Chang-Guo Zhan and David A. Dixon

Transcription

1 Journal of Molecular Spectroscopy 216, (2002) doi: /jmsp Electronic Excitations in Pyrrole: A Test Case for Determination of Chromophores in the Chromogenic Effects of Neurotoxic Hydrocarbons by Time-Dependent Density Functional Theory and Single-Excitation Configuration Interaction Methods Chang-Guo Zhan and David A. Dixon Theory, Modeling & Simulation, William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, MS K1-83, P.O. Box 999, Richland, Washington Received April 2, 2002 Time-dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) calculations on the electronic excitations in pyrrole have been performed to examine the reliability of these first-principles electronic structure methods in predicting electronic excitation spectra of pyrrole-containing compounds. Both the TD-DFT and CIS calculations led to satisfactory results when compared to available experimental data, particularly for low-lying excited states. The TD-DFT and CIS calculations provide lower and upper limits of the excitation energies, respectively, for low-lying singlet excited states. These results suggest that these methods can be used for the prediction of the excitation spectra, particularly the excitation energies for low-lying excited states, of chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons, which are believed to be substituted pyrroles and their adducts with proteins. As an example of a practical application, the spectrum of the widely used 2,5-dimethylpyrrole has been calculated. It is shown that the 2,5-dimethylpyrrole molecule does not have an absorption in the region of the visible spectrum ( nm), suggesting that the absorption observed at 530 nm and the color of 2,5-dimethylpyrrole is due to another species, probably a product of possible 2,5-dimethylpyrrole autoxidation. This suggests that the conclusions from previously reported experimental studies of biochemical reactions of neurotoxic γ -diketones need to be reexamined in terms of the relationship of chromogenicity to neurotoxicity. Key Words: time-dependent density functional theory; pyrrole; electronic excitations; neurotoxicity; CI singles. INTRODUCTION Pyrrole and its derivatives constitute an important class of heterocycles (1). Compounds containing the pyrrole ring are widely distributed in nature (2) and frequently display biological activity (3). Substituted pyrroles/pyrrole adducts can easily form from, for example, reactions of neurotoxic organic hydrocarbons with proteins and amino acids (4). Besides extensive biological interest in pyrrole derivatives, polymers derived from pyrrole have been used as conducting and nonlinear optical materials (5). Pyrrole and substituted pyrroles can easily undergo various oxidation reactions, including autoxidation leading to colored products. Detailed molecular mechanisms for most of the oxidation processes are not known. For example, pyrrole as a liquid turns brown in air (6) and 3- methylpyrrole is readily autoxidized, as evidenced by a rapid color change (7). The structures of the chromophores are unknown, although recently reported experiments on the autoxidation of the neopentylamine-derived from 3-methylpyrrole suggest that the chromophore could be pyrrolecarboxyaldehydes, pyrrole pyrrole dehydrodimers, or other adducts (7). Reliable prediction of electronic excitations in pyrrole-involving Supplementary data for this article may be found on the journal home page. molecules is critical for theoretically determining the chromophores and uncovering the molecular mechanisms of the color changes. We are studying, using ab initio electronic structure theory, the nature of the chromophores responsible for the chromogenic effects of a number of organic neurotoxicants, including aliphatic γ -diketones (such as 2,5-hexanedione) and aromatic hydrocarbons (such as 1,2-diethylbenzene) (4, 8). These organic compounds have a neurotoxic potential and are widely used as solvents or can be metabolized from widely used solvents e.g., 2,5-hexanedione from n-hexane). These compounds are present in fuels and solvents and, formerly, in consumer products; they also occur in contaminated soil and water at hazardous-waste sites (9). Certain aliphatic γ -diketones and aromatic hydrocarbons exhibit both chromogenic and neurotoxic effects at the same time (4). The neurotoxic effects include behavioral changes and changes associated with nerve fiber degeneration (central peripheral axonopathy). For the chromogenic effects, they form colored pigments on contact with proteins, skin, and other tissues. Rodents treated systemically with these compounds develop discoloration of skin, eyes, and internal organs, including the brain and spinal cord (8). On the basis of the available experimental data, it is believed that the chromogenic and neurotoxic properties are directly related through their reactions with amino /02 $35.00 All rights reserved.

2 82 ZHAN AND DIXON acids (4, 8). It has been proposed that the chromogenic and neurotoxic effects are associated with the formation of certain pyrrole or pyrrole-like adducts; for example, 2,5-hexanedione reacts with the ε-amino groups of lysine to form 2,5-dimethylpyrrole adducts with proteins, including neurofilament peptides (4). The actual chromophores are not known due to the complex mixtures that are produced. The prototypical pyrrole molecule has been extensively investigated by both experiment and computation. Here, we limit our discussion to the investigation of the electronic excitations of pyrrole. Experimentally, three types of electronic excitation spectra, vacuum ultraviolet and visible (UV vis), electron energy-loss, and ultraviolet photoelectron spectra, have been measured by a number of research groups (10). Numerous computational studies have been reported on pyrrole, and the calculation of the electronic excitation spectra of pyrrole has been considered as a benchmark for quantum mechanical investigations of molecular excited states (11). Early ab initio quantum mechanical studies revealed the underlying difficulties particularly due to the strong mixing of the valence and Rydberg excited states in determining the vertical excited states of pyrrole (12). Recent ab initio calculations have tested such theoretical methods as symmetry adapted cluster-configuration interaction (SAC-CI) (11), complete active space second-order perturbation (CASPT2) (13), multireference Møller Plesset (MRMP) perturbation (14), second-order algebraic diagrammatic construction ADC(2) (15), and a hierarchy of coupled cluster models such as CC3 (16). The electronic excitation energies calculated using these sophisticated methods with quite large basis sets are, on the whole, in good agreement with the corresponding experimental data (11). In principle, these methods and basis sets, which were used for pyrrole, can be extended to calculate the spectroscopic properties of other substituted pyrroles such as the ones in which we are interested. Unfortunately, most of the substituted pyrroles formed from reactions of the organic neurotoxicants with proteins are simply too large for these computationally expensive methods, which require large basis sets, for us to calculate the electronic spectra at the current time. It is, therefore, necessary to benchmark electronic structure methods which are more computationally efficient and can practically be applied to very large substituted pyrrole systems. One of the main reasons for the acceleration of the use of electronic structure theory in predicting molecular properties for larger molecules over the past two decades has been the development of density functional theory (DFT) (17 19). An important reason that DFT is becoming so popular for such studies is its lower computational cost, formally scaling as N 3 (with Coulomb fitting), where N is the number of basis functions, and that it includes the effect of electron correlation at some reasonable level. In contrast, conventional ab initio molecular orbital (MO) theory formally scales as N 4 at the Hartree Fock (HF) level and the effect of electron correlation is not included. If electron correlation is included in an MO calculation, the cheapest computational cost is formally N 5 for 2nd order Møller Plesset (MP2) theory. The combination of low computational cost with reasonable accuracy has led to the successful application of the DFT method to the prediction of a broad range of properties of molecules in the ground state (20). In contrast to the case of ground states, time-dependent density functional theory (TD-DFT) for treating excited-state properties (21 23) has only recently been applied to molecules (24, 25), although the theory itself was first proposed more than 20 years ago. Recent work has shown that TD-DFT can be used to reliably predict not only the location of the UV vis excitation but also the oscillator strength (intensity of the transition) for various molecular systems other than pyrrole (26, 27), although some concerns on the use of the TD-DFT method have been expressed in the literature (16b). Is the TD-DFT method suitable for predicting electronic excitation spectra of pyrrole ring-containing molecules? In the present study, we have performed TD-DFT calculations using various basis sets to determine electronic excitation energies of pyrrole. Less computationally expensive single-excitation configuration interaction (CIS) (28) calculations have also been performed to calculate the electronic excitation energies. In order to predict which chromophores provide the chromogenic effects of the neurotoxicants, we are interested only in the first few low-lying singlet excited states of pyrrole-containing molecules because only excitations to these excited states could produce absorption in the visible region of the spectrum. Detailed comparison of the calculated results with available experimental excitation energies clearly demonstrates the reliability of the TD-DFT and CIS methods in predicting electronic excitation spectra, at least for the excitation energies for low-lying states, of pyrrole ring-containing compounds. As an example of the practical applications of the benchmarked methods, the UV vis spectrum of the widely used 2,5-dimethylpyrrole has been investigated. COMPUTATIONAL DETAILS The geometry of pyrrole was fully optimized using gradientcorrected DFT with Becke s three-parameter hybrid exchange functional and the Lee Yang Parr correlation functional (B3LYP) (29) and with the 6-31G(d) and G(d) basis sets (30). Analytical second energy derivative calculations, which yield the vibrational frequencies, were performed at the optimized geometry to ensure that the optimized geometry is a minimum on the potential energy hypersurface (all real frequencies). The geometry optimized at the B3LYP/ G(d) level was used in the calculation of the vertical excitation energies of both the singlet and triplet excited states at both the single-excitation configuration interaction (CIS) level (28) and the time-dependent DFT (TD-DFT) level (31) with the B3LYP hybrid functional and nonhybrid functionals including Becke s 1988 exchange functional and the Lee Yang Parr correlation functional (BLYP) (29b, 32), Becke s 1988 exchange functional and Perdew s 1986 correlation functional (BP86) (32, 33), and Becke s 1988 exchange functional and Perdew and Wang s 1991

3 gradient-corrected correlation functional (BPW91) (32, 34). The basis set-dependence of the calculated excitation energies was studied using three kinds of basis sets, 6-31G(d), cc-pvdz, and cc-pvtz (35), each augmented by atom-centered Rydberg functions (1s1 p1d)(36) for all non-hydrogen (i.e., C and N) atoms. The Gaussian exponents of the Rydberg functions for the C atom are (s), (p), and (d). The Gaussian exponents of the Rydberg functions for the N atom are (s), ( p), and (d). For convenience, these three kinds of augmented basis sets are denoted by 6-31G(d) + Ryd(C,N), cc-pvdz + Ryd(C,N), and cc-pvtz + Ryd(C,N), respectively. We also used a set of Rydberg functions (3s3p3d) centered at the molecular center (37) with a cc-pvtz basis set. The Gaussian exponents of this set of Rydberg functions are (3s), (4s), (5s), (3p), (4p), (5p), (3d), (4d), and (5d). This set of Rydberg functions has been used in recently reported calculations of the electronic excitations in pyrrole (11, 37). For convenience, the cc-pvtz basis set augmented by this set of Rydberg functions (3s3p3d) centered at the molecular center (mc) is denoted by cc-pvtz + Ryd(mc). In addition, we optimized the geometries of 2,5-dimethylpyrrole and N-methyl-2,5-dimethylpyrrole at the B3LYP/ G(d) level and then performed CIS and TD-DFT/B3LYP calculations using the cc-pvdz + Ryd(C,N) basis set. The program NWChem (38) was used for the geometry optimizations and Gaussian98 (39) was used for the electronic excitation calculations. All calculations were performed on a 16-processor SGI Origin 2000 and a 512-processor IBM SP supercomputer. TD-DFT CALCULATIONS OF EXCITATIONS IN PYRROLE 83 RESULTS AND DISCUSSION Geometries The geometry of pyrrole (C 2v symmetry) is depicted in Fig. 1, with both the optimized and experimental parameters. The optimized geometries of 2,5-dimethylpyrrole and N-methyl- 2,5-dimethylpyrrole are also shown in Fig. 1. As shown in Fig. 1, the geometric parameters optimized for pyrrole at both the B3LYP/6-31G(d) and B3LYP/ G(d) levels are in excellent agreement with the corresponding experimental values (40). The largest deviation of the bond lengths level from the experimental values at the B3LYP/ G(d) is 0.01 Å, and the largest deviation of the optimized bond angles is 0.4 degree. We used the geometries optimized at the B3LYP/ G(d) level in our TD-DFT and CIS calculations. Electronic Excitations in Pyrrole at the CIS/cc-pVTZ + Ryd(mc) Level We calculated 49 vertical excited states of pyrrole, in addition to the 1 A 1 ground state. The 49 excited states include the 14 lowest 1 A 2 states, 14 lowest 1 B 1 states, 8 lowest 1 B 2 states, 8 lowest excited 1 A 1 states, lowest 3 B 2 state, lowest 3 A 2 state, low- FIG. 1. Optimized geometries of pyrrole, 2,5-dimethylpyrrole, and N- methyl-2,5-dimethylpyrrole in comparison with the corresponding experimental geometric parameters for pyrrole. Experimental data from Ref. (40). est 3 A 1 state, and lowest 3 B 1 state. Electronic excitations to the 1 A 2 states are symmetry-forbidden, and electronic excitations to all of the triplet states are spin-forbidden. Thus, the calculated oscillator strengths for these states are zero. The calculated vertical excitation energies are summarized in Table 1, together with

4 84 ZHAN AND DIXON TABLE 1 Electronic Excitation Energies ( E in ev) and Oscillator Strengths ( f ) Calculated at the CIS/cc-pVTZ + Ryd(mc) Level CIS (this work) SAC-CI b Excited state Assignment a E f E expt. c 1 A 2 3s R A 2 3p z R A 2 3d z2 R A 2 3d x2-y2 R A 2 4s R A 2 4p z R A 2 4d z2 R A 2 4d x2-y2 R A 2 5s R A 2 3p y /5p z R (5p z R only) 1 A 2 5d x2-y2 R A 2 5d z2 R A 2 3d yz R A 2 4d yz R B 1 3p y R B 1 3d yz R B 1 3s R B 1 4p y R B 1 3p z R B 1 4d yz R B 1 5p y R B 1 3d z2 R B 1 5d yz R B 1 3d x2-y2 R B 1 4s R B 1 5s R B 1 4d z2 R B 1 4d x2-y2 R B 2 3p x R/V B 2 V/3d xz R B 2 3d xz R/V B 2 4p x R B 2 4d xz R B 2 5p x R B 2 5d xz R B 2 3d xy R B 2 4d xy R A 1 V/3d xy R (V only) 1 A 1 3d xy R/V (3d xy R only) 1 A 1 3p x R A 1 V π A 1 4d xy R A 1 5d xy R A 1 4p x R A 1 3d xz R B 2 V A 2 3s R A 1 V B 1 3p y R a R and V denote Rydberg and valence excited state, respectively. All transitions means the electron excitations from 1a 2 (HOMO), unless with a prime indicating the excitation from 2b 1 (NHOMO). See text for details. b SAC-CI results from Ref. (11). c Experimental data from Refs. (10, 11, 13). the calculated oscillator strengths (f), and are compared with available experimental data and with the latest SAC-CI results reported by Wan et al. (11). The comparison is strictly based on the latest assignment (11) of the experimental electronic excitation spectra of pyrrole. For the electron-loss spectrum, the peaks observed at 4.2 ev and 5.10 ev were assigned to the lowest 3 B 2 and 3 A 1 states, respectively. The lowest 3 B 2 and 3 A 1 states correspond to electronic excitations from a π orbital (1a 2 ), the highest occupied molecular orbital (HOMO) to two π orbitals; i.e., they are π π transitions. For the electronic absorption spectrum, Wan et al. (11) assigned one peak (at 5.22 ev) to the lowest 1 A 2 state (1a 2 3s Rydberg state), six peaks (at 5.7, 6.42, , , 7.54, and 7.85 ev) to the 1 B 1 states, seven peaks (at 5.86, , 6.78, , 7.4, 7.7, and 8.0 ev) to the 1 B 2 states, and five peaks (at , 7.35, , 7.95, and 8.1 ev) to the excited 1 A 1 states. According to their assignment, the six peaks at 5.7, 6.42, , , 7.54, and 7.85 ev assigned to the 1 B 1 states are due to the excitations 1a 2 3p y,1a 2 3d yz,2b 1 3p z, 1a 2 4p y,1a 2 5p y, and 1a 2 5d yz, respectively, as indicated in Table 1. Note that 2b 1 is also a π orbital which is the next highest occupied molecular orbital or NHOMO. In Table 1, the transition 2b 1 3p z (Rydberg state) is represented by 3p z R. The prime refers to the electron excitation from the NHOMO 2b 1, instead of the excitation from the HOMO 1a 2. For the seven peaks at 5.86, , 6.78, , 7.4, 7.7, and 8.0 ev assigned to the 1 B 2 states, the first three are due to excitations from the 1a 2 HOMO to mixed Rydberg and valence excited states (i.e., 1a 2 3p x mixed with 1a 2 π,1a 2 π mixed with 1a 2 3d xz, and 1a 2 3d xz, mixed with 1a 2 π ), and the remaining due to transitions to Rydberg excited states (i.e., 1a 2 4p x,1a 2 4d xz,2b 1 3d xy, and 1a 2 5d xz ). The five peaks at 7.0 to 7.1, 7.35, 7.95, and 7.5 to 8.0 ev assigned to the 1 A 1 states are due to the excitations 2b 1 3p x, 1a 2 4d xy,2b 1 π,2b 1 4p x, and 1a 2 5d xy, respectively. We note that Wan et al. (11) assigned the 4 1 A 1,5 1 B 1, and 4 1 B 2 states to the excitation region ev. Our CIS results and the assignment summarized in Table 1 are, on the whole, in agreement with the latest SAC-CI results and the assignment reported by Wan et al. (11), particularly for low-lying excited states, although order inversion does exist in some high-lying excited states, as shown in Table 1. The overall agreement between the CIS results and the experimental data is surprisingly good considering the fact that the computational cost of the CIS method is the lowest of the currently available ab initio electronic structure methods for excited state energies. Based on the assignments, the CIS results associated with low-lying singlet excited states (< 7 ev) are in excellent agreement with the corresponding experimental excitation energies. The CIS calculations slightly overestimate the excitation energies corresponding to the low-lying excited states. The CIS results give the same ordering as the SAC-CI results (11) for the 1 A 2 states and for all but one pair of the 1 B 2 states. There are some switches for the ordering of the 1 B 1 states

5 TD-DFT CALCULATIONS OF EXCITATIONS IN PYRROLE 85 calculated by CIS as compared to the SAC-CI results. Similarly, there are some switches in the ordering of the 1 A 1 states and the CIS calculations show more mixing of Rydberg character into the first valence transition than predicted at the SAC-CI level. The experimental excitation energies corresponding to highlying excited states are also close to the corresponding CIS results, although a notable difference exists in the relative order of a few high-lying excited states. According to the experimental assignments, the excitation energy for the 1a 2 4p y transition (7.0 to 7.1 ev) is higher than the excitation energy for the 2b 1 3p z transition (6.5 to 6.7 ev) by ev, whereas the calculated excitation energy for the 1a 2 4p y transition (7.02 ev) is slightly lower than the calculated excitation energy for the 2b 1 3p z transition (7.17 ev). The experimental excitation energy for the 1a 2 5d xz transition ( 8.0 ev) is higher than the experimental excitation energy for the 2b 1 3d xy transition ( 7.7 ev) by 0.3 ev, whereas the calculated excitation energy for the 1a 2 5d xz transition (8.06 ev) is nearly identical to the calculated excitation energy for the 2b 1 3d xy transition (8.08 ev). The experimental excitation energy for the 2b 1 π transition (7.5 to 8.0 ev) is higher than the experimental excitation energy for the 1a 2 4d xy transition ( 7.35 ev) by ev, whereas the calculated excitation energy for the 2b 1 π transition (7.66 ev) is lower than the calculated excitation energy for the 1a 2 4d xy transition (8.03 ev) by 0.37 ev. The experimental excitation energy for the 1a 2 5d xy transition ( 8.1 ev) is higher than the experimental excitation energy for the 2b 1 4p x transition ( 7.95 ev) by 0.15 ev, whereas the calculated excitation energy for the 1a 2 5d xy transition (8.07 ev) is lower than the calculated excitation energy for the 2b 1 4p x transition (8.40 ev) by 0.33 ev. Electronic Excitations in Pyrrole at the TD-DFT-B3LYP/cc-pVTZ + Ryd(mc) Level Summarized in Table 2 are the vertical excitation energies and oscillator strengths for the 14 lowest 1 A 2 states, 14 lowest 1 B 1 states, 8 lowest 1 B 2 states, 8 lowest excited 1 A 1 states, lowest 3 B 2 state, lowest 3 A 2 state, lowest 3 A 1 state, and lowest 3 B 1 state of pyrrole determined by the TD-DFT calculations at the B3LYP/cc-pVTZ + Ryd(mc) level in comparison with the experimental excitation energies. The comparison is also based on the assignment reported by Wan et al. (11), which is consistent with the assignment based on the CIS results in Table 1. The assignment based on the TD-DFT results is more complicated than that based on using the CIS results for pyrrole. The Hartree Fock orbitals used for our CIS calculations are very close to those used in the SAC-CI calculations by Wan et al. (11), whereas the Kohn Sham orbitals used in the TD-DFT calculations are considerably different. The TD-DFT results show stronger mixing between different types of transitions within the same symmetry. As a result, the oscillator strengths TABLE 2 Electronic Excitation Energies ( E in ev) and Oscillator Strengths ( f ) Determined by TD-DFT Calculations at the B3LYP/ cc-pvtz + Ryd(mc) Level Excited state Assignment a E f expt. b 1 A 2 3s R A 2 3p z /4s R A 2 4s/3p z R A 2 4p z R A 2 3d z2 /3d x2-y2 R A 2 3d x2-y2 /3d z2 R A 2 5s R A 2 4d z2 /5p z R A 2 5p z /4d z2 R A 2 3p y R A 2 4d x2-y2 R A 2 4p y R A 2 5p y R A 2 5d x2-y2 R B 1 3p y /3d yz R B 1 3s /3p y /3d yz R B 1 3p y /3d yz /3s R B 1 3d yz /3p y R B 1 4d yz /4p y R B 1 4s /3p z R B 1 4p y /4d yz R B 1 3p z /4s R B 1 4p z /4s R B 1 4d yz /5p y /4s R B 1 5s /3d z2 R B 1 3d x2-y2 /3d z2 /5s R B 1 5d yz /5s R B 1 5p z R B 2 3p x R/V B 2 V/3d xz R B 2 3d xz /3p x R B 2 4p x /3d xz R B 2 4d xz /4p x R/V B 2 5p x /4d xz R B 2 3d xy R B 2 4d xy R B 2 5d xz R A 1 V/3d xy R A 1 3d xy R/V A 1 3p x R/V A 1 V /3p x R A 1 3d xz /3p x R A 1 4p x R A 1 4d xy R A 1 5d xy /3d xz R B 2 V A 2 3s R A 1 V B 1 3p y R a R and V denote Rydberg and valence excited state, respectively. All transitions means the electron excitations from 1a 2 (HOMO), unless with a prime indicating the excitation from 2b 1 (HOMO-1). See text for details. b Experimental data from Refs. (10, 11, 13).

6 86 ZHAN AND DIXON calculated by the TD-DFT method are significantly different from those calculated by the CIS method for some transitions. The main components of the mixed transitions are considered in the assignment when the TD-DFT results are compared with the SAC-CI results and experimental data. It should be noted that the relative order of the excitation energies corresponding to high-lying excited states calculated at the TD-DFT level is not the same as that at the CIS level, although the low-lying excited states calculated at the TD-DFT level are consistent with those calculated at the CIS level. Thus, the 14 lowest 1 A 2 states, 14 lowest 1 B 1 states, 8 lowest 1 B 2 states and 8 lowest excited 1 A 1 states (in Table 2) determined by the TD-DFT calculations are not all the same as those (in Table 1) determined by the CIS calculations. Compared to the overall agreement between the CIS results and the experimental data, the overall deviation of the TD-DFT results from the experimental data is larger, particularly for highlying excited states. The TD-DFT calculations underestimate all the singlet excitation energies, but the deviations for low-lying excited states are smaller. The TD-DFT calculations give reasonable results for the low-lying excited states and give worse results for high-lying excited states; a conclusion similar to this was also found based on TD-DFT calculations using different functionals on other small molecules (25b). It has been well established that most DFT functionals give the wrong ioniza- tion energy based on using Koopmanns theorem and that the calculated ionization potentials are too low, leading to an ionization threshold that is too low (41). The E(HOMO) value for every calculation for pyrrole is given in Table 3. The values from the Hartree Fock calculations are all between 8.0 and 8.1 ev, in excellent agreement with the experimental ionization potential of 8.21 ev (42, 43). As expected, the DFT values are much lower with the B3LYP/cc-pVTZ + Rydberg(mc) values near 6.0 ev and other functionals (see below), giving lower values near 5.0 ev (44). For our purpose of theoretically determining chromophores in the chromogenic effects of the neurotoxicants, we are interested only in the first few low-lying singlet excited states of pyrrole-containing molecules because only excitations to these excited states could produce absorption in the region of the visible spectrum. For low-lying singlet excited states, the CIS results are better than the corresponding TD-DFT results, as shown by comparing the values in Tables 1 and 2. Whereas the TD-DFT calculations systematically underestimate the excitation energies, the CIS calculations slightly overestimate the excitation energies and the CIS results are closer to the experimental data for low-lying singlet excited states. Thus, the TD-DFT and CIS calculations for low-lying singlet excited states can be used to provide lower and upper limits of the excitation energies of pyrrole, respectively. This feature should be very useful in predicting TABLE 3 Electronic Excitation Energies ( E in ev) and Oscillator Strengths ( f ) Calculated for Excitations to the Lowest Excited State for Each Type of Symmetry by Using the CIS and TD-DFT Methods with Various Basis Sets, Together with the Calculated E(HOMO) (ev) TD-DFT CIS Excited B3LYP BLYP BP86 BPW91 state BS0 a BS1 b BS2 c BS3 d BS4 e BS0 a BS1 b BS2 c BS3 d BS4 e BS3 d BS3 d BS3 d expt. f 1 A 2 E B 1 E f B 2 E f A 1 E f B 2 E A 2 E A 1 E B 1 E E(HOMO) a BS0 represents the G(d) basis set. b BS1 represents cc-pvtz + Ryd(mc), cc-pvtz augmented by a set of molecule-centered Rydberg functions (3s3p3d). c BS2 represents 6-31G(d) + Ryd(C,N), 6-31G(d) augmented by a set of Rydberg functions for each C and N atoms. d BS3 represents cc-pvdz + Ryd(C,N), cc-pvdz augmented by a set of Rydberg functions for each C and N atoms. e BS4 represents cc-pvtz + Ryd(C,N), cc-pvtz augmented by a set of Rydberg functions for each C and N atoms. f Experimental data from Ref. (11).

7 TD-DFT CALCULATIONS OF EXCITATIONS IN PYRROLE 87 electronic excitation spectra of substituted pyrroles and in future theoretical determinations of the chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons by using both the CIS and TD-DFT methods. Effects of Basis Set and Functional To examine the basis set-dependence of the CIS and TD- DFT calculations, the results calculated for excitations to the lowest excited states for all symmetry and spin combinations using various basis sets are summarized in Table 3, together with the experimental data, for comparison. As shown in Table 3, the calculated excitation energies are not particularly sensitive to the basis set used in the CIS and TD-DFT calculations. This shows that these basis sets should be adequate for CIS and TD-DFT calculations on larger molecules. In addition, as a simple test, we have also performed CIS and TD- DFT calculations using the G(d) basis set. Surprisingly, as shown in Table 3, the lowest excitation energies calculated with the G(d) basis set are not dramatically different from those calculated with the basis sets including the Rydberg functions, even though most of these excited states have considerable Rydberg character. The overall agreement between the experimental data and the results calculated with the Rydberg functions is better than those where the Rydberg functions are not explicitly included. We provide in the supplementary material a more complete listing of the various state energies at the CIS and B3LYP/TD-DFT levels with basis sets BS1, BS2, and BS3. We also tested TD-DFT calculations using three nonhybrid functionals. The results obtained by using the BLYP, BP86, and BPW91 functionals are also listed in Table 3 for comparison. The comparison of the TD-DFT results calculated using different functionals with the same cc-pvdz + Ryd(C,N) basis set show that the B3LYP results are, on the whole, closest to the experimental excitation energies. The BP86 and BPW91 results are close to the corresponding B3LYP results with the singlet excitation energies determined with TD-DFT and the BLYP functional systematically lower than those with TD-DFT calculations and the B3LYP hybrid functional. This is consistent with the above discussion, where we showed that the largest error in the calculated ionization energies is with these latter functionals in comparison to B3LYP. Color of 2,5-Dimethylpyrrole As an example of the practical application of the TD-DFT and CIS methods benchmarked in this study, we consider the electronic absorption of 2,5-dimethylpyrrole in the visible region of the spectrum. Commercially available 2,5-dimethylpyrrole has an absorption in the region of the visible spectrum (at 530 nm) (45) and is colored. The absorption at 530 nm of liquid 2,5-dimethylpyrrole has been used as a standard reference to determine the content of any 2,5-dimethylpyrrole or its adducts that were formed in previous experimental studies of the biochemical reactions of neurotoxic 2,5-hexanedione with protein (45). However, the first electronic excitation energy of 2,5-dimethylpyrrole is predicted by our CIS/cc-pVDZ + Ryd(C,N) and TD-DFT-B3LYP/cc-pVDZ + Ryd(C,N) calculations to be 4.94 ev (251 nm) and 4.11 ev (301 nm), respectively. Based on these results, the first electronic absorption of 2,5- dimethylpyrrole is expected to be between 4.94 ev and 4.11 ev ( nm). The calculated results are consistent with a previously reported UV vis spectrum of 2,5-dimethylpyrrole in which the absorption peak with the longest wavelength is at about 270 nm (42). These results are not surprising, because 2,5-dimethylpyrrole differs from pyrrole only in the substitution of two methyl groups and such a minor structural difference (replacement of hydrogen by a methyl group) would not be expected to produce a large shift of the lowest electronic excitation energy in going from pyrrole to 2,5-dimethylpyrrole. Thus, we can conclude that 2,5-dimethylpyrrole has no absorption in the region of the visible spectrum ( nm) (46) and that the absorption observed at 530 nm and the color of the 2,5-dimethylpyrrole chemical are due to some other compound co-existing with 2,5-dimethylpyrrole. The chromophore with an absorption at 530 nm is likely to be one of the products from the autoxidation of 2,5-dimethylpyrrole, although the existence of other colored impurities cannot be excluded. We are currently investigating the nature of this chromophore in our laboratory. We also calculated the absorption spectrum for N-methyl-2,5- dimethylpyrrole to investigate the effect of a substituent methyl on the nitrogen. The geometry was optimized at the same level as above (see Fig. 1). The first electronic excitation energy of N- methyl-2,5-dimethylpyrrole is predicted to be 4.98 ev (249 nm) and 4.10 ev (302 nm) at the CIS/cc-pVDZ + Ryd(C,N) and TD- DFT-B3LYP/cc-pVDZ + Ryd(C,N) levels, respectively. Thus, there is essentially no effect for substitution of a methyl group for H on the nitrogen in terms of the absorption spectra. The conclusion that the absorption at 530 nm is not due to 2,5-dimethylpyrrole suggests that the conclusions drawn from previously reported experimental studies of biochemical reactions of neurotoxic 2,5-hexanedione with proteins need to be reconsidered. We are currently working on possible molecular mechanisms of the neurotoxicity. CONCLUSION We have carried out a series of TD-DFT and CIS calculations on the electronic excitations in pyrrole in order to examine the reliability of these first-principles electronic structure methods in predicting electronic excitation spectra, particularly the excitation energies for low-lying excited states, of pyrrole ringcontaining compounds. Both the TD-DFT and CIS calculations led to qualitatively satisfactory results compared to available experimental data. Quantitatively, the TD-DFT calculations systematically underestimate the excitation energies by a few tenths of an ev, whereas the CIS calculations slightly overestimate the excitation energies for low-lying excited states. Thus, the

8 88 ZHAN AND DIXON TD-DFT and CIS calculations give lower and upper limits to the excitation energies, respectively, for low-lying excited states. These results suggest that we can use these electronic structure methods which have moderate computational costs to predict the electronic excitation spectra of a variety of substituted pyrroles and their adducts with proteins as well as in future studies of the chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons. As a simple example of the practical applications of the methods, the absorption spectrum of the widely used compound, 2,5-dimethylpyrrole, has been calculated. The calculated results are consistent with a previously reported UV vis spectrum of 2,5-dimethylpyrrole and lead us to conclude that the 2,5- dimethylpyrrole molecule itself has no absorption in the visible spectrum ( nm). The absorption observed at 530 nm and the color of the 2,5-dimethylpyrrole liquid are due to some other compound coexisting in the liquid. The actual chromophore with an absorption at 530 nm could be one of the products of the autoxidation of 2,5-dimethylpyrrole. ACKNOWLEDGMENTS This research was performed in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL) at the PNNL. The EMSL is a national user facility funded by the Office of Biological and Environmental Research in the U.S. Department of Energy. PNNL is a multiprogram national laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy. The work was funded in part by a subcontract to Battelle Pacific Northwest Division from Oregon Health Sciences University under the auspices of a National Institute of Environmental Health Sciences Superfund Basic Research Center Grant 5 P42 ES REFERENCES 1. For most recent work, see A. V. Kel in, A. W. Sromek, and V. Gevorgyan, J. Am. Chem. 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