Benchmarking Electronic Excitation Energies and Transitions in

Article pubs.acs.org/JPCA

Benchmarking Electronic Excitation Energies and Transitions in Peptide Radicals František Tureček* Department of Chemistry, University of Washington, Bagley Hall, Box 351700, Seattle, Washington 98195-1700, United States S Supporting Information *

ABSTRACT: Excited electronic states in several radical chromophores representing photochemically active groups in peptide and protein radicals and cation radicals were investigated computationally using equation-ofmotion coupled cluster (EOM-CCSD) and time-dependent density functional theory (TD-DFT) methods. The calculations identified the main transitions responsible for photodissociations of gas-phase peptide cation radicals in the near-UV region of the spectrum. Analysis of the EOM-CCSD benchmarks showed that no TD-DFT method was universally accurate across the various radical motifs that included Cα-amide, aminoketyl, formamidyl, guanidyl, carbamyl, benzyl, phenoxy, and tautomeric dihydrophenyl and imidazolyl radicals. Overall, the ωB97XD, M06-2X, and LC-BLYP hybrid functionals showed acceptable performance when benchmarked against EOM-CCSD calculations. However, the performance of these TD-DFT methods depended on the nature of the radical chromophore, emphasizing the need for benchmarking and careful analysis.

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INTRODUCTION Amino acid residues tyrosine, cysteine, and glycine are susceptible to radical hydrogen atom abstraction forming transient O-, S-, and Cα-radicals. These reactive intermediates play an important role in protein reactions catalyzed by several enzymes,1,2 as well as in radical-induced protein degradation.3,4 The formation of biological radical intermediates has been investigated using electron spin resonance,5,6 and their thermochemistry has been addressed by ab initio calculations.7−12 In the past few years, a remarkable progress has been made in generating biomolecular radicals derived from gasphase peptide ions to study their physical properties and reactivity as models of biochemical systems. This renaissance has been driven by new experimental methods of generation peptide and protein cation-radicals,13,14 as well as by interest in their unusual electronic properties.15−19 Among the different types of radicals, hydrogen-rich peptide radicals and cationradicals are produced by electron attachment to protonated peptides in the gas phase. Hydrogen-rich peptide cation-radicals undergo homolytic bond cleavages forming closed-shell and radical backbone fragments that are used to provide amino acid sequence information.20,21 Other types of open-shell species, which are called hydrogen-deficient peptide cation radicals, can be produced by several methods, involving electron induced dissociation of peptide ions, photolysis,22 or collision-induced dissociation23,24 of suitably derivatized peptides, and intramolecular electron transfer oxidation in peptide−transitionmetal complexes with auxiliary ligands.25−28 We have recently introduced a new method of peptide cation-radical analysis that relies on photodissociation in the © XXXX American Chemical Society

near-UV region of the spectrum (near-UVPD), specifically at 355 nm which is readily available as the third harmonics line from a Nd:YAG laser29 and which is currently being expanded to full action spectroscopy in the 210−700 nm region. In contrast to infrared multiphoton dissociation and shortwavelength (λ < 300 nm) UV photodissociation,30−32 nearUVPD selectively targets radical chromophores, whereas the bulk of peptide amide and side chain groups are transparent. To further explore and rationalize the phenomena associated with near-UVPD, we have combined experiments with theoretical analysis of electronic excitations in several peptide cationradicals using time-dependent density functional theory.33 However, due to the approximate nature of TD-DFT and its strong dependence on the type of functional used it appeared warranted to benchmark the excitation energies and transition moments using higher-level calculations. Previous benchmark computational studies of TD-DFT excitation energies used linear response methods34,35 to assess excitation energies, as extensively reviewed for several molecular systems with closed electron shells36−42 and transition metal complexes.43 Recently, Frison et al. reported benchmark calculations of excitation energies for model ammonium radicals, representing small lysine-containing charge-reduced peptides.44 The experimentally studied hydrogen-rich and−deficient peptide cation-radicals incorporate a range of different structure motifs derived from protonated and Received: June 29, 2015 Revised: August 31, 2015

A

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Structure motifs for chromophore groups in peptide radicals.

meric imidazoline radicals pertinent to histidine residues formed by H atom addition to the imidazole ring or singleelectron reduction of its protonated form. Radicals 14−18 have been studied previously33 and are included here for the sake of comprehensive analysis. Combined, all these species represent the major structure motifs encountered in peptide radicals and cation radicals produced by electron transfer, photodissociation, collision-induced dissociation, and one-electron oxidation. Computational Methods. Standard ab initio and density functional theory calculations were performed with the Gaussian 09 suite of programs.55 All structures were obtained by gradient optimization using the B3LYP56 and M06-2X57 hybrid functionals with the 6-31+G(d,p) basis set and confirmed as local energy minima by harmonic frequency calculations which gave all real frequencies. All calculations were performed for doublet spin states within the spinunrestricted formalism. Select structures were reoptimized at different levels of theory, as described in the text below. The optimized structures in the Cartesian coordinate format are collected in Tables S1−S16 of the Supporting Information. Vertical excitation energies for the doublet spin states were obtained by time-dependent DFT calculations58 using the B3LYP, M06-2X, LC-BLYP,59 and ωB97X-D60,61 functionals and the 6-311++G(2d,p) basis set in a spin unrestricted formalism. The lowest 15 excited states were located by TDDFT calculations that showed spin expectation values ranging from ⟨S2⟩ = 0.75 through 2.7. States corresponding to doublets were then selected, allowing for spin contamination up to ⟨S2⟩ < 1.5. The choice of density functionals was based on previous studies36−42 with particular regard to the results of Frison et al.44 Benchmark excitation energies were obtained by equationof-motion calculations62,63 with coupled clusters and single and double excitations (EOM-CCSD) using the 6-311++G(2d,p) and 6-31+G(d,p) basis sets. Radicals 4, 9, and 10 were too large for EOM-CCSD/6-311++G(2d,p) calculations and so only results obtained with the 6-31+G(d,p) basis set are reported.

neutral functional groups, as well as a variety of dissociation products. These polyatomic systems are too large for higherlevel calculations, and their electronic excitation can be addressed by TD-DFT methods at best. It is therefore useful to benchmark TD-DFT excitation energies and transition intensities for selected radical structure motifs in smaller molecular systems representing several chromophores that presumably appear in peptide radicals and affect their structure and reactivity. The goal is to examine the performance of TDDFT methods and choose the best performing ones to be used for large polyatomic radicals where high-level excited state calculations are beyond the capabilities of current technology. The typical radical structure motifs that are found in peptide radicals are shown in Figure 1. Structures 1 and 2 (R = CH3 throughout Figure 1) represent radical fragments of the z-type, which are truncated peptide Cα-radicals terminated at glycine and alanine, respectively. Radical 2 exists in two forms, the trans-isomer 2a and the cis-isomer 2b. Radicals of this type are formed by electron-induced backbone cleavage in multiply charged peptide and protein ions.14 Structures 3 and 4 represent captodative alanine Cα radicals related to intermediates of isomerization in hydrogen-deficient peptide cation radicals formed by intramolecular electron transfer in peptide− metal complexes.45−48 Structure 5 is a glycine proper aminoketyl radical49 representing reactive intermediates of peptide cation-radical dissociations by N−Cα backbone cleavage.14 Structures 6−8 represent intermediates of arginine radical reactions by deamination and hydrogen atom capture.50−52 Structure 9 represents fragments of the x-type which are carbamate radicals produced by Cα−CO homolytic bond cleavage in peptides upon electron capture or transfer. Structure 10 is an α-benzyl radical proposed as an intermediate of hydrogen atom migrations in phenylalanine and tyrosine residues.53,54 Structures 11 and stuctures 12 and 13 are related, respectively, to hydrogen atom abstraction and addition to tyrosine residues. Finally, structures 14−18 represent tautoB

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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RESULTS The goal of this study was to test the performance of several TD-DFT methods which were applied to several specific chromophores of relevance to peptide radical chemistry. Computational studies of peptide radicals and cation radicals are typically conducted using DFT methods at levels that include gradient optimization with a double-ζ quality basis set furnished with polarization and diffuse functions, for example, 6-31+G(d,p), followed by single-point energy calculations with a larger, typically triple-ζ, basis set furnished with additional polarization and diffuse functions, for example, the split-valence 6-311++G(2d,p) and 6-311++G(3df,2p), correlation-consistent aug-cc-pVTZ,64 or def-type basis sets.65 These larger basis sets have also been used for TD-DFT calculations of electronic excitation energies. This implied that the geometry of the ground electronic state was not identical with that of a local energy minimum corresponding to the level of theory used for the single-point calculations. Although it was reasonable to assume that increasing the size of the basis set would have only a small effect on optimized geometries when DFT methods were used, the magnitude of this effect on electronic excitation energies has been unknown. Effects of Ground State Geometry. We first investigated this geometry effect by calculating EOM-CCSD/6-311++G(2d,p) excitation energies and oscillator strengths for structures of 1 that were optimized with B3LYP/6-31+G(d,p), and then another set where geometries were optimized with B3LYP, M06-2X, ωB97X-D, MP2(full), and CCSD, all with the 6-311+ +G(2d,p) basis set. Table S17 (Supporting Information) shows that the effect on the excitation energies of the ground state geometry was quite small for the six lowest excited states of 1, giving root-mean square deviations from the EOM-CCSD/6311++G(2d,p)//CCSD/6-311++G(2d,p) calculation in the range of 0.02−0.09 eV. The largest deviation (rmsd = 0.09 eV) was found for excitation energies that were based on the B3LYP/6-31+G(d,p) optimized geometry, albeit still within the expected accuracy of EOM-CCSD calculations (ca. 0.2 eV).66−68 Similar effects of the ground state geometry were observed for TD-DFT and EOM-CCSD calculations that were run for several other radical systems as single-point jobs on B3LYP/631+G(d,p) optimized structures and on geometries that were fully optimized by the method in question, as compiled for the six lowest excited states (Table S18, Supporting Information). The data showed a few general trends. The LC-BLYP excitation energies were most sensitive to the radical geometry, giving root-mean square deviations that ranged from 0.04 eV for 2a to 0.33 eV for 4. Inspection by the structure type indicated that the phenoxy (11) and dihydrophenol radicals (12, 13) were least affected by variations in their optimized geometries. The ωB97X-D excitation energies appeared to be least sensitive to the radical geometry, showing only 0.02−0.08 eV rmsd when calculated with B3LYP/6-31G+(d,p) and fully optimized geometries. The EOM-CCSD excitation energies showed 0.02 to 0.22 eV rmsd for the same set, with the greatest deviations for the formamidine radicals 6 and 7, and the imidazole radicals 14, 16, and 17 (Table S18). Effects of Basis Set Size. Since the EOM-CCSD calculations scale with the sixth power of the number of atomic orbitals defined by the basis set, it was of interest to investigate the effect of the basis set size on the excited state calculations. This was carried out by comparing excitation

energies calculated with EOM-CCSD/6-311++G(2d,p) and 631+G(d,p) using radical ground-state geometries optimized with B3LYP/6-31+G(d,p). Figure 2a shows the rmsd for the six

Figure 2. Root-mean square deviations of EOM-CCSD and TD-DFT excitation energies to the first through sixth excited states referenced to (a) EOM-CCSD/6-311++G(2d,p)//B3LYP/6-31+G(d,p) and (b) EOM-CCSD/6-311++G(2d,p)//CCSD/6-311++G(2d,p) energies. (●) EOM-CCSD/6-31+G(d,p); (▼) ωB97X-D/6-311++G(2d,p); (△) M06-2X/6-311++G(2d,p); (○) LC-BLYP/6-311++G(2d,p); (■) B3LYP/6-311++G(2d,p). The blue symbols show combined rmsd for all excited states in all radicals.

lowest excited states for all radicals under study except 4, 8, and 9 for which EOM-CCSD/6-311++G(2d,p) calculations were not feasible. In general, using a smaller basis set in these EOMCCSD calculations resulted in higher excitation energies for all excited states. The rmsd for the two lowest excited states were quite small (0.08−0.11 eV) but increased to 0.2−0.25 eV at higher excited states. The overall rmsd across the five lowest excited states for all radicals under study was 0.17 eV which increased to 0.24 eV when the sixth excited state was included. The rmsd for the first five excited states is well within the expected accuracy of EOM-CCSD calculations.66−68 We conclude that EOM-CCSD calculations with the 6-31+G(d,p) basis set yield slightly higher excitation energies, but do not significantly degrade accuracy. We also examined the effect of the basis set in LC-BLYP calculations that were carried out for several radical systems with the 6-311++G(2d,p) and aug-ccC

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 1. Excitation Energies and Oscillator Strengths of Radical Excited States EOM-CCSDa radical 1

2a

2bf

3

4

5

6

7

8

9f

10f

11

12

13

14

state 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 4th 1st 2nd 3rd 1st 2nd 3rd 4th 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th

Eexcc 2.88 3.45 5.78 3.09 3.73 5.28 2.90 3.56 5.47 3.41 3.85 4.15 4.42 3.72g 4.05g 4.37g 3.13 3.72 3.98 4.11 3.21 4.30 4.55 3.35 5.02 5.73 2.81 3.51 3.68 3.94 4.06g 4.18g 5.31g 5.59g 3.60g 3.68g 4.65g 4.73g 4.88g 1.54 2.88 3.90 4.85 4.96 2.95 3.69 4.23 4.23 4.50 2.95 4.07 4.20 4.67 4.73 2.44 2.93 3.17 3.29 3.66

f

d

0.000 0.014 5 × 10−4 9 × 10−4 0.024 0.002 2 × 10−4 0.021 1 × 10−4 0.004 0.002 0.001 0.018 0.002 0.023 0.000 0.002 0.023 0.065 0.035 5 × 10−4 0.002 0.032 0.003 0.035 0.006 5 × 10−4 0.009 0.017 0.070 0.003 7 × 10−4 0.000 0.047 6 × 10−4 1 × 10−4 0.005 3 × 10−4 0.057 0.000 0.005 0.024 7 × 10−4 0.059 6 × 10−4 0.002 0.000 0.078 0.040 0.005 0.038 2 × 10−4 0.049 3 × 10−4 0.003 2 × 10−4 0.011 0.001 0.005

ωB97X-D

LC-BLYP Eexc 3.02 3.63 6.22 3.35 3.88 5.67 3.11 3.76 6.00 3.98 4.19 4.67 4.73 4.01 4.33 4.41 3.53 4.20 4.54 4.64 3.05 4.48 4.51 3.50 4.80 5.63 3.25 4.01 4.22 4.46 4.03 4.51 5.76 5.94 3.55 3.86 4.44 5.01 5.18 1.59 2.92 4.05 4.92 5.50 3.10 4.06 4.17 4.59 4.72 3.08 4.01 4.65 4.66 5.22 2.83 3.09 3.36 3.76 4.05

⟨S ⟩

2 e

f −4

1 × 10 0.022 0.004 5 × 10−4 0.025 0.001 2 × 10−4 0.021 1 × 10−4 0.005 0.001 0.025 0.005 0.001 0.024 1 × 10−4 0.002 0.020 0.074 0.024 0.001 0.004 0.030 0.003 0.014 0.006 6 × 10−4 0.007 0.014 0.070 0.004 2 × 10−4 0.002 0.042 0.002 6 × 10−4 0.021 1 × 10−4 0.389 0.000 0.008 0.042 0.051 0.000 0.001 0.088 0.002 0.016 0.000 0.009 0.045 1 × 10−4 0.033 4 × 10−4 0.004 0.009 8 × 10−4 3 × 10−4 0.009

0.98 1.14 1.53 1.00 1.17 0.96 1.00 1.17 0.96 1.02 0.81 1.21 0.84 1.01 1.20 1.66 0.81 0.81 0.79 0.81 0.77 0.77 0.86 0.78 1.14 1.74 0.81 0.83 0.85 0.82 0.76 0.80 0.76 0.94 1.40 1.04 1.68 0.90 0.83 1.01 0.84 0.88 0.92 1.02 0.83 0.95 0.92 1.71 0.91 0.87 0.98 0.92 1.69 0.98 0.85 1.48 0.88 0.85 0.91

D

Eexc 2.52 3.06 5.84 2.88 3.39 5.26 2.67 3.26 5.50 3.62 3.72 4.19 4.30 3.47 3.80 4.25 3.13 3.69 3.92 4.09 2.89 4.33 4.35 3.29 4.75 5.41 2.88 3.56 3.73 3.94 3.96 4.12 5.50 5.54 3.44 3.49 4.12 4.59 4.92 1.24 2.53 3.74 4.65 5.05 2.82 3.78 3.81 4.29 4.43 2.79 3.72 4.25 4.46 4.74 2.56 2.89 3.07 3.35 3.69

M06-2Xb ⟨S2⟩

f −4

3 × 10 0.018 0.005 6 × 10−4 0.022 0.001 2 × 10−4 0.016 1 × 10−4 0.004 0.002 0.019 0.001 0.002 0.022 0.044 0.003 0.022 0.068 0.021 7 × 10−4 0.019 0.014 0.003 0.014 0.010 5 × 10−4 0.007 0.016 0.060 0.002 0.002 0.025 0.002 0.001 6 × 10−4 0.036 0.000 0.365 0.000 0.006 0.036 0.048 0.000 0.001 0.002 0.095 0.000 0.009 0.008 0.051 1 × 10−4 0.026 1 × 10−4 0.004 0.009 0.002 8 × 10−4 0.006

0.88 0.95 1.10 0.89 0.97 0.86 0.89 0.97 0.86 0.78 0.89 0.99 0.79 0.89 1.26 1.05 0.79 0.78 0.78 0.79 0.77 0.81 0.81 0.78 1.17 1.26 0.79 0.80 0.81 0.80 0.77 0.78 0.79 0.85 1.07 0.99 1.06 0.82 0.79 0.87 0.80 0.78 0.84 0.98 0.79 0.84 0.85 0.83 1.55 0.81 0.83 0.84 1.73 0.87 0.82 1.15 0.84 0.82 0.86

Eexc 2.70 3.27 5.51 3.05 3.54 4.90 2.83 3.52 5.18 3.27 3.73 3.84 4.17 3.56 3.80 4.10 2.96 3.42 3.72 4.09 2.51 4.05 4.09 3.29 4.84 5.38 2.76 3.31 3.47 3.99 3.64 3.83 5.17 5.32 3.45 3.51 4.15 4.52 4.82 0.86 2.50 3.63 4.63 4.89 2.72 3.32 3.70 3.77 4.06 2.74 3.61 3.76 4.17 4.35 2.28 2.62 2.89 2.98 3.38

⟨S2⟩

f −4

4 × 10 0.018 0.004 3 × 10−4 0.023 0.001 2 × 10−4 0.016 1 × 10−4 0.003 0.002 0.001 0.019 0.002 0.022 0.038 0.008 0.028 0.049 0.039 5 × 10−4 0.005 0.028 0.001 0.014 4 × 10−4 3 × 10−4 0.004 0.014 0.031 0.002 7 × 10−4 0.033 0.006 0.001 0.001 0.035 0.002 0.263 0.000 0.007 0.034 0.052 0.000 6 × 10−4 0.001 0.094 0.000 0.001 0.006 0.053 1 × 10−4 2 × 10−4 0.034 0.001 7 × 10−4 0.011 4 × 10−4 0.003

0.93 1.00 1.04 0.94 1.02 0.83 0.94 1.02 0.83 0.77 0.93 0.78 1.01 0.93 1.00 1.00 0.77 0.78 0.77 0.77 0.76 0.76 0.81 0.80 1.32 1.62 0.79 0.79 0.80 0.80 0.76 0.78 0.85 0.81 0.97 0.95 0.81 1.04 0.82 0.86 0.81 0.77 0.85 0.97 0.79 0.80 0.78 0.80 0.79 0.80 0.79 0.81 0.81 1.25 0.80 0.81 0.97 0.81 0.84

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 1. continued EOM-CCSDa radical f

15

16

17

18f

state

Eexcc

1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th

3.33 3.70 3.89 4.13 4.36 3.35 3.69 3.80 4.26 4.44 3.36 3.90 4.19 4.49 4.57 3.09 3.39 3.72 4.13 4.22

Eexc

0.004 0.003 0.003 0.004 0.003 0.003 0.015 0.005 0.004 0.036 0.004 0.017 0.004 0.002 0.033 0.004 0.041 0.004 0.001 0.008

3.88 3.99 4.00 4.68 4.89 3.79 3.94 3.96 4.74 4.83 3.73 3.83 4.61 4.93 4.97 3.45 3.66 4.33 4.74 4.82

f

ωB97X-D

LC-BLYP

d

M06-2Xb

f

2 e

⟨S ⟩

Eexc

f

⟨S2⟩

Eexc

f

⟨S2⟩

0.002 0.002 0.003 0.100 0.004 0.008 0.006 0.015 0.042 0.033 0.004 0.007 0.003 0.039 3 × 10−4 0.062 0.006 0.004 0.001 0.007

0.82 0.96 0.85 0.88 0.83 0.76 0.95 0.84 0.91 0.85 1.66 0.86 0.88 1.13 0.85 0.75 0.86 0.85 0.84 0.85

3.64 3.69 3.78 4.38 4.56 3.52 3.73 3.77 4.37 4.52 3.38 3.51 4.14 4.46 4.47 3.30 3.38 3.89 4.26 4.35

0.003 0.003 0.004 0.002 0.090 0.004 0.008 0.010 0.003 0.028 0.005 0.013 0.003 9 × 10−4 0.030 0.010 0.047 0.004 0.001 0.008

0.80 0.79 0.85 0.79 0.84 0.80 0.77 0.85 0.80 0.82 0.89 1.05 0.82 0.81 0.85 0.81 0.76 0.81 0.80 0.80

3.17 3.62 3.72 3.91 4.09 3.12 3.53 3.60 3.86 4.07 3.14 3.50 3.85 4.10 4.43 2.80 3.28 3.39 3.74 3.89

0.002 0.001 0.011 0.002 0.002 0.001 0.001 0.024 0.001 0.006 0.002 0.014 5 × 10−4 5 × 10−4 0.026 0.003 0.042 0.001 0.001 0.006

0.78 0.88 0.77 0.77 0.77 0.79 0.86 0.75 0.78 0.78 0.80 1.07 0.82 0.81 0.81 0.79 0.75 0.78 0.78 0.78

a All calculations are with the 6-311++G(2d,p) basis set using geometries optimized with the same method unless stated otherwise. bUsing M06-2X/ 6-31+G(d,p) optimized geometries. cExcitation energies in electron volts. dOscillator strength. eExpectation values of the spin operator. fCalculations on B3LYP/6-31+G(d,p) optimized geometries. gFrom EOMCCSD/6-31+G(d,p) calculations on B3LYP/6-31+G(d,p) optimized geometries.

Table 2. Excited State Transitions in ●CH2CONHCH3 Radical 1 state/transitiona methoda

A

B

C

D

M06-2X

18β → 20β (0.94)b 18β → 27β (−0.22)

19β → 20β (0.94)

20α → 21α (0.91) 20α → 22α (−0.26)

19β → 21β (0.94)

LC-BLYP

18β → 20β (0.92) 18β → 27β (−0.21)

19β → 20β (0.91)

ωB97X-D

18β → 20β (0.88)

19β → 20β (0.87) 18β → 20β (−0.42)

20α → 21α (0.77) 20α → 22α (−0.31) 19β → 21β (0.21) 20α → 21α (0.85) 20α → 22α (−0.36)

EOM-CCSD

18β → 21β (0.82) 18β → 28β (−0.33) 18β → 31β (0.24)

19β → 21β (−0.83) 19β → 28β (0.28) 19β → 31β (−0.22)

20α → 21α (0.74) 20α → 22α (0.25) 20α → 26α (0.22)

14β → 20β (0.70) 15β → 20β (0.47) 16β → 20β (0.34) 17β → 20β (0.63) 19β → 21β (−0.43) 20α → 27α (0.30) 19β → 20β (−0.75) 19β → 26β (−0.28) 20α → 21α (0.21)

E

F

14β → 20β (0.60) 15β → 20β (0.55) 16β → 20β (−0.39) 19β → 21β (0.81) 19β → 26β (−0.23) 20α → 21α (−0.23) 19β → 21β (0.76) 17β → 20β (0.37)

17β → 20β (0.54) 20α → 27α (−0.35) 19α → 27α (−0.28) 19α → 35α (0.49) 19α → 27α (0.41) 19α → 32α (0.35) 14β → 20β (0.75) 16β → 20β (−0.46) 15β → 20β (−0.36) 17β → 21β (−0.58) 19α → 38α (0.39) 20α → 38α (−0.24) 17β → 28β (0.22)

19α → 21α (0.66) 20α → 22α (0.40) 20α → 23α (−0.26)

a

Calculations with the 6-311++G(2d,p) basis set on fully optimized geometries. bTransition amplitudes; only those with absolute values > 0.2 are listed.

(rmsd = 0.28 eV), whereas the LC-BLYP and B3LYP energies showed even more substantial deviations (rmsd = 0.47 and 0.53 eV, respectively). Another comparison of the TD-DFT and EOM-CCSD results was made for a subset of excitation energies that were based on structures of 1, 2a, 3, 5, 6−8, 11− 14, 16, and 17, which were fully optimized with the method used for the excited-state calculations and the 6-311++G(2d,p) basis set (Figure 2b). This data set again showed the best overall performance for ωB97X-D excitation energies, although the rmsd (0.20 eV) was not significantly different from that obtained when B3LYP/6-31+G(d,p) geometries were used. This is consistent with the above-mentioned low sensitivity of ωB97X-D excitation energies to the underlying radical geometry. The M06-2X and B3LYP excitation energies in Figure 2b showed somewhat worse fit (rmsd = 0.36 and 0.57

pVTZ basis sets. These calculations yielded excitation energies within 0.06 eV and can be considered equivalent. Comparison of EOM-CCSD and TD-DFT Excitation Energies. The major point of this work was to compare the TD-DFT calculated excitation energies with those from EOMCCSD/6-311++G(2d,p) benchmarks. An overall comparison is presented in Figure 2 where we plot the rmsd for excitation energies of the six lowest excited states that were calculated for 1−18. Figure 2a data used excitation energies for geometries that were optimized with B3LYP/6-31+G(d,p), except for M06-2X excitation energies that were calculated on M06-2X/631+G(d,p) optimized geometries throughout. This data set indicates that the ωB97X-D excitation energies gave a close overall match for the six lowest excited states with an rmsd of 0.21 eV. The fit was less tight for M06-2X excitation energies E

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

corresponding to a dipole-disallowed electron transition from a doubly occupied amide πxy MO18 to the singly occupied frontier πz orbital (SOMO, MO20 or 21, Figure 3). This valence-state transition had a very small oscillator strength (f = 0.000−0.0004, Table 1) and would give rise to a very weak band in the absorption or action spectrum. The lowest-energy observable transition was found in the near-UV (300−400 nm) region of the spectrum (Eexc = 3.45 eV, λ = 359 nm, f = 0.014), leading to the second excited state. A major component of this transition is valence-state excitation from the doubly occupied amide πz MO19 to the SOMO. The excitation energy of this experimentally important transition was well reproduced by LC-BLYP and M06-2X calculations with the respective absolute deviations of ΔE = 0.18 and −0.18 eV (Table 1). The higher excited states (C through F, Table 2) included combined transitions between the valence shell MOs and those from the SOMO to the virtual orbital space (MO21 and higher, Figure 3). Electron excitations in homologous Cα radicals 2a and 2b were analogous to those in 1. The bright second excited state in 2a (Eexc = 3.73 eV, λ = 332 nm, f = 0.024) showed a blue shift relative to the analogous transition in 1. Similar blue shifts were reproduced by all TD-DFT calculations (Table 1). The closest match with the benchmark EOM-CCSD excitation energy was obtained for LC-BLYP and M06-2X calculations, ΔE = 0.15 and −0.19 eV, respectively (Table 1). Molecular orbital analysis indicated very similar orbitals involved in the M06-2X and EOM-CCSD excitations of 2a compared to those for 1. The second excited state had a strong component in the electron transition from the doubly occupied amide πz MO23 to the SOMO (MO24) of the same πz type (Table S19, Figure S1, Supporting Information). The captodative Cα radical 3 showed two transitions in the near-UV region, corresponding to the first and second excited state of 3.41 and 3.85 eV excitation energies, respectively (Table 1). These were best matched by M06-2X calculations of ΔE = −0.14 eV and −0.12 eV, respectively. Molecular orbital analysis indicated that the first excited state involved an electron transition from MO28 (SOMO) to MO29 of a molecular Rydberg type (Table S20, Figure S2, Supporting Information). A major component of the second excited state was due to a transition from the πxy valence-state orbital (MO26) to the SOMO. Both these transitions are only weakly allowed and have low oscillator strengths (Table 1). The first dipole-allowed πz(MO27) → πz(MO35) transition of 4.42 eV excitation energy corresponds to the fourth excited state and occurs in the UV region. The N-formylated glycinamide radical 4 was the closest analogue of various internal Cα radicals in peptides of the R1CO-NH-C●(R2)CO-NH-R3 type.45−47,69,70 The first excited state of 4 from EOM-CCSD calculations, Eexc = 3.72 eV, λ = 334 nm, f = 0.002, was well reproduced by M06-2X calculations (ΔE = −0.16 eV). The second excited state (Eexc = 4.05 eV, λ = 306 nm, f = 0.023) was approximated by M06-2X and ωB97XD calculations at ΔE = −0.25 eV and by LC-BLYP at ΔE = 0.28 eV. It may be noted that a closer match for excitation energies of 4 was obtained for M06-2X and LC-BLYP singlepoint calculations that were based on B3LYP/6-31+G(d,p) optimized geometries, probably because of error cancellation. The molecular orbitals involved in the electron excitations of 4 are depicted in Table S21 and Figure S3 (Supporting Information). The first excited state is chiefly due to a transition from the πxy(MO28 or 29) to the πz(MO31) which is

eV, respectively), possibly because of less efficient error cancellation. The LC-BLYP excitation energies showed a slightly improved fit (rmsd = 0.38 eV) when based on LCBLYP/6-311++G(2d,p) optimized geometries. The rmsd values average deviations over the six lowest excited states, but differ for specific radical systems. The nature of these deviations is discussed for individual radical types below. The overall fits of the TD-DFT excitation energies, as expressed by the rmsd values, were further analyzed with respect to specific chromophores in these species so that the most appropriate DFT methods could be selected for calculations of larger peptide radicals. The calculated transition energies and oscillator strengths for the lowest 3−5 excited states are summarized in Table 1, and the data from the EOMCCSD calculations are discussed below. The goal was to include transitions at wavelengths above 250 nm that can be used to characterize radical chromophores in peptide ions without overlap with natural tyrosine and tryptophan chromophores. Cα and Aminoketyl Radicals. Radicals carrying the oddelectron defect on the α-carbon next to the amide carbonyl are the most common species in peptide cation-radical chemistry. Radicals 1 and radicals 2a and 2b represent C-terminal fragments (z-type ions) derived from deaminated glycine and alanine residues, respectively. The transitions and amplitudes for electron excitations in 1 are represented by M06-2X and EOM-CCSD calculations, as summarized in Table 2; the relevant molecular orbitals (MO) are depicted in Figure 3. Note that the MOs from M06-2X and EOM-CCSD analysis in Figure 3 are arranged according to their nodality and excitation energies, so their numbers do not match. The first excited state of 1 was in the visible region (Eexc = 2.88 eV, λ = 431 nm),

Figure 3. Molecular orbitals in radical 1. Left panel: Orbitals from M06-2X TD-DFT calculations. Right panel: orbitals from EOMCCSD calculations. For electron transitions involving these orbitals, see Table 2. F

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 3. Excited State Transitions in H2NCH2C●(OH)NHCH3 Radical 5 state/transitionsa method M06-2X LC-BLYP

A 25α 25α 25α 25α

→ → → →

26α 27α 26α 27α

B (0.84)b (0.42) (0.75) (0.41)

wB97X-D

25α → 26α (0.83) 25α → 27α (0.35)

EOM-CCSD

25α → 26α (0.75) 25α → 27α (0.33)

C

D

25α 25α 25α 25α 25α

→ → → → →

27α 26α 27α 28α 26α

(0.80) (−0.44) (0.59) (0.55) (−0.35)

25α 25α 25α 25α 25α

→ → → → →

28α 27α 28α 27α 29α

(0.90) (−0.31) (0.61) (−0.41) (−0.44)

25α 25α 25α 25α 25α 25α

→ → → → → →

27α 28α 26α 27α 28α 26α

(0.69) (0.51) (−0.34) (−0.59) (−0.50) (0.36)

25α 25α 25α 25α 25α 25α

→ → → → → →

28α 27α 26α 28α 27α 29α

(0.79) (−0.44) (0.25) (−0.70) (0.47) (0.21)

25α 25α 25α 25α 25α 25α 25α 25α

→ → → → → → → →

29α 30α 29α 31α 28α 27α 29α 27α

E (0.93) (−0.52) (0.75) (−0.25) (0.33) (−0.29) (0.88) (0.26)

25α → 29α (−0.82) 25α → 27α (0.24)

F

25α 25α 25α 25α 25α

→ → → → →

30α 30α 31α 26α 27α

(0.75) (0.54) (0.77) (−0.26) (−0.25)

25α 25α 25α 25α 25α 25α

→ → → → → →

31α 30α 26α 31α 30α 26α

(0.80) (0.28) (−0.24) (−0.63) (0.40) (−0.30)

25α → 31α (0.79) 25α → 30α (0.78) 25α → 33α (0.23) 25α → 31α (0.23) 25α → 30α (0.86) 25α → 31α (−0.33) 25α → 30α (0.74) 25α → 31α (0.42) 25α → 33α (0.24)

a Calculations are with the 6-311++G(2d,p) basis set on fully optimized geometries. bTransition amplitudes; only those with absolute values > 0.2 are listed.

the SOMO. This disallowed transition shows a low oscillator strength. The second excited state involves another valencestate electron excitation from the πz(MO30) to the SOMO. The excitation energy for this πz amide transition is lower for 4 than for 3, indicating a red shift in the corresponding absorption bands. A possible explanation for the lower excitation energy in 4 is a more extensive delocalization and hence a lower energy of the SOMO in the OC−NH−CH− CO−NH π-electron system compared to the SOMO in the H2N−CH−CO−NH group of 3. Electron excitations in the aminoketyl radical 5 were predicted by EOM-CCSD to lead to a weak absorption in the visible and a stronger absorption in the near-UV region. The corresponding excitation energies (Eexc = 3.13, 3.72, and 3.98 eV, Table 1) were best matched by ωB97X-D calculations, giving ΔE = 0.01, − 0.03, and −0.06 eV, respectively. LC-BLYP gave positive deviations, ΔE = 0.4−0.57 eV, while those from M06-2X were negative, ΔE = −0.17 to −0.31 eV. The nature of the electron excitations in 5 is illustrated by the transition amplitudes for the A−F states (Table 3) and the MOs involved (Figure 4). The SOMO in 5 (MO25) is a πz orbital delocalized over the C, N, and O atoms of the reduced amide group (Figure 4). All of the low excited states arise by excitation from the SOMO to the virtual orbital space with no involvement of lower valence-state MOs (Table 3). The MOs representing the excited states can be described according to their nodality as molecular Rydberg orbitals, for example, 3s, 3px, 3py, and 3pz for the A−D states. Alternatively, since the nodal surfaces in these MOs intercept the C−H an N−H bonds, these excited states can be viewed as having some σ*(X−H) character. The transitions lead to very similar MOs when calculated by M062X, LC-BLYP, and EOM-CCSD (Table 3), and so the deviations of the TD-DFT excitation energies cannot be assigned to a different nature of these excitations. The different nature and excitation energies of terminal Cα radicals of the type represented by 1 and 2a, and internal Cα radicals represented by 5 are important for isomer distinction by photodissociation of peptide cation-radicals.29 Arginine-Related Radicals. The arginine-related radicals 6−8 showed electronic excitations in the near-UV and visible region. The first excited state in the neutral radical 6 was at Eexc = 3.21 eV corresponding to a weak transition of f = 0.0005 (Table 1). Protonation (7) resulted in a blue shift of the first excited state to Eexc = 3.35 eV and a stronger transition of f =

Figure 4. Molecular orbitals representing the A−D excited states of 5. Left panel, MOs from M06-2X excited-state calculations; right panel, MOs from EOM-CCSD excited-state calculations. The excitation energies are in electron volts. For electron transitions involved in these excited states, see Table 3.

0.003. The second excited states showed the same trend in that ionization shifted the excitation energy from Eexc = 4.30 eV in 6 to 5.02 eV in 7. TD-DFT calculations mostly produced acceptable first and second excitation energies of 7 for LCBLYP, ωB97X-D, and M06-2X that gave absolute ΔE < 0.2 eV. With 6, the best agreement with the EOM-CCSD first and third excited state energies was obtained for LC-BLYP, whereas ωB97X-D and M06-2X showed negative deviations. Despite radicals 6 and 7 being isoelectronic, the electron transitions and pertinent molecular orbitals for excitations G

DOI: 10.1021/acs.jpca.5b06235 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A differ. The SOMO in 6 (MO16) is an orbital of a πxy type (Figure S4, Supporting Information). The first two excited states involve πz type orbitals (MO15 and MO23), leading to disallowed transitions of a low oscillator strength. The third excited state involves transitions between orbitals of the same nodality (MO14 → MO16, Table S22, Supporting Information) and correspondingly larger oscillator strength ( f = 0.032). In contrast, the SOMO in 7 (MO16) is a πz type orbital (Figure S4). The first excited state in 7 involves a disallowed MO15 → MO16 transition (Table S23, Supporting Information) which has a low oscillator strength (Table 1). The second excited state involves πz type orbitals (MO16 and MO17), leading to an allowed transition of f = 0.035. The different nature of the SOMO in 7 is due to the absence of a lone electron pair on the inner nitrogen atom that was used in protonation to form the N−H bond. This n → σ(N−H) orbital change upon protonation of 6 has a substantial effect on the nature of electronic excitations in these radicals. The guanidine radical 8 showed a weak transition to the first excited state at Eexc = 2.81 eV ( f = 0.0005) followed by three excited states with energies in the near-UV, Eexc = 3.51, 3.68, and 3.94 eV (Table 1). All these low-energy excitations can be depicted as resulting from promotion of an electron from the πz SOMO (MO21) to diffuse 3s (A state) and 3p (B and C states) Rydberg-like orbitals (Table S24, Figure S5, Supporting Information). The TD-DFT calculated excitation energies for the first four excited states showed a very good match for ωB97X-D and M06-2X where the ΔE were