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Theoretical Investigation of Molecular Properties of the First Excited State of the Phenoxyl

Radical

Chi-Wen Cheng, Yuan-Pern Lee, and Henryk A. Witek*

Institute of Molecular Science and Department of Applied Chemistry, National Chiao Tung UniVersity, 30010 Hsinchu, Taiwan

ReceiVed: NoVember 28, 2007; In Final Form: December 29, 2007

A theoretical study of molecular, electronic, and vibrational properties of the first excited state of the phenoxyl radical, A2B

2, is presented. The calculated molecular geometries, vertical and adiabatic excitation energies, and harmonic vibrational frequencies are compared with analogous results obtained for the ground state. The calculated excitation energies correspond well to experimental data. The harmonic vibrational frequencies of the A2B

2and the ground state are similar except for modes involving the vibrations of the CO bond.

Introduction

The phenoxyl radical (C6H5O) has been a subject of intensive experimental and theoretical investigations over a long period of time.1-7This situation can be primarily attributed to a very important role that this radical plays in combustion and biological processes.8,9A considerable amount of information has been collected on the vibrational,5ESR,10and electronic7 properties of C6H5O. The ground state of C6H5O, denoted as X2B

1, is a doublet with an unpaired electron localized almost entirely in theπ orbitals of the benzene ring.5,10No experimental data is available for the molecular structure of the radical. Theoretical calculations5,6,11-14show that the molecule has the C2Vsymmetry with approximately double CO bond and a ring structure intermediate between aromatic and quinoid.5Almost a complete set of the ground state vibrational frequencies has been determined experimentally15 using resonance Raman experiments,4,16-18gas-phase UV photoelectron spectroscopy,19 and matrix-isolation polarized FTIR spectroscopy.6Harmonic vibrational frequencies of the ground state were calculated by many authors.5,6,11-13,20The lowest optically active electronic state of C6H5O is B2A2; it is located at approximately 2.0 eV above the ground state. The computed oscillator strength for the X2B

1f B2A2transition is very small, which is consistent with very weak signal in the UV/vis spectrum.7,21The optimized geometry for this state was given by Liu et al.14and harmonic vibrational frequencies, by Johnston et al.21Next excited states, C2B

1and D2A2, were observed at 3.1 and 4.2 eV, respectively.7 Theoretical predictions suggest that D2A

2is overlapping with another unobserved electronic state of symmetry2B

1, which can be explained by a very small calculated oscillator strength of the latter state. (Note that the states B2A

2and D 2A2 were erroneously quoted as B2A

1and D2A1in refs 7 and 15.22) The highest observed electronic state of the phenoxyl radical, E2B

1, is located at approximately 6.0 eV. All these observed states correspond toπ-π* electronic transitions.

In this paper we present a theoretical study of the lowest electronically excited state of the phenoxyl radical, A2B

2, which is located at approximately 1.1 eV above the ground state.7,15,19 Because the transition X 2B

1 f A 2B2 is optically dipole-forbidden, little is known about this state. It was first detected in a gas-phase ultraviolet photoelectron spectroscopy

experi-ment19at 1.06 eV. Subsequently, it was observed at 1.10 eV in a polarized FTIR study7for C

6H5O isolated in cryogenic argon matrices. Unfortunately, the signal intensitysoriginating most probably from vibronic couplingswas too small to allow for a successful characterization of the A 2B

2 state. The vertical excitation energy for the A2B

2state was determined theoreti-cally by several authors.7,11,14,21,23-26The most accurate estima-tions (1.03 eV with UB3LYP/cc-pVTZ7 and 1.11 eV with UPBE/6-31(2+,2+)G(d,p)26) are obtained with time-dependent density functional theory (TDDFT). The optimized geometry of the phenoxyl radical in the A2B

2state was presented by Liu et al. at the UMP2/6-31G* level of theory.14

We present here the following properties of the phenoxyl radical in the A2B

2state: vertical excitation energies, adiabatic excitation energies, optimized geometries, and harmonic vibra-tional frequencies. The results are obtained using wave function and density based quantum chemical techniques. Along with the vibrational frequencies for C6H5O, we also present analogous data obtained for the isotopically substituted isomer, C6D5O. Our main motivation for presenting these results is a perspective of accurate experimental determination of molecular and optical properties of the A2B

2state of the phenoxyl radical using the cavity ringdown absorption spectroscopy.27,28 We hope to present such a study in the near future.

Computational Details

The molecular model of phenoxyl radical is shown in Figure 1. Following the previous ground state studies,5,7 we orient the molecule in the yz plane with the CO bond located on the z-axis. For both studied electronic states, the assumed molecular symmetry point group is C2V. This choice is confirmed later by the calculated harmonic vibrational frequencies. The orientation of the molecule as described above allows for identifying the C2Vsymmetry operations as follows: the C2axis is the z-axis, theσVplane is the xz plane, and theσ′Vplane is the yz plane. The chosen orientation also allows for labeling the molecularσ orbitals using the a1and b2irreps, and the molecular π orbitals, using the a2and b1irreps. In the chosen reference frame, the symmetry of the ground state is described as a doublet B1and the symmetry of the first excited state, as a doublet B2. The presented energies, geometries, and vibrational frequen-cies have been calculated using correlated quantum chemical * Corresponding author. E-mail: hwitek@mail.nctu.edu.tw.

10.1021/jp711267w CCC: $40.75 © 2008 American Chemical Society Published on Web 02/28/2008

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techniques: the complete active space self-consistent field (CASSCF) method, complete active space second-order per-turbation theory29,30(CASPT2), and density functional theory (DFT), and a set of four basis sets: cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ.31,32For the multireference wave-function-based calculations, we have used the MOLPRO program.33DFT and TDDFT calculations have been carried out using the Gaussian package.34In principle, DFT is a ground-state theory. However, it can also be formulated for excited states.35Gunnarsson and Lundqvist argued36that the validity of the Kohn-Sham scheme can be naturally extended to the energetically lowest electronic state in each of the symmetries with the same universal exchange-correlation functional. It was subsequently shown that this straightforward generalization works only if the electronic state in the non-interacting case reduces to a single Slater determinant.37Because, in many cases, the electronic nature of the excited states can be described well only by a multideterminantal wave function, it can be difficult to apply the technique of Gunnarsson and Lundqvist in a straightforward manner in a general case. Fortunately, the wave function of the first excited state of C6H5O is very well represented by a single Slater determinant and DFT can be applied for calculations on this state. We have found that the SCF optimization performed for the A2B

2state of the phenoxyl radical converged toward a local minimum in the orbital rotation space; i.e., all the unoccupied one-electron energy levels lie higher than all the occupied levels. The total energy of the global minimum in the orbital rotation space is approximately 1 eV lower; it corresponds to the ground state of the phenoxyl radical. All our DFT calculations, for both the ground and excited states, have used the same B3LYP functional38,39 together with the unrestricted Kohn-Sham formalism.40We have also success-fully used the Kohn-Sham ground state formalism to determine the vertical excitation energies for lowest excited states in each spatial or spin symmetry subspaces. The complete active space (CAS) in the CASSCF and CASPT2 calculations is constructed using all valenceπ orbitals (two of symmetry a2and five of symmetry b1) and one or two orbitals corresponding to the lone pairs on the oxygen atom (one of symmetry a1 and one of symmetry b2). The two resultant active spaces, (0a1, 2a2, 5b1, 1b2) and (1a1, 2a2, 5b1, 1b2), correlate nine and eleven active electrons, respectively. The (0a1, 2a2, 5b1, 1b2) active space has been used to optimize the geometry of both studied electronic

states of the phenoxyl radical, to calculate the vertical and adiabatic A2B

2r X2B1excitation energies, and to determine harmonic vibrational frequencies. The larger active space, (1a1, 2a2, 5b1, 1b2), has been used to determine the vertical excitation

energies for the lowest doublet and quartet electronic states in each symmetry. The augmentation with an additional a1orbital has been necessary to describe properly the lowest2A

1and4A1 states of the phenoxyl radical.

Results

(a) Electronic and Geometrical Structure of the A 2B 2 State. The optimized CASPT2 and DFT geometrical parameters

for the phenoxyl radical in the X2B

1and A2B2electronic states are given in Table 1. We show the well-studied structure of the ground state together with the results obtained for the excited state A2B

2to facilitate the comparison of structural changes between these two states. The presented results constitute at the moment the most accurate theoretical estimations of the equilibrium structure for both studied states of C6H5O. A compilation of previously calculated equilibrium bond lengths and angles for the ground state is given in Supporting Informa-tion (Table S). The atom numbering used in the definiInforma-tion of geometrical parameters is shown in Figure 1. The two most prominent structural differences observed between the structures corresponding to these two electronic states are (i) increased length of the CO bond in the state A2B

2and (ii) different shape of the six-member carbon ring. For the ground state, the equilibrium distance between the carbon and oxygen atoms corresponds to a weak double CO bond. Compare the calculated values of 1.255 Å (CASPT2/aug-cc-pVTZ) and 1.252 Å (DFT/ UB3LYP/aug-cc-pVTZ) with the experimental values of 1.215 Å for acetone, 1.205 Å for formaldehyde, 1.191 Å for cyclo-propanone, 1.202 Å for cyclobutanone, 1.225 Å for p-benzo-quinone, 1.216 Å for acetaldehyde, and 1.202 Å in acetic acid.41,42For the first excited state, the calculated length of the carbon-oxygen bond is similar to single CO bond. Compare the calculated values of 1.332 Å (CASPT2/aug-cc-pVTZ) and 1.321 Å (DFT/UB3LYP/aug-cc-pVTZ) with the experimental values of 1.364 Å for phenol, 1.377 Å for hydroquinone, 1.343 Å for formic acid, 1.361 Å for acetic acid, 1.362 Å for furan, 1.427 Å for methanol, 1.411 Å for dimethyl ether, 1.446 Å for oxetane, and 1.420 Å for ethanedial.41,43In the benzene molecule the equilibrium distance between the adjacent carbon atoms is equal to 1.397 Å.41Upon the substitution of one of the hydrogen atoms by some functional group, this regular pattern is somewhat perturbed. This perturbation has been usually neglected in the procedure of experimental determination of the equilibrium structure.44For example, the experimental equilibrium structures of phenol and aniline both assume a regular hexagon model for the benzene ring with average CC distance of 1.398 and 1.392 Å, respectively.41,44Recent experimental investigation45 of the molecular structure of phenol shows that in fact the CC bond distances may differ noticeably (in the ground state the r0 values are 1.383, 1.402, and 1.399, and in the S1state, they are 1.442, 1.452, and 1.422 Å). Similar information can be accessed directly from calculations. For phenol, the three unique CC bond lengths calculated using the DFT/B3LYP/6-31G(2df,p) com-putational scheme are 1.396, 1.393, and 1.392 Å, and for aniline, the analogous values are 1.402, 1.390, and 1.393 Å.41 For phenoxyl radical in the ground state, this perturbation is much stronger. The calculated CASPT2/aug-cc-pVTZ equilibrium CC bond lengths are 1.448, 1.379, and 1.408 Å. The corresponding values obtained with DFT/UB3LYP/aug-cc-pVTZ are 1.448, 1.371, and 1.405 Å. This bond distance pattern is structurally Figure 1. Molecular structure (C2V) of the phenoxyl radical in the X

2B

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similar to that one observed experimentally42for p-benzoquinone (1.477, 1.322, and 1.477 Å), which can be associated with an alternating chain of a single-double-single CC bonds. Chipman et al. described5the heavy-atom skeleton of the phenoxyl radical in the ground state as intermediate between aromatic and quinoid. In contrast with the ground state, the structure of the carbon ring in the first excited state, A 2B

2, is regular with similar length of all carbon-carbon bonds (1.402, 1.394, and 1.395 Å using CASPT2/aug-cc-pVTZ and 1.405, 1.387, and 1.389 Å using DFT/UB3LYP/aug-cc-pVTZ). Similarly, the calculated CCC angles are much closer to 120°than for the ground state. The structure of the carbon ring can then be described as almost aromatic with little quinoid character. Similar conclusion can be drawn from the previously published UMP2 results; however, this study14 seems to underestimate the length of the CO bond in the ground state and overestimate it in the A2B

2state. The difference between the geometrical structures of the phenoxyl radical in the ground and the first excited states may be compared to the difference between the experimental structures of p-benzoquinone and hydroquino-ne.42,43The more aromatic character of the benzene ring in the A2B

2state can be anticipated from theπ orbitals energy diagram shown in Figure 2. The energy pattern of theπ orbitals in the A2B

2state is similar to that in benzene, whereas for the X2B2 state, the discrepancy is much larger. Moreover, for A2B

2, the pxorbital of oxygen strongly dominates the lowestπ orbital of

the b1 symmetry and has only small contribution to other orbitals, whereas for X2B

2, it contributes significantly to almost allπ orbitals of the b1symmetry.

The electronic structure of the ground state and the first excited state of the phenoxyl radical and the corresponding

transition between these two states can be described adequately within the framework of molecular orbital theory. We want to stress here that this is an unusual situation because in most cases the electronic structure of radicalssespecially in excited elec-tronic statessrequires a multireference description. Before defining the Slater determinants corresponding to both wave functions, we describe chemically important molecular orbitals (MOs). We consider as such seven π orbitals, two MOs of symmetry a2and five MOs of symmetry b1, and twoσ orbitals, being the a1 and b2 linear combinations of the lone electron pairs on the oxygen atom. The remaining occupiedσ molecular orbitalsstwelve of symmetry a1and seven of symmetry b2s have considerably lower energy, and they remain doubly occupied in all important Slater determinants. To define the chemical character of the seven lowestπ orbitals we compare their one-electron energies with the weighted average of the 2p energies of carbon and oxygen (dotted horizontal line in Figure 2). The actual value of such an average obtained from atomic calculations is approximately equal to -0.10 hartree for all employed basis sets. Therefore, MOs with  < -0.10 are classified as bonding (π) and MOs with  > -0.10, as antibonding (π*). The orbitals with ≈ -0.10 are referred to as nonbonding (π°). One-electron energy diagrams of the π orbitals for both electronic states of C6H5O are shown in Figure 2. A schematic representation of the π orbitals as the linear combinations of the atomic pxorbitals is given in Figure 3. For

the ground state, the three lowestπ orbitals, two of symmetry b1and one of symmetry a2, are strongly bonding whereas the singly occupied b1orbital is nonbonding. For the first excited state, the four lowestπ orbitals, three of symmetry b1and one

TABLE 1: Geometrical Parameters for the X2B

1and A2B2States of the Phenoxyl Radical Optimized Using CASPT2 and DFT/B3LYPa

X2B 1

cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ

CASPT2 B3LYP CASPT2 B3LYP CASPT2 B3LYP CASPT2 B3LYP

rC1O 1.259 1.256 1.266 1.258 1.254 1.251 1.255 1.252 rC1C2 1.461 1.455 1.461 1.455 1.448 1.449 1.448 1.448 rC2C3 1.391 1.380 1.393 1.380 1.379 1.371 1.379 1.371 rC3C4 1.420 1.412 1.421 1.412 1.408 1.405 1.408 1.405 rC2H1 1.094 1.092 1.093 1.090 1.080 1.081 1.081 1.081 rC3H2 1.094 1.093 1.093 1.091 1.081 1.082 1.081 1.082 rC4H3 1.094 1.092 1.093 1.090 1.080 1.082 1.081 1.081 RC 6C1C2 117.1 117.0 117.6 117.3 117.3 117.0 117.5 117.1 RC 1C2C3 121.0 121.0 120.6 120.8 120.8 120.9 120.7 120.8 RC 2C3C4 120.2 120.2 120.3 120.3 120.2 120.3 120.3 120.3 RC 1C2H1 117.0 116.9 117.2 117.2 117.1 117.0 117.1 117.1 RC 4C3H2 119.6 119.5 119.6 119.5 119.6 119.4 119.6 119.4 A2B 2 cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ

CASPT2 B3LYP CASPT2 B3LYP CASPT2 B3LYP CASPT2 B3LYP

rC1O 1.335 1.323 1.345 1.323 1.330 1.320 1.332 1.321 rC1C2 1.415 1.413 1.415 1.413 1.402 1.405 1.402 1.405 rC2C3 1.405 1.394 1.407 1.394 1.393 1.387 1.394 1.387 rC3C4 1.407 1.397 1.408 1.397 1.394 1.389 1.395 1.389 rC2H1 1.093 1.090 1.092 1.090 1.079 1.080 1.080 1.079 rC3H2 1.094 1.093 1.093 1.093 1.081 1.082 1.081 1.082 rC4H3 1.093 1.091 1.092 1.091 1.079 1.080 1.080 1.080 RC 6C1C2 120.6 119.9 121.2 119.9 120.9 120.1 121.1 120.1 RC1C2C3 119.0 119.2 118.6 119.2 118.9 119.1 118.8 119.1 RC 2C3C4 121.1 121.4 121.1 121.4 121.1 121.4 121.1 121.4 RC 1C2H1 119.5 119.1 119.8 119.1 119.7 119.3 119.7 119.3 RC 4C3H2 120.2 120.2 120.1 120.2 120.2 120.1 120.1 120.1

aAll CASPT2 calculations use the same (0a

1, 2a2, 5b1, 1b2) active space described in detail in the text. Distances are given in Å and bonds, in

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of symmetry a2, are strongly bonding. The remainingπ orbitals are classified as antibonding.

In the ground state of the phenoxyl radical the dominant Slater determinant can be defined as a

1 2π b1 2σ b2 2π b1 2π a2 2π° b1 1π a2 /0 πb 1 /0 πb 1 /0 , with a singly occupiedπ orbital being a linear combination of the pxorbitals on oxygen and theπ orbitals of the benzene ring

(see Figure 3). The percentage contribution of this configuration in the CASSCF wave function is 83%. The next three most important configurations,a 1 2 πb 1 2 σb 2 2 πb 1 1 πa 2 2 π°b 1 1 πa 2 /0 πb 1 /1 πb 1 /0 ,a 1 2 πb 1 2 σb 2 2 πb 1 2 πa 2 1 π°b 1 1 πa 2 /1 πb 1 /0 πb 1 /0 , and a 1 2 πb 1 2 σb 2 2 πb 1 2 πa 2 0 π°b 1 1 πa 2 /2 πb 1 /0 πb 1 /0 , cor-respond to various distribution of electrons in the aromaticπ orbitals with the percentage contribution to the CASSCF wave function of 2.9%, 2.2%, and 2.0%, respectively. After accounting for dynamical correlation, the contribution of these leading configurations to the CASPT2 wave function is 64%, 2.2%, 1.7%, and 1.5%, respectively. For the first excited state, A2B

2, the leading electronic configuration,b

1 2σ a1 2π b1 2π a2 2π b1 2σ b2 1π a2 /0 πb 1 /0 πb 1 /0

, contributes 88% to the CASSCF wave function. The analogous contributions from the next three Slater determinants,

b1 2 σa 1 2 πb 1 2 πa 2 0 πb 1 2 σb 2 1 πa 2 /2 πb 1 /0 πb 1 /0 , b 1 2 σa 1 2 πb 1 2 πa 2 2 πb 1 0 σb 2 1 πa 2 /0 πb 1 /2 πb 1 /0 , and b1 2σ a1 2π b1 1π a2 1π b1 1σ b2 1π a2 /1 πb 1 /1 πb 1 /1 are 2.2%, 2.2%, and 2.0%, respectively. After accounting for dynamical correlation, the contribution from these leading configurations reduces to 68%, 1.7%, 1.7%, and 1.5%. The presented numerical results have been derived with the cc-pVDZ basis set. For larger basis sets, the calculated contributions to the CASSCF wave functions have similar values, whereas the contributions to the CASPT2 wave functions undergo further reductions owing to a larger portion of dynamical correlation covered by these basis sets. To complete the discussion of the character of wave functions for both electronic states, we have to add that that the occupation numbers for the antibonding active π orbitals are non-negligible: 0.12, 0.11, and 0.05 for the ground state and 0.10, 0.10, and 0.04 for the A2B

2state, which suggest considerable static correlation in the aromatic ring despite a single-determinant character of both wave functions.

According to the above discussion, the A 2B

2 r X 2B1 excitation can be described as a transfer of a single electron

Figure 2. Orbital energy diagram for the seven activeπ orbitals and one active σ orbital of C6H5O in the X2B1and A2B2states obtained from

the CASSCF(0a1, 2a2, 5b1, 1b2)/aug-cc-pVDZ calculations. Occupation numbers are given for every orbital.

Figure 3. Schematic representation of the seven activeπ orbitals in the X2B

1and A2B2states of C6H5O. Nodal planes are given by dotted lines.

The symbol in each circle denotes the sign of the linear combination coefficient for the pxorbitals at the CASSCF(0a1, 2a2, 5b1, 1b2)/aug-cc-pVDZ

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from the lone pair (or more precisely: the b2linear combination of the lone pairs on oxygen) on the oxygen atom to the nonbondingπ°b

1orbital delocalized over the oxygen atom and

the aromatic ring. This transfer causes a considerable stabiliza-tion of theπ orbitals system and results in a substantial lowering of the π°b

1 orbital energy and a significant raise of the

one-electron energy of the singly occupied σb2orbital. Note

that these findings contradict the usual classification of the A2B

2r X2B1excitation as the n-π* transition. The correct

assignment should read n-π°or even n-π, if one takes into account the substantial stabilization of the resultant doubly occupiedπb1orbital. The Mulliken charges extracted from the DFT/UB3LYP/cc-pVDZ calculations show that for the ground state, a fractional negative charge of 0.22 is located on the oxygen atom, whereas the corresponding positive charge is distributed almost equally over all carbon atoms. For the first excited state, the induced negative charge on the oxygen atom is smaller (0.11) and the corresponding positive charge is located Figure 4. Mulliken charges (a) and spin densities (b) for the X2B

1and A2B2states of C6H5O obtained from DFT calculation in four basis set

(cc-pVDZ, aug-cc-pvDZ, cc-pVTZ, aug-cc-pVTZ). Values in parentheses correspond to induced atomic charges with hydrogen contributions summed into adjacent carbon atoms.

TABLE 2: Total Energies, Vertical Excitation Energies, and Adiabatic Excitation Energies for the X2B

1and A2B2Electronic

States of Phenoxyl Radical Computed Using the CASPT2 and DFT/B3LYP Methodsa

total energies A2B

2rX2B1excitation energies

basis set X2B

1 A2B2(vertical) A2B2(adiabatic) verticalb adiabatic ∆EH0-0 ∆ED0-0

CASPT2 cc-pVDZ -305.920944 -305.876788 -305.884349 1.202 0.996 0.995 0.993 aug-cc-pVDZ -305.972746 -305.926807 -305.934095 1.250 1.052 1.049 1.047 cc-pVTZ -306.210241 -306.165644 -306.173021 1.214 1.013 1.010 1.008 aug-cc-pVTZ -306.231793 -306.186453 -306.193693 1.234 1.037 1.034 1.032 B3LYP cc-pVDZ -306.847702 -306.810021 -306.815859 1.025 (0.983) 0.867 0.865 0.864 aug-cc-pVDZ -306.866905 -306.827708 -306.833555 1.067 (1.035) 0.908 0.904 0.903 cc-pVTZ -306.939129 -306.900562 -306.906565 1.050 (1.029) 0.886 0.883 0.881 aug-cc-pVTZ -306.943226 -306.904275 -306.910234 1.060 (1.045) 0.898 0.895 0.893 exp 1.06c, 1.10d

aAll CASPT2 calculations use the same (0a

1, 2a2, 5b1, 1b2) active space described in detail in the text.∆EH0-0denotes the 0-0 excitation energy

for C6H5O and∆ED0-0, for C6D5O. Total energies are given in hartree and excitation energies, in eV.bValues in parentheses have been calculated

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primarily on the adjacent and the meta carbon atoms. The Mulliken charges extracted from the DFT calculations in larger basis sets confirm this trend, but at the same time show very strong dependence on the size of the basis set. (For details, see Figure 4.) This dependence is somewhat diminished by including the induced charge on hydrogens into the neighboring carbons but still does not provide a sound basis for further analysis. Figure 4 shows that the calculated spin densities are more reliable source of information about the actual charge distribu-tion in the phenoxyl radical molecule. The analysis of the cc-pVDZ DFT spin densities shows that for the ground state, the single electron is strongly delocalized over the oxygen atom (0.44) and the aromatic ring (-0.10, +0.30, -0.15, and +0.38 for the adjacent, ortho, meta, and para carbon atoms, respec-tively), but for the A2B

2state, it is almost entirely localized on the oxygen atom (0.92). This situation is in contrast with that in the recently studied46,47phenylthiyl radical (C

6H5S), where the single electron was strongly localized on the sulfur atom in both electronic states. The shape of the singly occupied molecular orbital (SOMO) in both electronic states coincided with the atomic-like pxor pyorbitals of sulfur. The large degree

of localization and the similarity of SOMO to the atomic orbitals of sulfur motivated the authors to use the term “intramolecular orbital alignment” while discussing the orientation of the SOMO orbital with respect to the molecular frame of reference. Our study shows that for C6H5O, the out-of-plane SOMO orbital is strongly delocalized over the whole aromatic ring. We believe that the main reason for this large degree of delocalization is much shorter distance between carbon and oxygen (1.252 Å using DFT/UB3LYP/aug-cc-pVTZ) than between carbon and sulfur (1.723 Å using DFT/UB3LYP/aug-cc-pVTZ) leading to more effective mixing of the pxorbitals of oxygen and carbon

in C6H5O than the px orbitals of sulfur and carbon in C6H5S. Therefore, the “intramolecular orbital alignment” phenom-enon,46,47observed for C

6H5S, is not confirmed for C6H5O by our theoretical calculations.

The comparison of the equilibrium geometry of both studied electronic states with their electronic structures gives somewhat counterintuitive conclusions. One may expect that transferring an electron from the nonbonding electron pair on the oxygen atom to the system of π orbitals may result in strengthening theπ bond system, which is ensued by shortening the CO bond. However, the optimized geometrical parameters show that the bond in fact becomes longer and loses its approximate double character. This rather surprising observation can be qualitatively understood by studying the composition of the bonding π orbitals given in Figure 3. Note that for discussing the bond order between carbon and oxygen, only the b1 orbitals are relevant, because the nodal structure of the a2orbitals enforces zero contribution from the px orbitals on oxygen and on the

adjacent carbon atom. For the ground state of the phenoxyl radical, the two lowest b1 orbitals contribute to the π bond between oxygen and carbon; this bond is slightly weakened by the antibonding contribution from the SOMO orbital, which has a nodal plane between the C and O atoms (see Figure 3). For the first excited state, the bonding contribution from the lowest b1 orbital is almost entirely cancelled by the antibonding contributions from the next two b1orbitals, which have nodal planes located between oxygen and the adjacent carbon. This analysis explains then the approximate double character of the CO bond in the ground state and the approximate single character of this bond in the first excited state. Note that this situation is quantitatively different than that observed46,47 for

the phenylthiyl radical (C6H5S), where the bond distance TABLE

3: Vertical Excitation Energies (in eV) for the Lowest Doublet and Quartet Excited States of the Phenoxyl Radical Computed Using the CASSCF, CAS PT2, and DFT/ B3LYP Methods a CASSCF CASPT2 TDDFT e(DFT) cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ exp e X 2B 1 -305.060620 -305.072141 -305.138148 -305.140843 -305.920967 -305.972759 -306.210162 -306.231701 -306.846951 -306.866236 -306.939128 -306.943223 0 A 2B 2 1.312 1.358 1.349 1.356 1.187 1.236 1.198 1.218 0.983 (1.025) 1.035 (1.067) 1.029 (1.050) 1.045 (1.060) 1.06, 1.10 B 2A 2 2.560 2.511 2.557 2.542 2.228 2.109 2.184 2.139 2.409 (2.429) 2.319 (2.332) 2.381 (2.395) 2.348 (2.361) 1.98, 2.03 C 2B 1 3.440 3.460 3.496 3.500 3.158 3.197 c 3.122 3.228 c 3.582 (...) 3.531 (...) 3.588 (...) 3.566 (...) 3.12 1 4B 1 4.231 4.220 4.293 4.289 4.200 4.166 b 4.226 4.239 b ... (4.375) ... (4.336) ... (4.421) ... (4.402) 1 4B 2 4.857 4.847 4.904 4.888 4.742 b 4.708 b 4.731 4.852 c 5.891 f(5.583) 5.948 f(5.572) 5.997 f(5.651) 6.010 f(5.636) 1 4A 2 5.661 5.639 5.721 5.714 5.343 5.346 c 5.337 5.401 c 5.476 f(5.593) 5.367 f(5.451) 5.488 f(5.581) 5.435 f(5.511) 1 4A 1 5.793 5.775 5.822 5.808 4.939 4.882 b 4.893 4.893 b 4.760 f(4.847) 4.775 f(4.814) 4.821 f(4.864) 4.821 f(4.841) 1 2A 1 5.976 5.960 6.015 6.000 5.383 c 5.432 d 5.312 c 5.432 d 4.907 (4.916) 4.859 (4.865) 4.903 (4.901) 4.879 (4.876) aAll the CASSCF/CASPT2 calculation use the same (1a 1 ,2 a2 ,5 b1 ,1 b2 ) active space described in detail in the text. Lowest excited state in each symmetry is given. bLevel shift R) 0.1 has been used to avoid intruder states. cLevel shift R) 0.2 has been used to avoid intruder states. dLevel shift R) 0.3 has been used to avoid intruder states. eReference 15. fTDDFT values for 1 4B 2 ,1 4A 2 , and 1 4A 1 are calculated using the 1 4B 1 reference function.

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between sulfur and the adjacent carbon is similar in both electronic states (1.723 Å for X2B

1and 1.763 Å for A2B2; DFT/UB3LYP/aug-cc-pVTZ calculations). Such a bond length is intermediate between typical aromatic (rCS ) 1.714 Å in thiophene41) and single bonds (r

CS ) 1.818 Å in

methane-thiol41). It is noticeably longer than a characteristic double CS bond (rCS) 1.611 Å in thioformaldehyde41). We believe that the necessity of breaking theπ bond in phenoxyl radical upon the A2B

2r X 2B1excitation is responsible for significantly higher excitation energyscompare 0.37 eV for C6H5S vs 1.06 eV for C6H5Osrequired for this transition.

(b) Vertical and Adiabatic A 2B

2 r X 2B1 Excitation Energies. The calculated values of vertical and adiabatic

A2B

2r X2B1excitation energies for the phenoxyl radical are given in Table 2. The presented values have been obtained using the CASPT2, DFT/UB3LYP, and TDDFT/UB3LYP methods.48 The analogous results obtained with the CASSCF method are given in Table K of the Supporting Information; we do not present these values here because the CASSCF energetics is usually not very accurate. It is difficult to state clearly which method reproduces the experimental data best, because of not obvious character of the experimental findings. If one assumes that the experimental energies of 1.10 and 1.06 eV correspond to vertical excitation, then the DFT/UB3LYP and TDDFT/ UB3LYP methods seem to reproduce the experimental data most accurately. If, on the contrary, one assumes that they correspond to adiabatic excitation, then the correspondence of the CASPT2 results to experiment is better. The difference between the calculated DFT and CASPT2 excitation energies is approxi-mately constant; the later are consistently 0.13 eV higher for all employed basis sets. Such a discrepancy is considered to be within the error bar for typical second-order multireference perturbation theory calculations.49-51This discrepancy is

some-what smaller if the larger active space is used in the CASPT2 calculations. The CASPT2 vertical excitation energies shown in Table 3, which have been computed using the (1a1, 2a2, 5b1, 1b2) active space, are approximately 0.015 eV smaller than those calculated with the (0a1, 2a2, 5b1, 1b2) active space (Table 2). To compute quantities that can be directly compared to experiment, we have calculated the 0-0 transition energies between the A2B

2and X2B1states of C6H5O and C6D5O. In fact, these values differ only slightly from the adiabatic excitation energies owing to almost identical zero-point energy corrections for both states. Note that we refer here to the adiabatic excitation energy as a difference between the minima of the calculated potential energy curves. The zero-point corrections have been calculated using the scaled harmonic vibrational frequencies computed separately for each basis set using the DFT/UB3LYP procedure (for details, see below). Because the CASPT2 frequencies could not be easily accessed, we have used the calculated DFT frequencies to estimate also the CASPT2 (Table 2) and CASSCF (Table K of Supporting Information) 0-0 transition energies.

Vertical excitation energies for low-lying doublet and quartet states of the phenoxyl radical are given in Table 3. The presented results are calculated using the CASSCF, CASPT2, DFT, and TDDFT methods. For the CASSCF and CASPT2 calculations, we have used the extended (1a1, 2a2, 5b1, 1b2) active space. We have decided to include these results in the present paper to visualize the energetics of the low-lying quartet states that can be easily studied using the CASSCF and CASPT2 tech-niques. As expected, the calculated excitation energies for the lowest quartet states are rather large. The lowest quartet state is4B

1located at approximately 4.2 eV higher than the ground state. Determination of CASPT2 energies for many of the high-lying excited states of C6H5O required using large values of

TABLE 4: Harmonic Vibrational Frequencies (Scaled) for the A2B

2Electronic State of C6H5O Computed Using the DFT/ B3LYP and CASSCF Methodsa

CASSCF B3LYP

symmetry mode cc-pVDZ aug-cc-pVDZ cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ

A1 V1 3085 3083 3108 3107 3098 3100 V2 3073 3070 3099 3098 3088 3091 V3 3054 3054 3069 3070 3059 3062 V4 1599 1591 1570 1556 1559 1556 V5 1483 1476 1403 1393 1412 1410 V6 1252 1233 1228 1201 1207 1202 V7 1146 1147 1143 1143 1154 1152 V8 999 999 1012 1008 1012 1011 V9 973 968 955 953 961 961 V10 794 789 802 797 803 802 V11 508 501 502 501 506 505 A2 V12 894 885 934 928 936 941 V13 769 761 797 787 797 799 V14 396 396 416 414 417 416 B1 V15 916 899 950 943 948 955 V16 824 813 855 847 857 861 V17 698 690 710 697 708 710 V18 650 634 675 674 676 673 V19 479 469 501 490 498 496 V20 230 230 223 218 221 219 B2 V21 3080 3077 3107 3106 3097 3099 V22 3063 3061 3074 3075 3064 3067 V23 1567 1563 1539 1529 1531 1529 V24 1429 1427 1406 1395 1410 1408 V25 1303 1305 1297 1291 1306 1304 V26 1190 1192 1235 1232 1222 1222 V27 1085 1081 1128 1130 1141 1139 V28 1047 1046 1053 1052 1058 1058 V29 603 608 600 599 605 604 V30 367 367 357 354 358 358

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level shift to avoid intruder states, especially when using augmented basis sets. TDDFT yields more accurate excitation energies than CASSCF and CASPT2 for the lowest excited state, A 2B

2. (See the discussion above about the character of experimental excitation energies.) For the higher states, B2A

2 and C2B

1, the CASPT2 method seems to be the most accurate with an average error of 0.10-0.15 eV, whereas the error of CASSCF and TDDFT can be as large as 0.3-0.5 eV. It is interesting to mention here that by solving the ground-state Kohn-Sham equations in each symmetry and/or spin subspace we have been able to obtain DFT vertical excitation energies of similar (or even better) quality like from the corresponding TDDFT calculations.

(c) Harmonic Vibrational Frequencies. Harmonic

vibra-tional frequencies for the A2B

2state of C6H5O calculated using the CASSCF and DFT/UB3LYP methods are given in Table 4. Analogous results computed for C6D5O are presented in Table 5. To analyze the change of vibrational frequencies upon the A2B

2r X2B1excitation, we have calculated also the harmonic vibrational frequencies for the ground state of phenoxyl radical. These results are presented in the Supporting Information (Table X1 for C6H5O and Table X2 for C6D5O). Because both the CASSCF and DFT harmonic vibrational frequencies have large systematic errors, the computed frequencies have been scaled to ensure better correspondence to experiment. We have used a single scaling factor for all type of vibrations. The scaling factors for each basis set and for each employed method have been computed separately using as a reference the well-known experimental frequencies of phenol.52,53The calculated CASSCF and DFT frequencies of phenol together with the determined scaling factors are presented in Supporting Information (Tables P1, P2, P3, and P4). The scaling factors for a given method vary only slightly upon the change of basis set or isotope

substitution. For the DFT/B3LYP procedure, the computed scaling factors are 0.967 for cc-pVDZ, 0.967 for aug-cc-pVDZ, 0.966 for cc-pVTZ, and 0.967 for aug-cc-pVTZ for the C6H5OH molecule and 0.970 for cc-pVDZ, 0.971 for aug-cc-pVDZ, 0.971 for cc-pVTZ, and 0.971 for aug-cc-pVTZ for the C6D5OD molecule. For the CASSCF procedure, the analogous factors are 0.915 (cc-pVDZ) and 0.917 (aug-cc-pVDZ) for C6H5OH and 0.919 (cc-pVDZ) and 0.922 (aug-cc-pVDZ) for C6D5OD. It would be very valuable to obtain some computa-tional error estimates for the calculated vibracomputa-tional frequencies of C6H5O and C6D5O in the A2B2state. To this end, we have compared the calculated scaled harmonic vibrational frequencies for the ground states of C6H5OH, C6D5OD, C6H5O, and C6D5O with the corresponding experimental data. The standard devia-tions and maximal absolute deviadevia-tions obtained with different computational procedures are presented in Table 6. The devia-tions for the CASSCF method are considerably larger than those calculated using the DFT data. The smallest deviations are obtained for the DFT/B3LYP method and the cc-pVTZ basis set. For the rest of this section, we analyze the vibrational spectrum of C6H5O and C6D5O in the A 2B2 state using the scaled DFT/B3LYP/cc-pVTZ harmonic frequencies given in Tables 4 and 5. Using the error estimates from Table 6, we assume that a standard deviation from experiment of the calculated frequencies is approximately 27 cm-1for C6H5O and 23 cm-1 for C6D5O and the maximal absolute error for the calculated frequencies is not larger than 61 cm-1 for C6H5O and 62 cm-1for C6D5O.

Most of the calculated frequencies for the A2B

2state have very similar values to the corresponding values obtained for the ground state. Although the frequency shift for some of the vibrational modes can be large, the overall change of zero-point energy (ZPE) is only -25 cm-1for C6H5O and -40 cm-1for

TABLE 5: Harmonic Vibrational Frequencies (Scaled) for the A2B

2Electronic State of C6D5O Computed Using the DFT/ B3LYP and CASSCF Methodsa

CASSCF B3LYP

symmetry mode cc-pVDZ aug-cc-pVDZ cc-pVDZ aug-cc-pVDZ cc-pVTZ aug-cc-pVTZ

A1 V1 2298 2299 2311 2312 2307 2306 V2 2283 2284 2300 2301 2296 2295 V3 2262 2265 2268 2272 2266 2266 V4 1565 1559 1538 1525 1525 1521 V5 1382 1368 1286 1269 1278 1274 V6 1186 1175 1200 1179 1188 1183 V7 937 936 925 922 931 930 V8 856 857 855 853 863 862 V9 819 821 814 816 826 824 V10 740 737 740 738 745 744 V11 497 490 492 491 497 495 A2 V12 721 715 760 758 764 768 V13 600 594 622 615 623 624 V14 352 351 364 361 366 364 B1 V15 747 724 792 799 794 804 V16 695 681 725 716 726 726 V17 586 575 587 576 586 585 V18 529 527 546 539 548 544 V19 418 411 432 424 430 429 V20 219 219 211 206 210 208 B2 V21 2292 2292 2306 2307 2301 2301 V22 2272 2274 2276 2279 2273 2273 V23 1531 1528 1506 1498 1496 1493 V24 1305 1301 1325 1314 1315 1312 V25 1145 1140 1234 1228 1219 1218 V26 1021 1025 998 996 1016 1014 V27 828 829 818 820 831 829 V28 802 804 798 801 811 809 V29 581 586 576 576 583 581 V30 355 355 345 343 347 346

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C6D5O. Frequencies for 9 vibrational modes of C6H5O and 11 vibrational modes of C6D5O differ by more than 30 cm-1from the corresponding frequencies of the ground state. Not surpris-ingly, the largest change in harmonic frequencies is observed for the vibrations involving the CO bond. For C6H5O, mode V6, corresponding to the CO stretch, is red-shifted by 167 cm-1, mode V30, corresponding to the in-plane CO bending, is red-shifted by 73 cm-1, and mode V20, corresponding to the out-of-plane CO bending, is blue-shifted by 38 cm-1 as X2B

1f A2B2. For C6D5O, the corresponding values are 217, 65, and 37 cm-1, respectively. Comparison of vibrational vectors shows that most modes may change substantially upon the A2B

2r X2B1excitation. For C6H5O, we have found that only four pairs of modes (V5and V6, V9and V10, V17and V18, and V23 and V24) have mixing angle larger than 20°. Here, we assume that the vibrational modes Viand Vj of the ground state span

approximately the same two-dimensional vector space like the vibrational modes Vi′and Vj′of the excited state. The mixing

angle is defined then as the angle between the vectors Viand Vi

in this two-dimensional space. For C6D5O, the mixing may involve more than two modes and the situation is more complicated. For example, the vibrational mode V6of A2B2, which is dominated by the CO stretch, is a mixture of V5, V6, and V4of X2B1with the mixing angle between V5and V6′as large as 46°. The main reason of vibrational mode mixing is large structural change of the aromatic ring and elongation of the carbon-oxygen bond. Such a mixing is not necessarily accompanied by a large change in harmonic frequencies. For example, the mixing of V23and V24upon the A2B2r X 2B1 excitation affects V23 by only -21 cm-1 and V24 by only

+34 cm-1.

Conclusion

Accurate quantum chemical methods (CASPT2, DFT, TD-DFT) are employed to study the equilibrium geometry, excita-tion energies, and harmonic vibraexcita-tional frequencies for the first excited electronic state (A 2B

2) of the phenoxyl radical. The calculated properties are compared to analogous data for the ground state. The presented results show that both the ground-state and the first excited-state wave functions are strongly dominated by single electronic configurations. The A2B

2r X2B1excitation can be described as a transfer of a single electron from the lone pair of oxygen to the nonbonding π°b

1orbital delocalized over the oxygen atom and the aromatic

ring. These findings show that the usual classification of the A2B

2r X2B1excitation as the n-π* transition is not cor-rect. The more appropriate assignment should read n-π° or even n-π, if one takes into account the substantial stabilization of the resultant doubly occupied πb1 orbital. The calculated

vertical (DFT, TDDFT) and adiabatic (CASPT2) excitation energies for the A2B

2r X2B1transition correspond well to experimentally determined excitation energies. Unfortunately,

this situation does not permit an unambiguous classification of the experimental findings as vertical or adiabatic excitation energies. The A 2B

2 r X 2B1 excitation causes substantial geometry changes in the chinoid-like structure of C6H5O in the ground state. The molecular structure of the A2B

2state can be described as aromatic with an oxygen atom attached to it by a single bond. The change of the CO bond order, from ap-proximately double in X2B

1to approximately single in A2B2, introduces also a large change in harmonic frequencies for the vibrational modes involving the CO bond. The largest change is observed for the CO stretch (-167 cm-1for C6H5O and -217 cm-1for C6D5O). The change of ZPE upon the A2B2r X2B1 excitation is much smaller (-25 cm-1for C6H5O and -40 cm-1 for C6D5O). The presented data show that the A2B2r X2B1 excitation in C6H5O has quite different characteristic than the analogous transition observed46,47recently in the phenylthiyl radical (C6H5S).

Acknowledgment. The National Science Council of Taiwan

is acknowledged for financial support (grants NSC96-2113-M009-022-MY3 and NSC96-2113-M009-025). This research has also been supported by the Institute of Nuclear Energy Research, Atomic Energy Council, Taiwan, under Contract No. NL940251, and by the Ministry of Education (MOE-ATU project). We thank the National Center for High-Performance Computing for computer time.

Supporting Information Available: A compilation of previous theoretical equilibrium structures for the ground state of phenoxyl radical, a set of harmonic vibrational frequencies for the ground states of C6H5O and C6D5O, four sets of harmonic vibrational frequencies for phenol that have been used to determine scaling factors, and CASSCF vertical excitation energies for the low-lying states of the phenoxyl radical constitute the Supporting Information for this study. This material is available free of charge via the Internet at http:// pubs.acs.org.

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數據

TABLE 1: Geometrical Parameters for the X 2 B
Figure 2. Orbital energy diagram for the seven active π orbitals and one active σ orbital of C 6 H 5 O in the X 2 B 1 and A 2 B 2 states obtained from
TABLE 2: Total Energies, Vertical Excitation Energies, and Adiabatic Excitation Energies for the X 2 B
TABLE 4: Harmonic Vibrational Frequencies (Scaled) for the A 2 B
+3

參考文獻

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