCH states, each at a different atomic site, probes the chemical environment of the two atomic sites more sensitively and, in particular, provides some information about the bonding between them, as well as the bonding of these atoms with others.3,4,16 As noted above, the interatomic generalized relaxation energy, IRC(a1b1), is a measure of such information. To be specific, a positive IRC means that the creation of core hole a1 enhances the relaxation of the creation of core hole b1 and vice versa. This concerted relaxation

4.1. Formamide. Formamide is regarded as a prototype target molecule for DCH spectroscopy of biomolecules because it contains one C, one N, and one O atom in the molecule, and the DCH states of this molecule have been studied at some levels of theory by Ågren et al.6 We calculated the SCH IPs and DCH DIPs of 1s core holes in formamide by means of the CASSCF and DFT methods. In the DFT calculations, three functionals were examined, namely, PD86PD91, PD91PD91, and PBEPBE. Table 1 summarizes the results obtained for the SCH IPs, together with experimental values49 and the previous theoretical values reported by Ågren et al.6 The relaxation energies (RC) calculated by eq 1 are also included. In Table 2, the results for the DCH DIPs are provided, along with the MP2 results of Ågren et al.6 The ab initio values of holehole repulsion energies RE, the relaxation energies ERC/2, and the interatomic relaxation energies IRC, evaluated by eqs 2, 5, and 6, respectively, are also listed. In the following tables and accompanying discussions, the DCH states are symbolized with the atoms having 1s vacancies; for example, IRC(CN) means the interatomic relaxation energy of the DCH states with core holes on C and N atoms. There are six DCH states in formamide. The SCH IPs calculated by the CASSCF/cc-pVTZ method show reasonable agreement with the experimental SCH IPs and 12073



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Table 2. DCH DIPs and Their Constituent Parts (in eV) for Formamide As Calculated with the CASSCF/cc-pVTZ and DFT/IGLO-III Methodsa CASSCF

DFT1d

DFT2d

DFT3d

MP2e

DIP(CC)

656.64

656.70

655.37

654.74

656.82

ΔE1(CC)

67.22

66.85

66.89

66.92

67.94

RE(CC)b

95.39

95.39

95.39

95.39

95.39

ERC/2(CC)

14.08

14.27

14.25

14.23

13.72

DIP(NN) ΔE1(NN)

891.05 78.11

889.56 76.89

888.00 76.98

887.32 76.98

892.61 79.89

RE(NN)b

112.17

112.17

112.17

112.17

112.17

ERC/2(NN)

17.03

17.64

17.60

17.59

16.14

DIP(OO)

1163.61

1165.59

1163.86

1163.07

1164.31

ΔE1(OO)

88.27

87.27

87.39

87.37

89.11

RE(OO)b

128.98

128.98

128.98

128.98

128.98

ERC/2(OO)

20.35

20.85

20.79

20.80

19.93

DIP(CN) (singlet) DIP(CN) (triplet)

709.84 709.92

709.48 709.53

707.98 708.03

707.30 707.35

709.35

ΔE2(CN)c

8.66

8.22

8.22

8.22

8.55

RE(CN)b

10.03

10.03

10.03

10.03

10.03

IRC(CN)c

1.37

1.81

1.81

1.82

1.48

DIP(CO) (singlet)

842.28

843.99

842.37

841.67

841.12

DIP(CO) (triplet)

842.36

843.74

842.09

841.40

ΔE2(CO)c

9.90

9.91

9.89

9.91

9.08

RE(CO)b IRC(CO)c

11.98 2.08

11.98 2.06

11.98 2.09

11.98 2.07

11.98 2.9

DIP(NO) (singlet)

952.54

953.23

951.49

950.76

952.51

DIP(NO) (triplet)

952.58

953.25

951.51

950.78

ΔE2(NO)c

8.40

7.74

7.75

7.74

RE(NO)b

6.21

6.21

6.21

6.21

6.21

IRC(NO)c

2.19

1.53

1.53

1.53

2.34

8.55

a

Calculations with the MP2/TZP method from a previous work are also listed. b Values obtained by ab initio calculations with the cc-pVTZ basis set. c Singlet state. d Different functional combinations: DFT1, PD86PD91; DFT2, PD91PD91; DFT3, PBEPBE. e Reference 6.

the previous MP2 IPs: The IPs were calculated as 294.71 eV (C 1s), 406.47 eV (N 1s), and 537.67 eV (O 1s) in comparison with the experimental values of 294.44, 406.36, and 537.6 eV, respectively. The SCH IPs calculated by the DFT methods depend slightly on the selection of functionals. Good agreement was obtained at the C K-edge with the PD91PD91 functionals, at the N K-edge with the PD86PD91 functionals, and at the O K-edge with the PBEPBE functionals. A functional dependence of the SCH IPs was also observed in the previous study.28 To estimate the SCH IPs correctly, one should select the proper functional combinations for each energy region. For the DCH states, the CASSCF and DFT DIPs also show reasonable agreement: the average deviations are 0.43 eV for PD86PD91, 1.15 eV for PD91PD91, and 1.85 eV for PBE PBE functional. The present results are also comparable to those of the previous MP2 calculations:6 The average deviation is 0.13 eV. It should be emphasized that the quantities in DCH spectroscopy, such as the energy difference ΔE in eq 4, the relaxation energy ERC/2 in eq 11, and the interatomic relaxation energy IRC in eq 6, obtained by the analysis described in the previous section, do not depend on the selection of functionals significantly, as shown in a previous work.20 This is because these

quantities are obtained by subtracting the effects included in the ground and SCH or DCH states equivalently, so that the numerical errors in the IPs originating in the DFT functionals are canceled. Based on the results for formamide, the PD86 PD91 functionals with the IGLO-III basis sets were used in the calculations of the nucleobases. We also confirmed that the IGLO-III basis set is sufficiently flexible to estimate the SCH and DCH states by DFT calculations in a previous work.20 The relativistic effect in the SCH IPs and DCH DIPs is not expected to be significant in the present systems, where the K-shell SCH and DCH states of the first-row atoms are concerned.16 Note that the relativistic effect is also partly canceled in the ΔE, ERC/2, and IRC values. Therefore, we conclude that the related physical properties in DCH spectroscopy can be calculated reasonably with the DFT method. As noted in the previous section, the relaxation energy can be obtained from the ssDCH DIP and SCH IP values determined experimentally. We demonstrate this using the CASSCF values. The ERC/2 values calculated by eq 5 are 14.08, 17.03, and 20.35 eV for the ssDCH states with two core holes at the C, N and O atoms, respectively (see Table 2). These values show reasonable agreement with the RC values in Table 1, where the respective values are 14.52, 17.36, and 21.93 eV. This means that the relaxation energy can be estimated from experiments. Another issue related to the ssDCH states is that the ERC/2 values increase with the nuclear charge Z of the core holes. It is natural that the relaxation energy ERC/2 increases with an increase in the number of electrons. This trend was discussed by Tashiro et al.16 as well. For tsDCH states, the sign of IRC depends on the chemical environment around the two core holes. More specifically, from the CASSCF calculations, IRC(CN) and IRC(CO) are positive, with values of 1.37 and 2.08 eV, respectively, whereas IRC(NO) is negative at 2.19 eV. The DFT method and the previous MP2 calculations also show the same trend. In the former case of a positive IRC, the atoms with a core hole are bonded directly, whereas, in the latter case of a negative IRC, the N and O atoms are separated by the C atom. The positive and negative signs of the IRC can be interpreted by considering the increase and decrease in the valence electron density around the core holes.16 In the case where the two core holes are in adjacent atoms, other atoms play the role of electron donors and enhance the relaxation of the DCH on both core-hole sites. On the other hand, in the case where the two core holes are separated, creation of the core hole on one site has already drawn the electron density from the atoms or functional groups between them and thus reduces the possibility of relaxation due to the creation of the second hole on the other site. The same trend was also obtained for triatomic molecules such as CO2 and N2O, as discussed by Tashiro et al.16 In Figure 2a, the DCH DIPs of formamide are shown. The ssDCH states are accessible using multielectron coincidence detection with conventional synchrotron radiation sources,14,15,21 although the cross sections to create ssDCH states are very small. The tsDCH states, on the other hand, are difficult to observe, and another type of spectroscopy might be more effective. XTPPS spectroscopy10 using a new X-ray FEL light source could allow access to the tsDCH states in molecules, as demonstrated by Berrah et al.13 In Figure 2b, the calculated kinetic energies of the first and second photoelectrons of formamide in the XTPPS spectroscopy are displayed in a two-dimensional (2D) plot. The photon energy in XTPPS is assumed to be 1 keV. The given assignment (AB), with 12074



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Figure 2. (a) K-shell DIPs of formamide calculated by the DFT/IGLO-III method. (b) Calculated kinetic energies of the first and second photoelectrons of DCH states of formamide in XTPPS. The photon energy was assumed to be 1 keV.

A and B being C, N, and/or O, of the point in Figure 2b means that the first electron is emitted from site A and the second electron is from site B. All of the data points are well-separated in this figure. In principle, it is possible to measure this type of 2D XTPPS spectrum experimentally, using multielectron coincidence detection or a covariance technique.50 It should be noted, however, that, experimentally, one measures only the energies of electrons and does not distinguish whether the electron is produced in the first or second step. As a result, in the experimental correlation map, one expects not only the points at (E1, E2) but also the points at (E2, E1) for a pair of electrons with energies E1 and E2. As a result, the point AB once appears again close to the point BA. It is of interest to see the charge redistribution accompanied by DCH creation. The electron density differences of the valence electrons between the ground and DCH states of formamide are shown in Figure 3. The 2D contour maps illustrate the change in charge density in the mirror plane, except for the 1s electron density of the core holes. In the blue region, valence electron density increases, whereas it decreases in the red region. In all cases, the electron density flow occurs into the atoms with core holes, indicating that the valence electrons are attracted by the core holes, as expected. On the other hand, the electron density around the atoms without core holes decreases. For example, the electron densities on the H, N, and O atoms in the ssDCH(CC) state decrease, contributing to the orbital relaxation. It is also worth noting that the decreases of the density on the O atom by ssDCH(NN) creation and on the N atom by ssDCH(OO) creation are larger than those on the C atom. This finding suggests that the charges on the O and N atoms are more free to move than those on the C atom. The increase of the valence electron density of the core-hole atoms for the tsDCH states is less than that for the ssDCH states, simply because the core-hole positive charge per site for tsDCH states is one-half that for ssDCH states. Singlet and triplet energy splitting on different atomic sites was also examined for the tsDCH states. Singlet and triplet energy splitting at the tsDCH states should be small because the origin of this splitting is the exchange integral between two well-separated core holes.6,19 The two core holes are strongly localized, so it is expected that the exchange integral should be quite small. In the CASSCF results, the energy splittings are quite small for all cases, namely, 0.08 eV for the tsDCH(CN,CO) states and 0.04 eV for the tsDCH(NO) state, depending on the distance of two core

holes. The DFT calculations also provided small values except for the tsDCH(CO) state. The present DFT calculation of the triplet DCH states is based on the unrestricted method, so that spin contamination might appear, and for the tsDCH(CO) states, severe spin contamination occurs. 4.2. Nucleobases. In the previous section, we confirmed the applicability of the DFT method to DCH spectroscopy using the formamide molecule. Next, we performed DFT calculations of the SCH IPs and DCH DIPs of the nucleobases, namely, three pyrimidine derivatives, two purine derivatives, and pyrimidine and purine themselves. These molecules are too large to investigate the DCH states with the CASSCF method. Thus, in the present study, we applied only DFT calculations to them. The calculated SCH IPs of the nucleobases are summarized, along with the experimental values, in Table 3. Experimental measurements of the IPs of nucleobases using XPS have been performed in both the gas32,3537 and solid34 phases. In the solidphase experiments, the work function and some other effects, with a magnitude of about 5 eV, are involved in the IPs, so that these values cannot be compared with the calculated values directly.31 Most of our DFT values show reasonable agreement with the experimental values in the gas phase. Some previously calculated SCH IPs are also listed in Table 3. Takahata et al.31 calculated the SCH states of pyrimidine and purine derivatives, and Saha et al.33 reported the SCH IPs of adenine and purine at the DFT level of theory. Comprehensive studies of the SCH states for nucleobases were described by Prince and co-workers in several articles. Specifically, Plekan et al.32 investigated those of thymine and adenine, Feyer et al.35 examined tautomerism in cytosine and uracil, and Plekan et al.36 investigated tautomerism in guanine. The theoretical approach used in these reports was the ADC(4) level of theory. Bolognesi et al.37 studied the SCH states of pyrimidine and halogenated pyrimidine at the DFT level. The present calculated values are consistent with the previous calculated values. The results for the DCH DIPs of uracil are presented in Tables 4 and 5, together with the relaxation energies, RC = ERC/ 2, and the interatomic relaxation energies, IRC, which were evaluated using eqs 11 and 6, respectively. The ab initio values of holehole repulsion energies, RE, are also included in the tables. The DCH states of the nucleobases have never been investigated. For other molecules, the calculated DCH DIPs are listed in the Supporting Information. All singlet and triplet energy splittings 12075



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Figure 3. Valence electron density differences between the ground and DCH states of formamide for DCHs at the (a) CC, (b) CN, (c) CO, (d) NN, (e) NO, and (f) OO sites. Blue (red) region indicates an increase (decrease) of the valence electron density.

for the tsDCH states are quite small, and these values are omitted from these tables. We first examine the gross features of DIPs. The calculated Kshell DIPs of the seven nucleobases are shown in Figure 4. Each thick line indicates a group of lines for DCH states. In the case of pyrimidine, purine, and adenine, there are five groups of lines. These correspond to the ssDCH(CC) and ssDCH(NN) states

and the tsDCH(CN), tsDCH(CC0 ), and tsDCH(NN0 ) states. The tsDCH(CC0 ) and tsDCH(NN0 ) states have two vacancies on the same kind of atoms at the different sites. This new class of tsDCH states, which is absent in formamide, appears because pyrimidine, purine, and adenine contain multiple C and N atoms. In the case of cytosine and guanine, there are eight groups of lines. Because these molecules have multiple C and N atoms and 12076



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Table 3. SCH IPs (in eV) for Nucleobases As Calculated with the DFT/IGLO-III Method and the PD86PD91 Functionalsa core hole

previous theoretical work(s)

this work

Table 3. Continued core hole

experiment

Pyrimidine C2

292.48b

292.4

292.48b

C4

292.08b

292.1

292.08b

C5

291.09b

291.2

291.09b

C6 N1

292.08b 405.14b

292.1 405.3

292.08b 405.23b

N2

405.14b

405.3

405.23b

C2

295.54,c 295.07d

295.1

295.4c

C4

294.41,c 294.12d

294.1

294.4c

C5

290.86,c 291.14d

291.1

291.0c

C6

292.78,c 292.85d

292.9

292.8c

N1

406.92,c 407.14d

407.3

406.8c

N3 O7

406.50,c 406.67d 537.41,c 537.66d

406.9 537.8

406.8c 537.6c

O8

537.70,c 537.33d

537.4

537.6c

293.5

293.9c

C4

c

293.03, 293.11

d

292.9

293.2c

C5

c

290.47, 290.71

d

290.3

290.6c

C6

c

291.62, 292.32

d

291.5

291.7c

N1

c

404.58, 406.34

d

404.4

404.5c

N3 N7

c

d

404.77, 404.11 405.97,c 406.13d

404.6 406.1

404.5c 406.1c

O8

539.43,c 536.45d

539.4

539.4c

C2

294.75,d 295.36e

294.7

295.2e

C4

d

293.79, 294.19

e

293.7

294.2e

C5

d

290.95, 290.67

e

291.0

291.0e

C6

d

292.27, 292.29

e

292.3

292.3e

C9 N1

d

e

291.18, 290.95 406.91,d 406.80e

291.2 407.0

291.0e 406.7e

N3

406.56,d 406.52e

406.7

406.7e

O7

d

537.45, 537.46

e

537.5

537.3e

O8

d

537.25, 537.24

e

537.2

537.3e

C2

291.43,f 291.71g

292.0

C4

291.96,f 292.73g

292.6

C5

290.85,f 291.58g

291.5

C6 C8

291.05,f 291.71g 292.02,f 292.67g

291.6 292.5

N1

403.29,f 404.84g

404.9

N3

403.61,f 405.19g

405.2

N7

403.47,f 405.09g

405.1

N9

405.29,f 407.16g

407.2

C2

291.66,d 291.94e

291.6

292.5e

C4 C5

d

e

292.15, 292.47 290.96,d 291.19e

292.5 291.0

292.5e 291.0e

C6

292.64,d 292.96e

292.1

292.5e

C2

293.75,c 293.72d

Thymine

Purine

Adenine

this work

experiment

C8 N1

e

292.13, 292.66 404.23,d 404.27e

292.1 404.5

292.5e 404.4e

N3

404.37,d 404.40e

404.3

404.4e

N7

d

e

404.78, 404.99

404.8

404.4e

N9

d

e

406.74, 406.63

406.9

406.7e

d

e

405.8

405.7e

d

N10

405.86, 405.62

C2

293.74,d 293.87h

Guanine

Uracil

Cytosine

previous theoretical work(s)

293.5

293.8h

C4 C5

h

292.20, 291.59 290.68,d 291.05h

291.2 292.1

292.1h 290.9h

C6

293.30,d 293.97h

d

293.6

293.8h

C8

c

h

291.79, 292.10

291.9

292.1h

N1

d

h

406.42, 406.33

406.6

406.3h

N3

d

h

404.72, 404.13

404.6

404.5h

N7

d

h

404.53, 406.66

404.6

404.5h

N9

d

h

406.65, 404.42

407.0

406.3h

d

h

406.3 536.9

406.3h 536.7h

N11 O10

406.46, 406.14 536.71,d 536.76h

a

Previous theoretical works and experimental values in the gas phase also included. Labels for the core atoms are given in Figure 1. For cytosine and guanine, IPs of the most stable rotamer are listed. b Reference 37. c Reference 35. d Reference 31. e Reference 32. f Reference 38. g Reference 33. h Reference 36.

only one O atom, new groups of lines for (CO), (NO), and (OO) appear in addition to (CC0 ), (CC), (CN), (NN0 ), and (NN). In the case of uracil and thymine, which have multiple C, N, and O atoms, there are nine groups of lines, for (CC0 ), (CC), (CN), (CO), (NN0 ), (NN), (NO), (OO0 ), and (OO). All of these groups are well-separated from the other groups. The closest groups are the tsDCH(NN0 ) and tsDCH(CO) states, whose energy separation is about 10 eV. We have examined the 2D XTPPS spectra for all these molecules. As an example, the calculated kinetic energies of the first and second photoelectrons of uracil are illustrated in the 2D XTPPS spectrum in Figure 5. Similar plots for other molecules are in the Supporting Information. Again, the photon energy is assumed to be 1 keV, and the given assignment (AB), where A and B are C, N, and/or O, of a point in Figure 5 means that the first electron is emitted from site A and the second electron is from site B. There are 12 islands (groups of points) in the 2D spectrum of Figure 5. All of the islands are well-separated in this 2D spectrum. In Figure 6, we enlarge each of the islands so that the components (points) of each island in Figure 5 are visible. As typical examples, (CC), (CC0 ), (CN), and (NC) are shown. In Figure 6a, four points for (CC) corresponding to the four ssDCH(CC) states are located along a line of slope ∼1. The difference in IPs of the SCH(C2) and SCH(C5) states is 4.0 eV. This difference can be directly seen as the energy difference of the two points (C2, C2) and (C5, C5) along the horizontal axis of Figure 6a. The difference in DIPs of the ssDCH(C2, C2) and ssDCH(C5, C5) states is 8.4 eV. This difference results in a difference of 4.4 eV between the two points (C2, C2) and (C5, C5) along the vertical axis of Figure 6a. This example illustrates that XTPPS for the ssDCH states does not improve the chemical sensitivity much. However, based on XTPPS for ssDCH states, one can disentangle the initial-state-bonding shift and the relaxation 12077



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Table 4. ssDCH DIPs and Their Constituent Parts (in eV) for Uracil As Calculated with the DFT/IGLO-III Method and the PD86PD91 Functionals

a

core holes

DIP (eV)

ΔE1 (eV)

RE(a2) a (eV)

ERC/2 (eV)

C2, C2

654.9

64.7

94.8

15.1

C4, C4

652.9

64.7

94.8

15.1

C5, C5

646.5

64.4

94.8

15.2

C6, C6

650.2

64.5

94.8

15.1

N1, N1 N3, N3

889.7 888.6

75.0 74.9

111.6 111.6

18.3 18.4

O7, O7

1161.3

85.7

128.5

21.4

O8, O8

1160.2

85.4

128.5

21.5

Values obtained by ab initio calculations with the cc-pVTZ basis set.

Table 5. tsDCH DIPs and Their Constituent Parts (in eV) for Uracil As Calculated with the DFT/IGLO-III Method and the PD86PD91 Functionals core holes DIP (eV) ΔE2 (eV) R (Å) RE(a1b1) a (eV) IRC (eV)

a

C2, C4

594.8

5.6

2.509

5.7

0.1

C2, C5

591.7

5.5

2.851

5.1

0.4

C2, C6

593.3

5.4

2.429

5.9

0.5

C4, C5

591.8

6.7

1.453

9.9

3.2

C4, C6

592.8

5.9

2.423

5.9

0.0

C5, C6 N1, N3

591.7 819.7

7.8 5.5

1.348 2.301

10.7 6.3

2.9 0.8

O7, O8

1080.1

4.9

4.572

3.1

1.8

C2, N1

709.3

6.9

1.385

10.4

3.5

C2, N3

708.7

6.7

1.380

10.4

3.7

C2, O7

840.0

7.1

1.214

11.9

4.8

C2, O8

837.7

5.2

3.584

4.0

1.2

C4, N1

706.9

5.5

2.796

5.1

0.4

C4, N3 C4, O7

707.5 837.0

6.5 5.1

1.404 3.612

10.3 4.0

3.8 1.1

C4, O8

838.6

7.1

1.219

11.8

4.7

C5, N1

704.6

6.2

2.377

6.1

0.1

C5, N3

703.4

5.4

2.386

6.0

0.6

C5, O7

834.0

5.1

4.065

3.5

1.6

C5, O8

834.1

5.6

2.384

6.0

0.4

C6, N1

706.6

6.4

1.370

10.5

4.1

C6, N3 C6, O7

704.9 835.5

5.2 4.9

2.679 3.541

5.4 4.1

0.2 0.8

C6, O8

835.6

5.4

3.565

4.0

1.4

N1, O7

951.4

6.2

2.286

6.3

0.1

N1, O8

950.0

5.3

4.013

3.6

1.7

N3, O7

950.8

6.2

2.294

6.3

0.1

N3, O8

950.4

6.1

2.279

6.3

0.2

Values obtained by ab initio calculations with the cc-pVTZ basis set.

energy following the recipe given in section 3 and gain insight into the chemical shift. Specifically, the difference between the first (higher-energy) and second (lower-energy) electrons is equal to the energy difference ΔE1 given by eq 4. (See Tashiro et al.16) The holehole repulsion energy RE can be obtained by ab initio calculations with the cc-pVTZ basis set. Then, using eq 11, the relaxation energy RC for SCH creation at each of these

Figure 4. DCH DIPs of seven nucleobases calculated by the DFT/ IGLO-III method. DCH states assigned in the same DCHs are connected with vertical dashed lines.

Figure 5. Calculated kinetic energies of the first and second photoelectrons of the DCH DIPs states of uracil in XTPPS. The photon energy was assumed to be 1 keV.

four different C sites can be extracted. We found that the relaxation energies are almost the same for these four carbon sites (see Table 4) and, thus, that the differences in the chemical shifts observed by XPS are mostly attributable to the differences in the initial-state-bonding shifts. In the 2D XTPPS plots of Figure 6b, there are 12 points made of six tsDCH(CC0 ) states. The energy spread of these points is approximately 4 eV for both axes, and thus, again, one can consider that XTPPS does not provide a gain in chemical sensitivity even for the tsDCH states. However, based on XTPPS for tsDCH states, following the recipe given in section 3, one can gain the insight into the structure and/or the chemical environment around the specific bonds. That is, the energy difference ΔE2 between the first and second electrons is directly related to the 12078



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Figure 6. Enlargement of Figure 5: (a) two holes at the same carbon site; (b) two holes at two different carbon sites; (c,d) two holes at carbon and nitrogen sites, with the first ionization from the (c) carbon and (d) nitrogen atoms. Detailed plots of Figure 5 for (a) ssDCH(C), (b) tsDCH(C,C0 ), (c) tsDCH(C,N) with first ionization from C, and (d) tsDCH(N,C) with first ionization from N.

difference of the holehole repulsion energy, RE = 1/r, and the interatomic relaxation energy IRC, ΔE2 = 1/r IRC (see eq 6). Strictly speaking, one can separate RE and IRC only by knowing in advance the structure and the assignments of the data points in XTPPS data, say, with the help of ab initio calculations, as shown here. We assume that we have the experimental XTPPS data as in Figure 6b and are trying to assign the peaks, having structural information obtained by ab initio calculations, as given in the Supporting Information. For molecules with the size of uracil, ΔE2 is still dominated by 1/r rather than IRC. Comparing six values of ΔE2(CC0 ) as given in Table 5, one can see that ΔE2(C4C5) and ΔE2(C5C6) are significantly larger than the other values, and thus, one can expect that the pairs C4 and C5 and C5 and C6 are directly bonded. This expectation is, of course, consistent with our knowledge of the assignments. Upon extracting the value of the IRC using the ab initio structure information, one finds that IRC(C4C5) and IRC(C5C6) are definitely positive, at ∼3 eV. Again, this finding is in accordance with the fact that C4 and C5 and C5 and C6 are next to one another, according to the general rule described in section 3. The definite negative IRC(C2C5) of 0.5 eV is consistent with the fact that C2 and C5 are the most distant pair among the four C atoms, as discussed later in terms of general trends. The examples of CN in Figure 6c and NC in Figure 6d might be the most interesting. The IPs of the two nitrogen atoms, SCH(N1) and SCH(N3), in uracil are almost degenerate. The difference is 0.4 eV according to the present calculations and

practically 0 according to the experiments, as seen in Table 3. Thus, they cannot be resolved by conventional XPS. Accordingly, the data points in Figure 6d, where the N core hole is created first, do not spread along the horizontal axis. They cannot be resolved even with ssDCH spectroscopy because not only the chemical shifts but also the relaxation energies are almost the same for these two SCH(N1) and SCH(N3) states, as seen in Table 4. However, they can be resolved by tsDCH spectroscopy, making a core hole, for example, on C6 next to N1, as clearly seen in Figure 6c. This is a clear example of the significant enhancement in chemical sensitivity of tsDCH spectroscopy. This increase in sensitivity stems from the fact that, in tsDCH spectroscopy, one can vary ΔE2, or the holehole repulsion energy 1/r and the interatomic relaxation energy IRC, by selecting a different pair of sites for core-hole creation. In the rest of the article, we discuss the general trends of the scattered components as given in Figure 6. We first focus on the ssDCH states of the nucleobases. In Figure 7, the energy difference ΔE1 and the relaxation energy ERC/2 are summarized as a function of natural bond orbital (NBO) charge. Tashiro et al. showed that the ERC/2 values have an interrelation with the chemical environment by plotting them against the atomic number Z.16 We investigated another aspect in the present study. There are three layered structures in this figure, and the gaps between pairs of layers are about equal. This corresponds to the Z dependence of ERC/2 described by Tashiro et al. In other words, ERC/2 reflects the nuclear charge on the core hole, or the number 12079



Figure 7. (a) Energy difference ΔE1 and (b) relaxation energy ERC/2 for ssDCH states calculated by eq 11 as a function of NBO charge.

of total electrons around the core hole. There is a small distribution along the vertical axis for each atom with core holes because of varying chemical environment. For the DCH(CC) states, the NBO charges are widely distributed in the range from 0.6 to 0.8 because of the chemical environment around the C atoms with core holes. The DCH state that is located at the lowest NBO charge of 0.6 corresponds to the C atom of the methyl group in thymine. For the ssDCH(NN) and ssDCH(OO) states, the ERC/2 value decreases as the NBO charge becomes more negative. This means that, if Z is the same, the relaxation increases with a decrease in electron density. In Figure 8, the energy difference ΔE2 and the interatomic relaxation energy IRC are displayed as functions of the interatomic bond distance r. Both ΔE2 and IRC decrease as the bond distance r increases. In the present system of nucleobases, the IRCs are distributed in the wide range from a negative value of about 2 eV to a positive value of 5 eV. One can see three islands in both figures, and the tsDCH states can be categorized with respect to the bond distance r. An island around r ≈ 2.2 Bohr represents the tsDCH states with atoms of core holes bonded directly, an island around r ≈ 4.2 Bohr corresponds to the tsDCH states with atoms of core holes bonded through one another atom, and the third island corresponds to the group of tsDCH states whose core holes are separated by two or more atoms. As seen in formamide and also in triatomic molecules studied in a previous work,16 the IRC values of the first group, whose atoms with core holes are bonded directly, are positive. This is because all other parts contribute to the relaxation. For the second group, the IRC values are close to 0. Depending on the surrounding chemical bonds, the IRC values can be negative or positive. As a general trend, the IRC value decreases with increasing distance

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Figure 8. (a) Energy difference ΔE2 and (b) interatomic relaxation energy IRC for tsDCH states calculated by eq 6 as a function of the distance between the core holes, r.

between the two centers. As a result, the third group has negative IRC values. The above-described general features of ERC/2 and IRC reflect the chemical environments around the core holes and, therefore, indicate the potential application of DCH spectroscopy for sensitive chemical analysis, as described for the specific example uracil.

5. SUMMARY In the present study, theoretical DCH spectroscopy has been applied to biochemical systems, namely, the RNA/DNA nucleobases, pyrimidine, and purine, using DFT calculations. Prior to the study of the nucleobases, we examined the reliability of DFT calculations for DCH spectroscopy for C, N, and O core holes by calculating the SCH IPs and DCH DIPs of formamide with both the CASSCF and DFT methods. The present DFT results were in reasonable agreement with CASSCF and other previous calculations. Furthermore, the theoretical 2D XTTPS spectrum of formamide was presented and discussed in detail. The DFT results for the SCH IPs of the nucleobases showed reasonable agreement with the experimental values. The possible ssDCH and tsDCH states of the nucleobases were calculated, and the relaxation energies and interatomic relaxation energies were evaluated. The ssDCH state probes the chemical environment around the atom with core holes, whereas the tsDCH state probes the chemical bonding in different ways. As an example, the 2D XTTPS spectrum of uracil was discussed in detail. Specifically, we showed that the relaxation energies and the interatomic relaxation energies can be extracted from the 12080


The Journal of Physical Chemistry A experimental 2D XTTPS spectrum. In particular, we demonstrated that the core holes of the same atomic species that are not discernible by the SCH IPs or ssDCH DIPs can be separately probed using the chemical sensitivity of the tsDCH states. Using all of the data on the nucleobases studied here, we examined the general trends of the relaxation energy, ERC/2, and the interatomic relaxation energy, IRC. In particular, we showed that the NBO charge and the ERC/2 value in the ssDCH states are related and that the interatomic relaxation energies IRC can be grouped by interatomic bond distance. These general characteristics are useful for the chemical analysis of large systems such as biologically relevant molecules. Experimental 2D XTPPS studies are in progress for some of the molecules studied in the present theoretical work.

’ ASSOCIATED CONTENT

bS Supporting Information. Optimized structure parameters of formamide, pyrimidine, uracil, cytosine, thymine, purine, adenine, and guanine at the MP2/cc-pVTZ level of theory. Scatter plots of DCH DIPs of our target nucleobases as a function of the kinetic energies of the first and second electrons (photon energy is assumed to be 1 keV). Single- and two-site DCH DIPs, energy differences ΔE1 and ΔE2, excess and interatomic relaxation energy ERC/2 and IRC (in eV) for our target nucleobases as calculated with DFT/IGLO-III methods using the PD86PD91 functionals. This material is available free of charge via the Internet at http:// pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel.: +81-82-424-7497. Fax: +81-82-424-0727.

’ ACKNOWLEDGMENT The authors thank K. C. Prince for helpful discussions and suggestions on the manuscript. O.T. acknowledges support from the Cooperative Research Program of “Network Joint Research Center for Materials and Devices” and from a Grant-in-Aid for Scientific Research from JSPS of Japan. M.E. acknowledges the support from JST-CREST and Grants-in-Aid for Scientific Research from JSPS and MEXT of Japan. K.U. acknowledges support from the Budget for “Promotion of X-ray Free Electron Laser Research” from MEXT, from Management Expenses Grants for National Universities Corporations from MEXT, from Grants-in-Aid for Scientific Research from JSPS, and from the IMRAM research program. The authors thank the Information Media Center at Hiroshima University for the use of a grid with high-performance PCs and the Research Center for Computational Science, Okazaki, Japan, for the use of a Fujitsu PRIMEQUEST server. ’ REFERENCES (1) Siegbahn, K.; Nordling, C.; Fahlman, A.; Nordberg, R.; Hamrin, K.; Hedman, J.; Johansson, G.; Bergmark, T.; Karlsonn, S.; Lindgren, I.; Lindberg, B. ESCA-Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy; North-Holland Publishing Company: Amsterdam, 1966. (2) St€ohr, J. NEXAFS Spectroscopy; Springer-Verlag: Berlin, 1992. (3) Cederbaum, L. S.; Tarantelli, F.; Sgamellotti, A.; Schirmer, J. J. Chem. Phys. 1986, 85, 6513.

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