Calculated Vertical Ionization Energies of the Common α-Amino Acids

Mar 16, 2011 - (1) The guanyl radical is a fairly strong oxidizing agent and is ..... with respect to conformer CF1 with the bifurcated NH2····Oâ•...
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ARTICLE pubs.acs.org/JPCA

Calculated Vertical Ionization Energies of the Common r-Amino Acids in the Gas Phase and in Solution David M. Close* Department of Physics, Box 70652, East Tennessee State University, Johnson City, Tennessee 37614, United States

bS Supporting Information ABSTRACT: The vertical ionization energies of the low-lying conformers of the R-amino acids found in proteins have been calculated. Geometry optimizations were first performed at the B3LYP/6-311G(d,p) level of theory, and then reoptimized at the MP2/6-311G(d,p) level of theory. Vertical ionization energies were then computed by three methods, electron propagator in the partial third-order (P3) approximation, Outer-Valence-Green’s Functions, and by evaluating the difference in the total energy between the cation radical and the neutral amino acid in the geometry of the neutral species. When available, the results are compared to the experimental vertical ionization energies. The vertical ionization energies calculated using the MP2/P3 method gave the best overall agreement with the experimental results. Next, the ionization energies in solution are calculated for the zwitterionic forms of the R-amino acids by using IEFPCM methods. To obtain the vertical ionization energy in solution, it is necessary to use the nonequilibrium polarizable continuum model (NEPCM), the results of which are reported here for the R-amino acids.

’ INTRODUCTION Oxidation of proteins has been suggested to be the cause of pathological disorders, such a protein turnover, cataract-genesis, atherosclerosis, and tissue injury. The primary step in protein oxidation is the formation of a protein or peptide radical either by hydrogen abstraction or by one-electron oxidation of the protein or peptide. While radiation damage to DNA involving one-electron oxidation occurs at random sites, the damage shows a strong tendency to migrate to a guanine base.1 The guanyl radical is a fairly strong oxidizing agent and is capable of accepting electrons from even mild reducing agents, such as ascorbate. However, such reducing agents may be hindered in their access to nucleosomal DNA. It is possible that DNA binding proteins such as histones possess the capacity to donate an electron to guanyl radicals. The side chains of some amino acids are able to behave as mild reducing agents. It is therefore of interest to know the ionization energies of the amino acids found in proteins. A paper entitled “Vertical Ionization Energies of R-L-Amino Acids as a Function of Their Conformation: Ab Initio Study” by Dehareng and Dive2 contains lots of valuable information pertinent to the calculations presented here. An important table in this paper has the relative energies for different conformers of each amino acids computed at the B3LYP/6-31G(d,p) level of theory. The two most important conformations, CF1 and CF2, are shown in Figure 1. Figure 1 actually shows two versions of CF2. For glycine, it has been shown that CF2a, with Cs symmetry, is a saddle point in calculations involving larger basis sets (for example, 6-31G(d, p)), whereas the genuine local minimum on the energy r 2011 American Chemical Society

hypersurface is CF2b, with symmetry C1.3 It is not clear that this observation has been recognized in some more recent studies of amino acids. The paper by Dehareng and Dive2 has an extensive table that lists the vertical ionization energies (VIE) for the lowest energy conformations of the amino acids. For glycine, the energy of the CF1 conformer is slightly less than the energy of the CF2 conformer, while for the 17 other amino acids studied the energy of CF2 < CF1 (that is, without the zero-point energy correction as discussed below). It is also interesting to observe that, for this later case, the vertical ionization energies are ca. 0.2 eV higher. This same table includes a detailed description of the 5-6 lowest-lying molecular orbitals (in terms of the σ or π character) of each conformer. There are several problems with the study by Dehareng and Dive.2 First, the vertical ionization energies were calculated using Outer-Valence-Green’s Functions (OVGF) methods. At the time this work was performed, OVGF calculations were timeconsuming for the aromatic amino acids. Therefore, the authors reduced the size of the virtual orbital space in their calculations on the larger amino acids. This had some effect on their VIE results. There is, however, no way to properly judge the validity of these calculations because the authors make no reference to the experimental vertical ionization energies. Therefore, in the present work, every effort has been made to find reliable experimental ionization energies to compare with the theoretical Received: January 17, 2011 Revised: February 14, 2011 Published: March 16, 2011 2900

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Figure 1. From left to right CF1, CF2a (symmetry Cs), and CF2b (symmetry C1).

calculations presented. The following new vertical ionization energy calculations are performed: (a) OVGF calculations, which included all virtual orbitals, (b) reliable electron propagator calculations in the partial third-order (P3) approximation, and (c) standard DFT and MP2 calculations to evaluate the difference in the total energy between the cation radical and the neutral amino acid in the geometry of the neutral species.

’ PART I: GAS PHASE Conformations. It might appear that the study of isolated amino acids in the gas phase would be straightforward. However, intramolecular H-bonds between functional groups give rise to numerous low-lying conformers. These interactions are important as they affect the shape, interactions, and biological function of proteins. The number of trial conformations for a particular amino acid can be very large. For aspartic acid, Chen and Lin explored 1296 conformations.4 In a systematic variation of all rotational degrees of freedom, Ling et al. count ∼1.99 million conformations of arginine.5 For the present study, the literature has been searched for previous studies of the low energy conformations of each amino acid. As mentioned above, the work of Dehareng and Dive2 is a good place to start. However, as that work was published in 2004, it was necessary to search for more recent studies. An important point to consider is that for a given amino acid, the lowest-lying conformers are typically very close in energy. Therefore, at the elevated temperatures required for experimental measurements of ionization energies, one can expect several conformations to coexist with comparable populations. Here, it is useful to look at a detailed experimental and theoretical study of alanine by Powis et al.6 Calculations at the B3LYP/6-31G(d,p) level of theory on alanine show that structure CF2 is lower in energy than CF1 by 0.34 kcal/mol, while calculations at the MP2/6-311þþG(d,p) level of theory have CF1 lower in energy than CF2 by 0.48 kcal/ mol.6 A careful analysis of the valence photoelectron spectrum shows that conformation CF1 gives the best fit to the experimental spectrum with good matches for 10 peaks in the 9-19 eV region. In this case, at least the MP2 calculations give the best agreement with the experimental results. Methods. Table 1 has the vertical ionization energies of the low energy structures of the amino acids. The last two columns have the results of electron propagator in the partial third-order (P3) approximation using the 6-311G(d,p) basis set for the CF1 and CF2 conformers. The calculations are performed on the geometry optimized structures. Preliminary geometry optimizations were performed at the B3LYP/6-311G(d,p) level of theory. The local minima obtained were then reoptimized at the MP2 level of theory using the same basis set. Finally, frequency calculations were performed to verify stationary points. These frequency calculations provide the zero-point energy (ZPE)

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corrections, which are also found in Table 1. All of these calculations were done with the Gaussian 98 suite of programs.7 For the latter part of this Article, there is a need to have the vertical ionization energies calculated with density functional theory. These results follow this section and are presented in Table 2. Solvent effects were studied by performing self-consistent reaction field (SCRF) calculations using a polarizable continuum model (PCM) with the integral equation formalism (SCRF = IEFPCM) on the zwitterionic form of the R-amino acids.8 To obtain the vertical ionization energy in solution, it is necessary to use the nonequilibrium polarizable continuum model (NEPCM).9 These calculations were performed on the Gaussian 09 suite of programs.10 The results presented here include the ionization energies of only the lowest-lying conformers of each amino acids. The calculations return all of the ionization energies for each conformer and are useful for comparisons with the actual experimental spectra. Therefore, all of the calculated results are included as Supporting Information. Comparisons with Previous Studies. The primary emphasis here is in the calculation of vertical ionization energies. Because the ionization energies depend on conformations, it is necessary to examine several of the lowest-lying conformations. It is not, however, possible to examine all of the low-lying conformations, especially those involving rotations of the longer side groups. Ortiz and co-workers use the MP2/6-311G(d,p) level of theory to optimize molecules before doing a P3 calculation.11 As this has been shown to be a reliable method for calculating vertical ionization energies, this is the method used in the calculations presented here. It has to be noted that the ordering of the lowest-lying conformers may differ from those in the literature. These are, however, very small differences that result from slightly different methods. Some of the calculations cited from the literature involve diffuse functions (as in 6-311þþG(d, p)), optimizations at DFT and then only single point MP2 calculations, and only partial use of the zero-point energy correction on selected calculations. Experimental Results. Experimental studies of gas-phase amino acids have been hindered by their high melting points and associated low vapor pressures. Amino acids also have low thermal stability, so they tend to decompose before melting. This can be seen in the original HeI photoelectron spectroscopy paper of Klasinc.12 The pure aliphatic compounds yielded spectra. Yet the amino acids with -OH, -NH2, or -SH decomposed in the inlet system. These studies were extended by Cannington and Ham13 who present photoelectric spectra on most of the amino acids. As their spectral features are rather broad, it seems as if several conformers are present in these studies. Cannington and Ham13 have shown how spectral feature assignments can be made from studies of model compounds. For example, the lowest ionization energy of methylamine at 9.6 eV is associated with excitation from the lone-pair orbital of the nitrogen atom, while the lowest ionization energy of acetic acid at 10.9 eV is associated with excitation from the lone-pair of the oxygen atom of the carbonyl group. The situation becomes more complex when the highest occupied molecular orbital is on the side chain. Seki and Inokuchi14 have shown that the photoelectron spectrum of tryptophan can be separated into two distinct subunits: an alanine moiety (with peaks between 9.5 and 10.5 eV) and an indole moiety (with peaks in a band between 7.5 and 9.0 eV). More examples of spectral deconvolution can be found in an article by Campbell et al.15 and will be discussed herein. 2901

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Table 1. Energies and Vertical Ionization Energies of the Amino Acids amino acid glycine alanine

CF1 E (hartrees)

CF2 E (hartrees)

CF1

E (eV)

CF2

E (eV)

ZPE below

ZPE below

MP/P3

OVGFa

MP/P3

OVGFa

9.92

10.03

10.03

-283.7727843

-283.7717289

-283.6916793

-283.690011

-322.9724903

-322.9725584

-322.862929

-322.8623285

9.91

(9.82) 9.77

-401.3653405

-401.3647916 -401.197321

leucine

-440.5611603 -440.3548882

-440.5620223 -440.3553847

9.61

isoleucine

-440.5596845

-440.561144

9.56

-440.3532126

-440.3543552

-511.1566887

-511.1568951

-511.031242

-511.031021

asparagine

-491.2966175

-491.3053949

-491.159160

-491.1628793

serine

-398.0443764 -397.9214745

aspartic acid

threonine cysteine

9.60

9.79

9.83

9.50

9.77

10.05

10.16

10.10 10.00 (9.93)

(9.99)

-398.04410092 -397.9209059

10.12

10.04 (9.99)

10.08

9.95

9.98

9.70

-437.2463106

-437.24419899 -437.09180927

-720.6366482

-720.6391879

-720.526495

-720.528309

(9.31)

(9.80)

(9.80) 9.17

8.88

lysine

-495.7769639 -495.5496971

-495.7739218 -495.5467587

9.15

arginine

-605.0471672

-605.05122677

9.19

-604.8078083

-604.8100901

-547.4350185

-547.44071391

-547.26266112

-547.27431458

-553.37737745

-553.38109507

-553.17537576

-553.17842244

tyrosine

-628.45359272 -628.24638952

-628.45781337 -628.24993763

8.33

tryptophan

-684.614691332

-684.62255769

7.46

-684.38120323

-684.38857717

-400.1635184

-400.1667917

-400.016690

-400.019497

8.31

8.95 8.46 8.67

9.08

8.52

(8.46)

8.74

8.72 9.16 8.53

7.27

7.84

(7.07) 8.90

8.55 8.96 (8.57)

7.94 (7.77)

(8.75)

8.41

(8.43)

(8.40)

8.87

8.85 (8.67) (8.67)

(8.34) 8.93

8.66 (8.60)

9.07 (8.98)

8.49

9.04 (9.21)

(8.09)

8.67

9.66 (9.75)

(8.66) 8.14

9.77

10.14

9.46

-437.0937870

9.84 (9.70) (9.65)

9.59

-799.0215042

proline

9.56 (9.51)

9.69

9.73 (9.69)

(10.08)

-798.8434766

phenylalanine

9.75

(9.45)

-799.0229068

histidine

9.54

9.88 (9.85)

(9.50)

-798.8450784

methionine

(9.98) 9.90

(9.67)

-401.198268

valine

9.71

8.15 (7.94) 7.62 (7.34)

9.43

9.38 (9.36)

For the OVGF, the new calculations are presented in the first row of each amino acid. The results in parentheses in the second row are the results presented by Dehareng and Dive.2 a

It is possible to perform microwave spectroscopy on jet-cooled amino acids to determine detailed structural information of the individual conformers, because the different gas-phase lowenergy conformers give rise to independent rotational spectra. While these experiments do not yield ionization energies, it is interesting to read the studies on alanine,16 valine,17 aspartic acid,18 leucine,19 isoleucine,20 threonine,21 and cysteine22 (details of which are presented below).

’ RESULTS AND DISCUSSION Results for the Individual Amino Acids (Gas Phase). Glycine. An important paper by Ortiz’s group has studied the con-

formational effects on the ionization energy of glycine.11 This report discusses the five lowest energy conformations, which lie within 6 kcal/mol of each other. MP2 and B3LYP calculations

show that structure I (CF1) is the most stable isomer. Recent experimental results from a jet-cooled Raman spectrum have confirmed that structure I is the most stable glycine conformer.23 As a check on the methods used in this work, the calculations performed by Herrera et al.11 have been repeated and are presented in Table 1 (and in the Supporting Information). One sees that the results agree that structure CF1 (Figure 2) is the most stable glycine conformer. Also shown in Figure 2 is the HOMO associated with structure CF1. One sees that the HOMO primarily involves the nitrogen and the carbonyl oxygen lone pairs. The HOMO in Figure 2 is nearly identical to the σ1 Dyson orbital shown for the CF1 structure in the paper by Herrera et al.11 It differs, however, from the HOMO shown by Maul et al.24 for the CF1 structure. Their calculations involve plane waves that give rise to a HOMO that mainly consists of a π-orbital at the N atom. 2902

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Table 2. Comparison of Vertical IP’s Calculated with P3 Theory and DFT amino acid

conformer

VIE P3 (eV)a

exp. VIE (eV)b 10.0 (ref 13)

VIE DFT (eV)c

VIE DFT (eV)d

glycine

CF1

9.91 (-0.09)

9.70 (-0.30)

10.0 (ref 61)

alanine

CF1

9.77 (-0.08)

9.85 (ref 13)

9.54 (-0.31)

9.58 (ref 6)

valine

CF2

9.60 (-0.08)

9.68 (ref 12)

9.37 (-0.31)

leucine

CF2

9.83 (þ.18)

9.65 (ref 12)

9.45 (-0.20)

isoleucine

CF2

9.77 (þ.20)

9.57 (ref 12)

9.31 (-0.26)

aspartic acid

CF1

9.79

9.39

asparagine

CF2

10.16

9.37

serine threonine

CF1 CF1

10.12 (þ.12) 9.95 (-0.25)

cysteine

CF2

8.95

methionine

CF2

8.46 (-0.19)

8.65 (ref 13) 9.50 (ref 13)

10.0 (ref 13) 10.2 (ref 13)

9.46 (ref 30) 9.48 (ref 4)

9.57 (-0.43) 9.41 (-0.79) 9.25

9.06 (ref 24)

8.50 (-0.15)

lysine

CF1

9.15 (-0.35)

8.62 (-0.88)

8.55 (ref 37)

arginine

CF2

8.52

8.20

8.32 (ref 5)

histidine

CF2

8.72

8.38

8.30 (ref 41)

phenylalanine

CF2

9.16 (þ.16)

9.00 (ref 58)

8.72 (-0.28)

8.72 (ref 58)

tyrosine tryptophan

CF2 CF2

8.53 (þ.03) 7.84 (-.06)

8.50 (ref 13) 7.90 (ref 13)

8.19 (-0.31) 7.43 (-0.47)

proline

CF2

9.43 (þ.43)

9.00 (ref 13)

9.07 (þ.07)

9.41 (ref 59)

a

The numbers in parentheses are differences between the calculated VIE’s and the experimental VIE’s in column 4. b The numbers in parentheses are the reference to the experimental data. c The numbers in parentheses are differences between the calculated VIE’s and the experimental VIE’s in column 4. d The numbers in parentheses are the reference to the theoretical papers.

Figure 2. (Left) Optimized structure of glycine CF1; (right) HOMO of CF1.

Low-resolution photoelectric spectroscopy of glycine was performed in the 1970s. Klasinc reports three peaks in the photoelectric spectrum at 10.0, 11.1, and 12.1 eV.12 The theoretical calculations on structure I agree with these experimental results, but the same can be said for the calculation on two other isomers. Calculations at several levels of theory in Table 1 give a VIE of 9.91 eV for CF1 and 10.03 eV for CF2. The experimental VIE of glycine was measured to be 10.0 eV.13 OVGF calculations are also presented in Table 1. For structure CF1, the OVGF calculated VIE is 9.92 eV. For this same structure, Dehareng and Dive report VIE’s of 9.82 and 9.55 eV for calculations involving reduced sets of the virtual orbitals.2 For structure CF2, the OVGF calculated VIE is 10.03 eV, as compared to Dehareng and Dive who reported 9.98 and 9.72 eV for calculations involving reduced sets of the virtual orbitals. It is also not clear which model of structure CF2 Dehareng and Dive2 are using. These authors show a picture of structure CF2 that looks like the symmetric Cs structure, which at the level of theory used would lead to a saddle point. The authors make no mention of using frequency calculations to distinguish between saddle points and true minima. Alanine. There are several good papers that describe low energy conformers of alanine. See, for example, papers by Gronert and O’Hair,25 and by Powis.26 In the article by Powis,

Figure 3. (Left) Optimized structure of alanine CF1; (right) HOMO of CF1.

structure 1 corresponds to CF1 herein (Figure 3). Their structures 2-3 correspond to CF2a and CF2b. As with the case of glycine, the version of CF2 with higher symmetry (Cs) is actually a saddle point. Therefore, the results presented here pertain to CF2b (with C1 symmetry), which is the true local minimum. As discussed above, calculations performed by Powis et al.26 at the MP2/6-311þþG(d,p) level of theory have CF1 lower in energy than CF2 by 0.48 kcal/mol. Figure 3 shows the HOMO associated with structure CF1. One sees that the HOMO primarily involves the nitrogen and the carbonyl oxygen lone pairs. The HOMO shown in Figure 3 is nearly identical to that shown by Powis et al.6 These authors also calculated the VIE’s for a number of alanine conformers. Their methods involved the OVGF method, and a cc-pVDZ basis set yielded a VIE of 9.58 and 9.74 eV for CF1 and CF2, respectively. This shows then a small but significant influence of conformation in the calculated VIE. The results of new calculations on alanine are presented in Table 1. First, one notes that at the MP2 level of theory, conformer CF2 is lower in energy than conformer CF1. However, the order is reversed after applying the zero-point energy correction. Next, one sees the vertical ionization energies calculated at the P3 level of theory (9.77 eV for CF1 and 9.90 eV for CF2). These results are followed by vertical ionization energies 2903

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Figure 4. (Left) Optimized structure of valine CF1; (right) HOMO of CF1.

calculated at the OVGF level of theory. Here, one sees 9.71 eV (9.67 eV) for CF1 and 9.88 eV (9.85 eV). The values in parentheses are from Dehareng and Dive for comparison.2 Gas-phase data on alanine were obtained from the photoelectric spectra by Cannington and Ham.13 The lowest ionization energy obtained was 9.85 eV and has been assigned to conformation CF1. All of the calculated results on alanine in Table 1 are close to the experimental value. It is important to look back at the paper by Powis et al.,6 which has calculated ionization energies on top of the photoelectric spectrum of alanine by Klasinc.12 The lowest ionization energy is 9.58 eV for conformer CF1, which was calculated at the ROVGF/cc-pVDZ level of theory. This value is slightly lower than that shown in Table 1. This results from a slightly different procedure. Powis performed the ROVGF calculation on the conformers optimized with DFT, while the results in Table 1 are on conformers reoptimized at the MP2 level of theory. It is interesting to observe that in these original experiments (photoelectron spectroscopy) only a single conformer was detected. Later experiments detected the existence of CF2 at 1/8 the abundance of CF1. More recent jet-cooled experiments performed by Blanco et al. agree with these results that CF1 is the lowest-lying conformer of alanine in the gas phase.16 A paper by Ipolyi et al.27 has electron impact ionization data on alanine in the gas phase. They report the adiabatic ionization energy to be 9.12 eV, which is higher than the calculated values discussed in Table 1. There is no way to determine the conformation of the product detected by these authors, so it is difficult to compare these results with the present calculations. Valine. Previous calculations at the HF/6-31G(d) level of theory have shown the five most stable conformations of valine.28 The calculations show conformer CF2 to be lowest in energy. A subsequent study by Stepanian et al.29 used the B3LYP/631þþG(d,p) level of theory to calculate the energies of the CF1 and CF2 motifs as the aliphatic side chain of valine is rotated around the CR-C6 bond. At the DFT level of theory used, conformer CF1 was shown to be slightly lower in energy than CF2. There are interesting comments in the Stepanian et al. paper about the influence the zero-point energy correction has on changing the order of stability of the low energy conformers.29 Calculations at the MP2 level of theory presented in Table 1 follow the trend noted by Stepanian et al.,29 which show that the energy of the CF1 conformer of valine is slightly lower than the energy of CF2 after making the ZPE correction. This trend was also noted above for alanine. For both alanine and valine, then the ZPE correction destabilizes conformer CF2 with the N 3 3 3 3 H-O intramolecular H-bond with respect to conformer CF1 with the bifurcated NH2 3 3 3 3 OdC H-bond. Figure 4 shows the HOMO associated with structure CF1. One sees that again the HOMO is primarily associated with the nitrogen lone pair. There is also a contribution from the lone pair

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Figure 5. (Left) Optimized structure of leucine CF2; (right) HOMO of CF2.

of the carbonyl oxygen, and a very small delocalization onto the aliphatic side chain. These results are followed in Table 1 by MP2/P3 calculations on valine. One sees a small difference in the first ionization energy between the two conformers CF1 and CF2. The same trend is observed for the OVGF ionization energies of these two conformers. Whether calculations of the first ionization energy are calculated at the P3 level or at OVGF level, the answers are close to the experimental value of 9.68 eV.12 Leucine. A paper by Rai et al.30 explores the conformational space of leucine. A more up to date study by Dokmaisrijan et al.31 reviews previous DFT calculations and adds new high level calculations on the various conformations of leucine. Calculations at both DFT and MP2 levels of theory agree that the conformer with the intramolecular N-H 3 3 3 OdC H-bond (as in CF1) has the lowest energy after making the ZPE correction. One sees that in Table 1 conformer CF2 is slightly lower in energy than CF1 after making the ZPE correction. The difference here is that the results in Table 1 were obtained using optimizations at the MP2/6-311G(d,p) level of theory, while Dokmaisrijan et al.31 report calculations using MP2/6311þþG(2d,2p). One sees a small difference in Table 1 in the first ionization energy between the two conformers CF1 and CF2 for leucine. The same trend is observed for the OVGF ionization energies of these two conformers. Whether calculations of the first ionization energy are calculated at the P3 level or at the OVGF level, the answers are close to the experimental value of 9.65 eV.12 Figure 5 shows the HOMO associated with leucine conformer CF2. As with glycine, alanine, and valine, the HOMO primarily involves the nitrogen and the carbonyl oxygen lone pairs. Here, however, one notes a small delocalization of the HOMO onto the methylene moiety of the side chain. In experiments performed by Cocinero et al.,19 only two structures have been detected in the jet-cooled rotational spectrum of leucine. These experiments are sensitive to the intramolecular hydrogen-bonding interactions between the amino and carboxylic groups. The experiments show that the most abundant species in the jet is conformer CF1, which is present in about a 3-fold excess to conformer CF2. It is interesting to note that the isobutyl side chain adopts the same configuration in the two conformers of leucine. Isoleucine. Experimental studies involving FT-microwave spectroscopy have detected two configurations of isoleucine in the gas phase.20 The most stable configuration involves an intramolecular amine-to-carboxylic N-H 3 3 3 OdC H-bond and a cis-carboxylic functional group (as in CF1), while a second configuration involves an intramolecular hydrogen bond between the hydroxyl group and the lone pair at the nitrogen atom N 3 3 3 H-O (as in CF2). DFT and MP2 calculations with the 6-311þþG(d,p) basis set were used to determine the energy 2904

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Figure 6. (Left) Optimized structure of isoleucine CF2; (right) HOMO of CF2.

Figure 8. (a) (Left) Optimized structure of compact asparagine CF2; (right) HOMO of CF2. (b) (Left) Optimized structure of open asparagine CF2; (right) HOMO of CF2.

Figure 7. (Left) Optimized structure of aspartic acid CF1; (right) HOMO of CF1.

ordering of the conformers. Calculations with the zero-point energy correction have CF1 slightly less in energy than CF2. A more recent theoretical study by Dokmaisrijan et al.31 agrees with this observation, but has a different energy order for the higher energy conformers. The calculations in Table 1 have the MP2 energy of CF2 < CF1 (energies listed with and without the zero-point energy correction). One sees a small difference in the first ionization energy between the two conformers CF1 and CF2 for isoleucine. The same trend is observed for the OVGF ionization energies of these two conformers. Calculations of the first ionization energy at the P3 level or the OVGF level of theory are close to the experimental value of 9.57 eV.12 Figure 6 shows the HOMO associated with isoleucine conformer CF2. One sees now that the HOMO is not primarily on the nitrogen lone pair. Rather, it seems that the HOMO is more equally distributed between the nitrogen and the carbonyl oxygen lone pairs. Also, in comparison with leucine, there seems to be even further delocalization of the HOMO onto the aliphatic side chain. Aspartic Acid. Up to this point, things have been rather straightforward. The amino acids discussed so far all have aliphatic side chains. Things are different in aspartic acid, an amino acid with two carboxylic groups. The presence of this polar side chain exerts a substantial influence on the conformational preferences. A paper by Chen and Lin4 has both theoretical and experimental results of numerous conformations of aspartic acid. They have the conformer with the lowest energy that is stabilized by two N-H 3 3 3 OdC H-bonds between the amino group and each of the carboxylic groups (both carboxylic groups in the cis configuration). A more recent paper by Sanz et al.18 has this same structure as the most abundant conformer in a molecular beam experiment, but has a different structure for the lowest energy conformer that is a variant of the CF2 motif. The calculations in Table 1 show the energy of conformer CF2 < CF1 without the ZPE correction. However, the order is reversed after making the ZPE correction. The optimized structure of the conformer CF1 is shown in Figure 7, along with

the HOMO of CF1. The HOMO primarily involves the nitrogen and the carbonyl oxygen lone pairs with a very small delocalization onto the carbonyl oxygen of the side chain and is essentially the same as shown by Chen and Lin4 for their structure 1. In Table 1, one sees a small difference in the first ionization energy between the two conformers CF1 and CF2 for aspartic acid. The same trend is observed for the new OVGF calculated excitation energies of these two conformers, but is not shown in the calculations of Dehareng and Dive.2 It is not clear why this is so; however, it is likely that Dehareng and Dive did not do their calculation on the structure of CF1 shown in Figure 7. Calculation on the version of CF1 with a bifurcated amine-to-carbonyl hydrogen bond (as in Figure 1) does yield ionization energies more in line with those reported by Dehareng and Dive. There does not appear to be an experimental value of the ionization energy of aspartic acid in the literature. Cannington and Ham state that aspartic acid decomposes upon heating.13 Asparagine. A paper by Chen et al.32 explores the conformational space of asparagine. Optimizations at the B3LYP/6311þþG(d,p) level followed by single point MP2/6-311þþG(d,p) calculations conclude that the CF2 conformer of asparagine is the global energy minimum. Calculations presented in Table 1, which represent optimized geometries at the MP2/6311G(d,p) level of theory, also show that conformer CF2 is the energy minimum (both with and without the ZPE correction). In Table 1, one sees a considerable difference in the P3 calculations of the first ionization energy between the two conformers CF1 and CF2 for asparagine. The same trend is observed for the new OVGF calculations and the OVGF calculations performed by Dehareng and Dive.2 There do not appear to be any reports in the literature on the gas-phase ionization energies of asparagine because asparagine decomposes on heating. Figure 8a shows the HOMO associated with conformer CF2 primarily involves the pyramidal nitrogen lone pairs and the carbonyl oxygen lone pair of the side chain. Quite a different pattern is seen in the more open structure of conformer CF2 where the HOMO is more evenly distributed between the backbone and the side chain (Figure 8b). Changes in the hydrogen-bonding pattern influence the ionization energies. The ionization energy of the open asparagine CF2 conformer is 9.89 eV and increases to 10.16 eV for the compact CF2 conformer. From similar results in Table 1, it seems as if the 2905

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Figure 9. (Left) Optimized structure of serine CF1; (right) HOMO of CF1.

Figure 10. (Left) Optimized structure of threonine CF1; (right) HOMO of CF1.

calculated first ionization energy for conformer CF2 of 10.16 eV is on the high side (given the lowest ionization energy of methylamine at 9.6 eV). Another interesting feature of conformer CF2 is that the HOMO and the HOMO-1 have the same energy (see the Supporting Information). As shown in Figure 8a, the HOMO resides predominantly on the heteroatoms of the side chain. The HOMO-1 of this conformer, however, is predominantly on the heteroatoms of the backbone. Serine. The OH group in the side chain of serine can act as a hydrogen-bond donor or acceptor with the NH2 or the carboxyl group. In a theoretical study, Gronert and O’Hair25 show more than 50 conformers of serine. The two lowest-lying conformers are CF1 and CF2. Jet-cooled experiments by Blanco et al.33 have reported seven different conformers of serine. The lowest-lying conformer was determined to be CF1. Calculations at the MP2 level of theory presented in Table 1 show that the energy of the CF1 conformer of serine is lower than the energy of CF2 with and without the ZPE correction. Figure 9 shows that the HOMO associated with conformer CF1 is delocalized over the entire molecule. In Table 1, one sees only a very small difference in the first ionization energy between the two conformers CF1 and CF2 for serine computed at the P3 level of theory. The same can be said for the new OVGF calculations and the OVGF calculations performed by Dehareng and Dive.2 The calculated ionization energies of serine in Table 1, both at the P3 and at the OVGF level of theory, are all about 10.0 eV and agree well with the experimental value of 10.0 eV reported by Cannington and Ham.13 The reason for this small difference in ionization energies between conformers CF1 and CF2 likely has to do with the HOMOs associated with each conformer. Both HOMOs are delocalized over the entire molecule. Also, both HOMOs primarily involve the nitrogen lone pair and the carbonyl oxygen lone pair on the side chain. Even though conformers CF1 and CF2 have different intramolecular H-bonds arrangements, it appears as if the electron removed upon one electron oxidation comes from basically the same environment.

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Figure 11. (Left) Optimized structure of cysteine CF2; (right) HOMO of CF2.

Threonine. Experimental studies involving FT-microwave spectroscopy have detected seven configurations of threonine in the gas phase.21 The most stable structure is a variant of conformer CF1. In the CF1 conformers discussed above (Figures 3 and 4), the COOH group adopts a planar cis configuration, and a bifurcated hydrogen bond is formed between the amino group and the carbonyl oxygen. In threonine, conformer CF1 (shown in Figure 10) has a hydrogen bond between only one of the -NH2 H atoms and the carbonyl oxygen. There is then an additional hydrogen bond between the hydroxyl group side chain and the lone pair of the nitrogen atom. As with serine and asparagine, the HOMO associated with conformer CF1 is seen in Figure 10 to be spread out over the entire molecule. The next lowest conformer of threonine, CF2, has a HOMO localized on the side chain, primarily on the lone pair of the -OH group. Calculations at the MP2 level of theory presented in Table 1 show that the energy of the CF1 conformer of threonine is slightly lower than the energy of CF2 after making the ZPE correction. Calculations on threonine by Powis et al.6 using DFT have conformer CF2 lower in energy than conformer CF1. The calculations for the first ionization energy of threonine at the P3 or OVGF level of theory shown in Table 1 are about 9.95 eV for conformer CF1. This is below the experimental value of 10.2 eV reported by Cannington and Ham.13 There is a discussion in the paper by Campbell et al.15 that this experimental value seems to be too high. Cysteine. A paper by Gronert and O’Hair25 explores the conformational space of cysteine. At the MP2/6-31þG(d) level of theory, the conformer CF2 is the most stable structure, which agrees with the calculations of Dehareng and Dive.2 Recently, the jet-cooled rotational spectrum of cysteine has been obtained by Sanz et al.22 These experiments detected six low-lying conformers of cysteine, of which conformer CF2 was the lowest in energy. Calculations reported in Table 1 show that conformer CF2 is lower than the energy of CF1 with and without the ZPE correction. In Figure 11, one sees the HOMO associated with conformer CF2. The HOMO is primarily associated with the sulfur π lone pair orbital and looks like the HOMO shown by Maul et al. for conformer CF2.24 In Table 1, one sees only a small difference in the first ionization energy between the two conformers CF1 and CF2 cysteine computed at the P3 level of theory. The same can be said for the new OVGF calculations. The OVGF calculations performed by Dehareng and Dive do not agree very well with the new OVGF calculations presented here. This is likely due to the reduced the size of the virtual orbital space used in the calculations performed by Dehareng and Dive.2 At both the P3 and the OVGF levels of theory, the first ionization energy of cysteine is calculated to be ∼8.9 eV 2906

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Figure 12. (Left) Optimized structure of methionine CF2; (right) HOMO of CF2.

(Table 1). This is very close to the ionization energy of Smethylcysteine (8.8 eV).13 There is no experimental value for the ionization energy of cysteine. However, Cannington and Ham mention a methylation shift of 0.7 eV observed in the ionization energy of some thiols and predict that the ionization energy of cysteine to be 9.5 eV.13 This might be valid if the HOMO were confined to the sulfur π lone pair orbital, but at least at the level of theory used here, the HOMO of cysteine is slightly delocalized on the side chain. Methionine. For the amino acids discussed above, there were previous studies available that located the lowest energy conformers of each amino acid. There do not appear to be comparable studies of methionine. There is a paper by Lioe et al.34 that claims a CF1 conformer of neutral methionine is the global minima obtained at the MP2/6-311þG(d,p)//B3LYP/6311þG(d,p) level of theory. However, the authors do not list other low energy conformers of methionine to support this claim. Dehareng and Dive2 do have methionine included in their study, and they show that conformer CF2 is lower in energy than conformer CF1. Actually, Dehareng and Dive list two variants of CF2, but do not indicate the difference in the position of the side chain for either CF2(1) or CF2(2). Calculations reported in Table 1 show that the energy of conformer CF1 of methionine is lower than the energy of CF2 with and without the ZPE correction. Dehareng and Dive have conformer CF2 lower in energy than CF1 for calculations performed with DFT.2 Turning to the calculation of the ionization energies in Table 1, one sees a distinct difference between CF1 and CF2. The first ionization energy for methionine calculated at the P3 level for conformer CF1 is 8.14 eV, while it is 8.46 eV for conformer CF2. This is the biggest difference noted so far in Table 1. The same trend is noted in the OVGF calculations. A problem here is that the experimental value for the first ionization energy of methionine is 8.65 eV reported by Cannington and Ham13 and by Plekan et al.35 There is no peak in the photoemission spectrum that would correspond to the low ionization energy of conformer CF1. It appears as if conformer CF1 is not sufficiently populated under the experimental conditions to be detected. In Figure 12, one sees the HOMO associated with conformer CF2.36 The HOMO is primarily associated with the sulfur π lone pair orbital. In the photoelectron spectrum of methionine, there is a sharp line at 8.65 eV, and then a broader line at about 9.8 eV that corresponds with the calculated vertical ionization energy of 9.86 eV of the HOMO-1. This correlates well with the P3 calculations for methionine shown in the Supporting Information. Lysine. Previous studies of lysine by Leng et al.37 find notable differences between the relative conformation energies computed with DFT and MP2 theory. However, the lowest conformer calculated at both levels of theory seems to be a variant of conformer CF1. Dehareng and Dive2 included lysine in their

Figure 13. (a) (Left) Optimized structure of linear lysine CF1; (right) HOMO of CF1. (b) (Left) Optimized structure of compact lysine CF1; (right) HOMO of this structure.

study and have conformers CF1 and CF2 very close in energy. The initial calculations on lysine involved a linear model, much like that used above for methionine, as shown in Figure 13a. Calculations done here on these linear models show that conformer CF1 of lysine is lower than the energy of CF2 with and without the ZPE correction. The ionization energies for the linear models of lysine are almost the same (about 9.10 eV) for conformers CF1 and CF2 at the P3 and OVGF levels of theory. Cannington and Ham report that the first ionization energy of lysine is 9.5 eV.13 This is more than 0.4 eV higher than the P3 calculated value. Because lysine has a terminal NH2 on the side chain, the structure is likely more compact in the gas phase. Dehareng and Dive2 include a structure of lysine (conformer CF3) in which the carboxylic group interacts with the side chain. Figure 13b shows a more compact structure of lysine, with the terminal NH2 of the side chain near the carboxylic group. New calculations performed on this structure are presented in Table 1. Both new structures (CF1 and CF2) are lower in energy than their open structure counterparts. Again, one notes that conformer CF1 is lower in energy than conformer CF2. The difference in energy between CF1 and CF2 for the open structure was 0.55 kcal/mol, but it is 1.84 kcal/mol for the compact structure. Both the “open” and the “compact” conformers are shown in the paper by Leng et al.37 and correspond to their C21 and C1 conformers. Figure 13b also shows the HOMO for the compact lysine CF1 conformer, which is localized on the carboxyl and amine moieties. However, in looking at the new ionization energies calculated for the compact lysine CF1 and CF2 conformers, it seems as if they are much the same as with the calculations for the open lysine structures. For the lysine structures examined so far, none have given first ionization energies as high as the experimental value of 9.5 eV reported by Cannington and Ham.13 From the results presented here, we see that the electron removed upon ionization comes from either the NH2 of the side chain or the NH2 of the backbone. Therefore, one expects the first ionization energy to be something like 9.5-9.6 eV as observed experimentally. It is not clear then why the calculated ionization energies are approximately 0.4 eV below this value unless under the experimental conditions there is only a small population of conformers with this low ionization energy that have so far escaped detection. 2907

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Figure 14. (Left) Optimized structure of compact arginine CF2; (right) HOMO of CF2. Figure 16. (Left) Optimized structure of phenylalanine CF2; (right) HOMO of CF2.

Figure 15. (Left) Optimized structure of histidine CF2; (right) HOMO of CF2.

Arginine. Arginine is the most basic natural amino acid because of its strongly basic guanidine side chain. Early studies in the literature suggested that the zwitterionic form of arginine was more stable than the canonical form in the gas phase.38 When the internal-geometry space of arginine was explored in a wider range, it could be shown that arginine remains a neutral structure in the gas phase.39 There do not appear to be reports on the experimental ionization energies of arginine. There is a recent paper by Ling et al.5 that uses high level calculations to characterize the low-lying stable conformers of arginine. Table 1 shows that at the MP2 level of theory, conformer CF2 is lower in energy than conformer CF1 both before and after applying the zero-point energy correction. Next, one sees the first ionization energy calculated at the P3 and OVGF levels of theory is significantly higher for conformer CF1 than for the CF2 conformer. Figure 14 shows that the HOMO associated with the CF2 conformer is localized on the guanidine side chain. It is interesting to note that the experimental value of the ionization energy of N-methylguanidine is 8.6 eV,40 in close agreement with the calculated value for the CF2 conformer shown in Figure 14. The HOMO of the CF1 conformer of arginine has much the same π-electron structure of the guanidine side chain as does the CF2 conformer, but also has a considerable delocalization onto the backbone (on the NH2 and on the COOH). There is another difference between these two conformers. Figure 14 shows that the backbone NH2 forms an H-bond with the side chain. This N-H 3 3 3 N< H-bond is 2.137 Å. In the CF1 conformer, the backbone to side chain is via C-O-H 3 3 3 N< H-bond that is only 1.706 Å. The net result is a considerably higher first ionization energy of the CF1 conformer as compared to the CF2 conformer. Histidine. Histidine has an imidazole ring at the side chain, which has two tautomers (Nε2 and Nδ1). At pH 7, the Nε-H form is dominant, so that is the tautomer studied here. A paper by Huang et al.41 explores the conformational space of histidine. Calculations in Table 1 show that at the MP2 level of theory, conformer CF2 is considerably lower in energy than conformer CF1. This energy difference was noted by Huang et al., and they say “the most stable conformer of histidine is dominant in the gas phase”. There are no experimental data on histidine to justify this

statement. Actually, Wilson et al.42 conclude that at the temperature needed to get histidine into the gas phase (373 K) there are likely several low-lying conformers present. Turning to the ionization energy calculations presented in Table 1, one sees that at the MP2 level of theory there is only a small difference in the first ionization energy between the two conformers CF1 and CF2 for histidine. Figure 15 shows the HOMO associated with conformer CF2, which is seen to be localized on the imidazole ring of the side chain. While there are no reports of the vertical ionization energy of histidine in the literature, the experimental value for the ionization energy of imidazole is reported to be 8.78 eV,43 which is close to the calculated P3 value (in Table 1) of 8.72 eV. Perhaps a better model is 1-methyl-1H-imidazole, whose vertical ionization energy has been measured to be 8.66 eV.44 Phenylalanine. There is a lot of information in the literature about phenylalanine. Phenylalanine is one of the aromatic amino acids in the gas-phase electronic spectrum study by Levy’s group.45 Also, there are several studies of the low-lying conformations of phenylalanine46,47 and a paper by Lee et al.48 on the conformational-dependent ionization energies of phenylalanine. Cannington and Ham report that the first ionization energy of phenylalanine is 9.4 eV.13 Campbell et al.15 have analyzed the broad peak between 8 and 10 eV in the photoelectric spectrum of phenylalanine and conclude that it is made up of three peaks (one from the amine nitrogen lone pair, and two from the side chain). Their analysis shows that the first peak, at 8.9 eV, is from the π3 orbital on the phenyl ring. This result is in agreement with recent resonant two-photon ionization studies by Lee et al.48 that have the vertical ionization energy of conformer CF2 at 9.0 eV. A paper by Snoek et al.46 explores the conformational space of phenylalanine. They report that the structure shown in Figure 16 is the most stable conformer calculated at the MP2/6-311G(d,p) level of theory. They show that the calculated stability of conformers was dependent on the level of calculation. The results presented in Table 1 agree with the results of Snoek et al.46 that at the MP2 level of theory conformer CF2 is lower in energy than conformer CF1. In Table 1, one sees that at the MP2 level of theory there is only a small difference in the calculated first ionization energy between the two conformers CF1 and CF2 for phenylalanine. Figure 16 shows that the HOMO associated with conformer CF2 is localized in a π-orbital of the phenyl ring, in agreement with the analysis above by Campbell et al.15 It is interesting to compare the ionization energies computed at the P3 level of theory with the idea discussed above that the broad peak in the photoelectric spectrum of phenylalanine is made up of three peaks. The HOMO is at 9.16 eV, the HOMO-1 (associated with the 2908

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Figure 17. (Left) Optimized structure of tyrosine CF2; (right) HOMO of CF2.

backbone and the side chain) is at 9.33 eV, and the HOMO-2 (on the amine nitrogen lone pair) is at 9.74 eV (see the Supporting Information), all in agreement with the analysis above by Campbell et al.15 Tyrosine. Tyrosine is simply phenylalanine with a hydroxyl group para-subsituted to the benzene ring. This modification is expected to influence the ionization energy however. From the phenylalanine results discussed above, we expect the HOMO of tyrosine to reside on the phenol ring. There are numerous experimental results in the NIST Webbook listing the vertical ionization energy of phenol between 8.5 and 8.6 eV.49 Experimental studies of tyrosine include the work of Levy and co-workers that analyzes the electronic spectra of tyrosine and shows that the vibrational spectra result from the presence of several conformers.45 Further studies of the vibrational spectra of tyrosine have been performed by Grace et al.50 A structural assignment of the conformers of gaseous tyrosine has been performed by Zhang et al.51 This paper has an interesting discussion on the large ZPE corrections of the low-lying conformers that have the most intramolecular H-bonds. Table 1 shows that at the MP2 level of theory, conformer CF2 is lower in energy than conformer CF1 both before and after ZPE correction. Figure 17 shows the HOMO associated with conformer CF2. As expected, the HOMO is confined to the phenol side chain and looks pretty much like the HOMO of phenylalanine except for the significant delocalization onto the π-orbital of the hydroxyl group. Table 1 has the calculated first ionization energy for the CF2 conformer calculated at the P3 level of theory to be 8.53 eV, in excellent agreement with the experimental value of 8.5 eV.13 The same calculation performed at the OVGF level of theory seems to be too low. One notes that the calculated first ionization energy for the CF1 conformer is about 0.2 eV lower than that for the CF2 conformer. The photoelectron spectrum of tyrosine obtained by Cannington and Ham has a second peak at about 9.5 eV.13 Calculations at the P3 level of theory have the HOMO-1 at 9.43 eV and the HOMO-2 at 9.74 eV. The orbitals associated with these two peaks are mainly associated with the backbone structure, but are also delocalized onto the phenol side chain (see the Supporting Information). Tryptophan. Tryptophan has been the subject of numerous investigations due to the dominant role of its indole chromophore in the near-ultraviolent absorption and fluorescence of many proteins. Levy and co-workers carried out an extensive study of the UV spectroscopy of jet-cooled tryptophan and identified six conformations in the resonantly enhanced twophoton ionization spectrum.52 Huang and Lin53 have performed detailed calculations of the conformers of gaseous tryptophan.

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Figure 18. (Left) Optimized structure of tryptophan CF2; (right) HOMO of CF2.

They have determined that the most stable conformer involves the CF2 conformation with an intramolecular COOH 3 3 3 3 NH2 and an additional H-bonding interaction between the amino group and the π-electron system of the indole group. The results presented in Table 1 agree with the calculations of Huang and Lin53 that at the MP2 level of theory conformer CF2 is lower in energy than conformer CF1. Figure 18 shows the HOMO associated with conformer CF2 is localized in a π-orbital of the indole ring. Table 1 has the first ionization energy of tryptophan calculated at the P3 level of theory to be 7.84 eV, in good agreement with the experimental value of 7.9 eV reported by Cannington and Ham.13 Also, one sees that the first ionization energy calculated at the OVGF level of theory is 7.62 eV, which is not in agreement with the value of 7.34 eV calculated by Dehareng and Dive.2 This most likely has to do with restricting the size of the virtual orbital space in their calculations. The complete list of ionization energies for all the amino acids considered here has been listed in the Supporting Information. For tryptophan, several of the ionization energies had pole strengths below 0.85 and are thus considered unreliable. Proline. In proline, the backbone amine group is part of a fivemembered pyrrolidine ring. Different proline conformers result from the carboxyl cis and trans orientations, and different pyrrolidine ring puckering. The notation in Figure 1 can be applied to proline with CF1 denoting an interaction that links the imino hydrogen to the oxygen atom of the carboxyl (N-H 3 3 3 OdC) and CF2 denoting H-bonding between the lone pair of the nitrogen atom and the hydroxyl group H-atom (N 3 3 3 HO). There are several papers that calculate the energies of various low-lying conformers of proline.54-56 It is interesting to note that there are actually four lowest-lying energy conformers that can be energetically distinguished as two pairs. The two pairs are conformers of CF1 and CF2. The two conformers in each pair differ by the pyrrolidine ring puckering. Both Stepanian et al.55 and Lesarri et al.56 have variants of conformer CF2 lower in energy than those of conformer CF1. Table 1 shows that at the MP2 level of theory, conformer CF2 is lower in energy than conformer CF1 both before and after ZPE correction. Looking at the first ionization energies shown in Table 1, one sees a difference of nearly 0.5 eV between the first ionization energy of conformer CF1 (8.87 eV) and the first ionization energy of CF2 (9.43 eV). This is one of the largest differences in ionization energy among the amino acids shown in Table 1. Cannington and Ham13 report that the ionization energy of proline is 9.0 eV. The HOMOs of CF1 and CF2 are shown in Figure 19a,b. One sees that in CF1 the HOMO is localized on the pyrrolidine ring and largely confined to the nitrogen lone pair orbital. Thus, the ionization energy of the CF1 conformer (8.87 eV) is close to that of pyrrolidine (8.8 eV).57 On the other hand, the HOMO of the 2909

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Figure 19. (a) (Left) Optimized structure of proline CF2; (right) HOMO of CF2. (b) (Left) Optimized structure of proline CF1; (right) HOMO of CF1.

CF2 conformer is delocalized over the entire molecule. However, the biggest difference between CF1 and CF2 is the intramolecular H-bond. In conformer CF1, the N-H 3 3 3 OdC H-bond is 2.187 Å, while in CF2, the N 3 3 3 H-O H-bond is 1.807 Å. For conformer CF2, the combination of the delocalization of the HOMO onto the COOH group and the short H-bond results in an increase of 0.5 eV in the first ionization energy.

’ PART II: IONIZATION ENERGIES OF THE AMINO ACIDS IN SOLUTION The next part of this study involves calculating the ionization energies of the common amino acids in solutions. In solution, and in the solid state, amino acids exist as zwitterions. For the calculations of the ionization energies in the gas phase, it was easy to find the configurations of many of the low-lying conformers of most of the amino acids in the literature. This is not the case for the zwitterions of the amino acids. Geometry optimizations using the PCM model are much more time-consuming than gas-phase optimizations. Furthermore, calculations to optimize structures of the amino acids in solution can be plagued with oscillations. This can be very time-consuming if one were to use MP2 theory as discussed above. To help speed up calculations, it was decided to begin with DFT calculations on the amino acid zwitterions in solution. As a first step, it is necessary to compare ionization energies computed above with MP2/P3 techniques with ionization energies computed with DFT theory, because these calculations tend to slightly underestimate vertical ionizations energies. The results are presented in Table 2. Column three in Table 2 has the vertical ionization energies calculated at the MP2/P3 level of theory (from Table 1). In 10 cases, there are experimental ionization energies that are seen to agree well with the calculations. In column five, one sees that the vertical ionization energies calculated with the density functional theory are mostly 0.3-0.4 eV less than the experimental values (although there are a few cases of larger deviations). There are several reports on DFT calculations of vertical ionization energies of the amino acids in the literature using various basis set. The references are given in the last column of Table 2. One notes that the calculations presented here compare

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very well with the DFT calculations of others despite the variety of basis sets used. There are discussions in the literature comparing the results of DFT and MP2 calculations. Some time ago, Del Bene et al.60 noted that B3LYP/6-31G(d,p) calculations failed to give reliable binding energies, intermolecular distances, and vibrational frequency shifts. They warned about using DFT for studies of hydrogen-bonded complexes. It is interesting to note that in Table 2 the amino acids with the complex intramolecular hydrogen bonds have the largest deviations between the DFT calculated ionization energy and the experimental ionization energy. In a study of phenylalanine by Lee et al.,58 it is reported that calculations at the B3LYP/6-311þG(d) level of theory tend to underestimate the experimental ionization energies by about 0.3 eV on a number of conformers. However, a paper by Ling et al.5 has DFT and CCSD calculations of 25 conformers of arginine. For some of the CF1-type conformers of arginine, the vertical ionization energies calculated with DFT and with CCSD differ by 0.75 eV. It appears then that care must be taken in performing calculations of ionization energies on the amino acids with DFT. For the amino acids with aliphatic side chain, it seems as if the calculated ionization energy is about 0.3 eV below the experimental ionization energies. Of the remaining amino acids, there are several problems. First, for five amino acids there are no experimental results. For serine and threonine, because the MP2 calculations of the VIE agree well with the experimental value, one suspects there is something wrong with the DFT calculation. For lysine and tryptophan, both the MP2 and the DFT calculations are at odds with the experimental results. For these outliers, then there are too many uncertainties to estimate just how good DFT is in calculating ionization energies. The first step is to calculate the ionization energies of the amino acids. Most of the papers discussed above for the gas-phase calculations involved vertical ionization energies, which are evaluated as the difference in the total energy between the cation radical and the neutral amino acid in the geometry of the neutral species (optimizations of the neutral molecule using the 6-311G(d, p) basis set followed by a single point calculation on the cation). If instead the cation were also optimized, then the difference in energy would represent the adiabatic ionization energy. This procedure has been carried out for the amino acids. The results for the vertical ionization energies (VIE) for the amino acids in a PCM cavity are presented in Table 3. The primary emphasis of this study has been the calculation of vertical ionization energies. To obtain the vertical ionization energy in solution, it is necessary to use the nonequilibrium polarizable continuum model (NEPCM).9 In the NEPCM procedure, the reaction field is optimized only for the parent species before ionization. With the NEPCM method, only the fast electron component of the solvent response to ionization is accounted for. The slow component of this response (nuclear relaxation) is omitted. The results of calculations with the NEPCM model on the amino acids are also presented in Table 3. Also included is the difference between the NEPCM values and the ionization energies calculated by the equilibrium PCM method. One sees that the equilibrium PCM method underestimates the vertical ionization energy by about 1.2 eV due to the additional nuclear polarization of the solvent about the cation. These calculations represent the first step in understanding the effect of solvation on the ionization energy. PCM models are 2910

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Table 3. Vertical Ionization Energies of the Amino Acids amino acid

VIE DFT (eV) VIE DFT IEFPCMa VIE DFT NEPCMb

glycine

9.70

6.71 (2.99)

8.26 (1.44)

alanine

9.54

7.06 (2.48)

8.18 (1.36)

valine

9.37

7.09 (2.28)

8.46 (0.91)

leucine

9.45

6.77 (2.68)

8.02 (1.43)

isoleucine

9.31

6.66 (2.65)

8.00 (1.31)

aspartic acid

9.39

6.82 (2.57)

8.28 (1.11)

asparagine

9.37

6.79 (2.58)

8.07 (1.30)

serine threonine

9.57 9.41

6.95 (2.62) 6.77 (2.64)

8.38 (1.29) 8.18 (1.23)

cysteine

9.25

6.72 (2.53)

7.92 (1.33)

methionine

8.50

6.31 (2.19)

7.49 (1.01)

lysine

8.62

6.42 (2.20)

7.52 (1.10)

arginine

8.20

6.11 (2.09)

7.27 (0.66)

histidine

8.38

6.34 (2.04)

7.54 (0.84)

phenylalanine

8.72

6.57 (2.15)

7.66 (1.06)

tyrosine tryptophan

8.19 7.43

5.94 (2.25) 5.23 (2.20)

7.07 (1.12) 6.67 (0.76)

proline

9.07

6.69 (2.38)

8.09 (0.98)

a

The numbers in parentheses are the differences between the gas phase VIE’s and the VIE’s calculated in a PCM cavity. b The numbers in parentheses are the differences between the gas phase VIE’s and the VIE’s calculated with the NEPCM model.

not expected to accurately describe the details of solvation within the first solvation shell of water. Therefore, it is necessary to perform detailed calculations with each amino acid microhydrated with discrete water molecules, and then to repeat the NEPCM calculations on these supermolecules. The advantage of the “supermolecular” approach is the ability to account for the specific effects of hydrogen bonding of the solvated molecule and the long-range effects of the solvent.

’ CONCLUSIONS The gas-phase vertical ionization energies calculated at the MP2/P3 level of theory give the best fit to the experimental results as shown in Table 2. In 10 cases, there are experimental ionization energies that are seen to agree well with these calculations. For the remaining amino acids listed in Tables 1 and 2, there are some problems. First, there are no reported calculations on the low energy conformers of methionine and lysine. Also, the calculations in Table 1 show that the CF1 conformer of methionine has the lowest energy. However, the calculated VIE associated with this conformer is 8.12 eV, and there is no corresponding peak at this energy in the experimental data. There are also some problems with the comparisons between the VIEs computed with MP2/P3 versus the DFT calculations in Table 2. For the amino acids with aliphatic side chains, it seems as if the DFT calculations underestimate the VIE by about 0.3 eV. However, in Table 2, there are greater differences between some of the DFT and the MP2/P3 calculations. This may have to do with problems others have noted that DFT theory has with the estimation of the strength of H-bonds. These concerns are being addressed. The calculations presented here on the ionization energies of the amino acids in solution are preliminary. Future work will

involve the NEPCM calculations on the microhydrated amino acids.

’ ASSOCIATED CONTENT

bS

Supporting Information. All of the ionization energies of each CF1 and CF2 conformers are tabulated. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Thanks are due to Kelly Hensley at the Sherrod Library (ETSU) for help with Inter-Library Loans used to acquire many of the references used herein. Also, thanks go to Olga Dolgounitcheva, Auburn University, for helpful discussions on P3 calculations. ’ REFERENCES (1) Bernhard, W. A.; Close, D. M. DNA Damage Dictates the Biological Consequences of Ionizing Irradiation: The Chemical Pathways; Marcel Dekker: New York/Basel, 2004. (2) Dehareng, D.; Dive, G. Int. J. Mol. Sci. 2004, 5, 301. (3) Ramek, M.; Cheng, V. K. W.; Frey, R. F.; Newton, S. Q.; Sch€afer, L. J. Mol. Struct. 1991, 235, 1. (4) Chen, M.; Lin, Z. J. Chem. Phys. 200, 127, 154314–1. (5) Ling, S.; Yu, W.; Huang, Z.; Lin, Z.; Hara~ nczyk, M.; Gutowski, M. J. Phys. Chem. A 2006, 110, 12282–12291. (6) Powis, I.; Rennie, E. E.; Hergenhahn, U.; Kugeler, O.; BussySocrate, R. J. Phys. Chem. A 2003, 107, 25. (7) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.11; Gaussian, Inc.: Pittsburgh, PA, 1998. (8) Barone, V.; Cossi, M.; Tomasi, J. J. Chem. Phys. 1997, 107, 3210. (9) Slavícek, P.; Winter, B.; Faubel, M.; Bradforth, S.; Jungwirth, P. J. Am. Chem. Soc. 2009, 131, 6460. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, € Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; S.; Daniels, A. D.; Farkas, O.; 2911

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