Computational and Theoretical Chemistry 1020 (2013) 14–21

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Computational and Theoretical Chemistry

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Thorough theoretical search of conformations of neutral, protonatedand deprotonated glutamine in gas phase

2210-271X/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comptc.2013.07.016

⇑ Corresponding author.E-mail address: zjlin@ustc.edu.cn (Z. Lin).

Rui Pang a, Minghao Guo a, Sanliang Ling b, Zijing Lin a,⇑a Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, Chinab Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 March 2013Received in revised form 12 July 2013Accepted 13 July 2013Available online 23 July 2013

Keywords:First principle calculationStructureHydrogen bondProton affinityProton dissociation energyEntropy effect

There are large discrepancies among the theoretical and experimental results of the proton affinity (PA)of glutamine (Gln). To provide a reliable basis for the theoretical investigation, extensive conformationalsearches have been performed for neutral, protonated and deprotonated Gln in gas phase by optimizingthe trial structures generated by allowing for all combinations of internal single-bond rotamers. Thestructures and hydrogen bonding features, relative electronic energies, zero point vibrational energies,rotational constants, dipole moments, vertical ionization energies of the low energy conformers and equi-librium conformational distributions are presented. PA, GB (gas phase basicity), PDE (proton dissociationenthalpy) and GA (gas phase acidity) of Gln were computed by the theoretical approaches of BHandHLYP,B3LYP, B97D, MP2, G3MP2B3, M062X and CCSD. The computed relative conformational energies and PA,GB, PDE and GA are dependent on the theoretical approach and the basis set. Analysis of the computa-tional results shows that the extended kinetic method provides an accurate estimate of PA and overesti-mate of the entropic effect, while all other experiments underestimate PA of Gln. The best theoreticalestimates of PA, GB, PDE, GA and the protonation and deprotanation entropies for Gln are 987.2 ± 4.0,945.1 ± 5.8, 1385.3 ± 9.0, 1362.9 ± 9.1 kJ/mol and �32.4 ± 6.2 and 33.9 ± 5.1 J/mol/K, respectively.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Studying biomolecules in gas phase is important for revealingtheir intrinsic properties free of the influence of the interactingenvironment [1,2] and the gas phase properties are also indicativeof that in solution [3]. Many experimental approaches have beenemployed to determine the structures and properties of gaseousamino acids, such as proton affinity (PA) and gas phase basicity(GB) [4–9], proton dissociation enthalpy (PDE) and gas phase acid-ity (GA) [10,11], dipole moments, rotational constants [12], IR andUV spectra [13,14], ionization potentials [15], two-photon circulardichroism [16], etc. With the rapid development in quantumchemistry methods and computer hardware, increasingly morecomputational investigations are reported [17–21]. The advantageof computation is that it offers results in the exact ideal situationwithout experimental uncertainties. It also provides informationsuch as geometries and hydrogen bondings that are difficult tomeasure directly by the experiment.

PA, GB, PDE and GA are important thermochemical properties ofmolecule. Early literatures on the thermo-chemical properties ofamino acids have been summarized by Harrison [22] and Hunter

and Lias [5]. However, due to the intrinsic difficulties associatedwith the handling of these involatile and thermally labilemolecules and with the methods of measuring thermochemicalproperties, the obtained data should be used with care [6–8]. Forexample, the results obtained by equilibrium constant measure-ments [4] and thermo kinetic methods [5] are often somewhat dif-ferent and require corrections using the Hunter and Lias scale [23].

Because of their fundamental importance, the thermochemicalquantities for most amino acids have been repeatedly measuredover the last decades and the results have been compiled in a re-cent review by Bouchoux [23]. Overall speaking, the experimentaldata are in acceptable agreement with each other and with themost reliable computational results. However, glutamine (Gln) isa severe exception. The GB of Gln measured by the equilibriummethod is smaller than that obtained with the extended kineticmethod (EKM) by about 50 kJ/mol [23]. The PA of Gln determinedby EKM is larger than the average measured by the simple kineticmethod (SKM) by over 30 kJ/mol [23]. However, the theoretical re-sults show a relatively small spread and are closer to the results ofEKM [23,24]. Nevertheless, the results by EKM are believed to beclearly too high [23], an assertion that is not well justified.

Gln is an elemental amino acid that composes proteins inbiological systems [25,26]. Gln is the main source of nitrogen inhuman bodies and comprises approximately 50% of the

R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21 15

whole-body pool of free amino acid. It is the most important aminoacids in muscle growth, and is involved in the synthesis of a varietyof enzymes. It is considered as important fuel for many kinds ofcells. The polar groups in Gln tend to form hydrogen bonds(H-bonds). However, the tendency to form H-bonds and thestrengths of the H-bonds may be significantly enhanced in proton-ated Gln. The large entropic difference in neutral and protonatedGln is ignored in SKM, but easily captured in EKM. Moreover, thereported EKM data show that the isothermal point may bedetermined with a limited uncertainty for Gln [27]. Therefore,the EKM result should be more reliable than that of SKM and theassertion that there is a large error in the EKM result is unjustified.Fortunately, the computational method is ideally suited to resolvethe dispute as it may easily take the entropic effect into consider-ation. Nevertheless, a high quality computational study is requiredto draw a convincing conclusion.

Numerous theoretical studies on the PA of Gln have been re-ported. Maksic and Kovacevic calculated the PA of Gln at theMP2/6-31+G(d,p) level, but the conformations of neutral and pro-tonated Gln structures were not reliably determined [28]. Dina-dayalane et al. searched the conformations of neutral andprotonated Gln based on chemical intuition [29]. Bleiholder et al.[30] improved the conformational search by using a simulatedannealing technique combined with an empirical Hamiltonian asa pretreatment to deal with a large number of trail structures,and the final result of PA was determined at the level of B3LYP/6-31G(p,d) and G2MP2. As the stochastic nature of the simulatedannealing technique has a considerable possibility of missing theglobal minimum [18] and the basis set of 6-31G(p,d) is often insuf-ficient for obtaining accurate results, the cause for the differencebetween the theoretical and experimental results is uncertain. Ber-tran and coworkers [31] used a Monte Carlo multiple minimumtechnique combined with the MMFF94s force field [32] and thenon-local meta-hybrid MPWB1K density functional in the searchof Gln conformations. They found three low energy structuresbased on the assumption that there is one intramolecular H-bondin the most stable conformer. Bouchoux determined the PA valuebased on the G3MP2B3 theory [23]. Guo performed detailedconformational searches and calculated the PA of Gln at theMP2/6-311++G⁄⁄ level [24]. The theoretical basis for Guo’s resultseems solid. Nevertheless, further validation may be needed assubstantial differences in different DFT approaches and other tradi-tional first principle calculations have been observed [33].

Though to a less extent, the difference between the theoreticaland experimental PDE results of Gln is also notable. The experi-mental values are 1388 and 1385 kJ/mol as determined by O’Hairet al. [11] and by Jones et al. [10], respectively. Jones et al. alsoreported a theoretical value of 1378 kJ/mol obtained at theB3LYP/6-311++G⁄⁄ level. However, a value of 1368 kJ/mol is ob-tained by Guo at the MP2/6-311++G⁄⁄ level based on an improvedconformational search [24]. Though the latter is not very differentfrom the former theoretical result, its difference from the experi-mental ones is about 20 kJ/mol and uncomfortably large. It ismeaningful to present a more thorough theoretical examination.

In this study, systematic searches of the conformational spacesof neutral, protonated and deprotonated Gln by varying all reason-able rotational degrees of freedom were performed. A series of lo-cal minima on the potential energy surfaces of these Gln specieswere obtained by systematic search of all the reasonable rotamers[18]. A new set of PA, GB, PDE and GA data are obtained and com-pared with previous experimental and theoretical results. Discus-sion on the theoretical and experimental difference is given tosupport the current theoretical results. Analysis also shows thatthe extended kinetic method is a reliable way of determining PAand PDE of amino acid.

2. Computational method

The representative structures of neutral, protonated and depro-tonated Gln are shown in Fig. 1. The conformational spaces of thethree Gln species are thoroughly searched by optimizing trialstructures generated by combinations of all reasonable internalsingle-bond rotamers [18]. For Gln, as the C–N bond rotation inthe acyl group is prevented by the electron conjugation on the Cand N atoms, there are 6, 5 and 5 bond rotational degrees of free-dom for the neutral canonical, protonated and deprotonated Gln,respectively. The bond rotational degrees of freedom are illustratedin Fig. 2 for neutral canonical Gln. As a result, a total of 7776 trialstructures were generated for canonical Gln. All these trial struc-tures were optimized at the PM3 level [34,35], resulting in 1200unique structures. These structures were re-optimized at the HF/3-21G⁄ level, and the unique structures thus obtained were furtherrefined at the BHandHLYP/6-31G⁄ level [21]. A total of 143 con-formers were found for neutral canonical Gln. The 21 lowest en-ergy conformers that spanned an energy range of 3 kcal/molwere further optimized at the level of BHandHLYP/6-311++G⁄⁄.The vertical ionization energies (VIEs) were determined at theBHandHLYP/6-311++G(2df,2pd) level. For comparison, VIEs werealso computed with the outer valence Green’s function (OVGF)[36] method. The 6-311++G⁄⁄ basis set is used for the OVGF calcu-lations in order to save the computational cost. As a side note, thezwitterionic forms of Gln were also similarly searched and no zwit-terions were found to correspond to the local minima in the poten-tial energy surface (PES) of neutral Gln.

The numbers of trial structures for protonated and deproto-nated Gln were 2592 and 3888, respectively. The trial structureswere first optimized at the HF/3-21G⁄ level and the uniquestructures thus obtained were re-optimized at the level ofBHandHLYP/6-31G⁄. The lowest energy conformers in the rangeof 3 kcal/mol were further optimized at the BHandHLYP/6-311++G⁄⁄ level.

Single point energies of the low energy conformers were calcu-lated using the computational approaches of BHandHLYP, B3LYP[37–40], MP2 [41], B97D [42], M062X [43,44] and CCSD [45], com-bined with one or more of the following basis sets: 6-311++G⁄⁄, 6-311++G(2df,2pd), cc-PVTZ and cc-PVQZ. The vibrational frequen-cies were determined at the BHandHLYP/6-311++G⁄⁄ level andscaled with a factor of 0.93 [46]. The zero point vibrational energies(ZPVEs), the thermal corrections for enthalpy and free energy arescaled with a factor of 0.95 and 0.94, respectively [46]. These re-sults were combined with the electronic energies at various levelsto determine the conformational distributions of canonical, pro-tonated and deprotonated Gln species.

The low energy conformers were also optimized at the BHandH-LYP/cc-PVTZ level to check their basis set dependencies. They arealso optimized with the B97D and M062X methods to see the influ-ence of the DFT functionals on the geometries.

The standard PA (GB) is calculated as the negative of the enthal-py (Gibbs free energy) change for the gas-phase protonation reac-tion at room temperature, T = 298 K. The enthalpy of H+, H(H+), isthe sum of the translational energy of H+ and the PV work fromthe reaction and is calculated as H(H+) = E + PV = 5/2RT. The protonfree energy is calculated to be �26.2 kJ/mol [21]. The free energyand enthalpy for a given species were obtained through weightedaveraging over its conformations. Moreover, the free energy calcu-lations also take into account the entropy of mixing, �R

Pixi ln xi,

where xi is the population of conformer i [23]. The PDE and GA ofGln were similarly calculated based on the gas-phase deprotona-tion reaction.

The CCSD calculations were performed with Molpro [47]. Allother calculations were carried out with the GAUSSIAN09 suite of

Deprotonated ProtonatedCanonical

Fig. 1. Representative structures of neutral, protonated and deprotonated glutamine.

Fig. 2. Bond rotational degrees of freedom of canonical glutamine.

16 R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21

programs using the default parameter settings [48]. For example,the geometry optimizations were carried out using the redundantcoordinates with the thresholds of 0.00045, 0.0003, 0.0018 and0.0012 in natural units (Hartrees-Bohrs) for the maximum force,the root mean square force, the maximum displacement and theroot mean square displacement, respectively. The grid size for inte-grals of the exchange–correlation functional was (75,302).

3. Results and discussion

3.1. Conformations of gaseous canonical Gln

Table 1 shows the relative electronic energies calculated withdifferent methods at the BHandHLYP/6-311++G⁄⁄ geometries, rela-tive ZPVEs, relative thermal corrections to the free energy at thestandard state and rotational constants for the 21 lowest energyconformers of Gln. The Cartesian coordinates of these conformersmay be found in the Supplementary material. The relative elec-tronic energies calculated by the approaches of BHandHLYP,B3LYP, MP2 and CCSD with the basis set of 6-311++G⁄⁄ are denotedin the table as EBH0, EMP20, and ECCSD0, respectively. Results obtained

Table 1Relative electronic energies, relative ZPVEs (DVE), relative thermal corrections to the freecanonical conformers (conf.) of Gln. All energies are in kJ/mol.

Conf. Relative electronic energy

ECCSD0 EBH EBH0 EMP2 EMP20 EB3LYP

c1 0.00 0.00 0.00 0.00 0.00 0.00c2 2.35 4.85 3.83 7.60 4.78 6.62c3 4.66 0.24 0.18 4.03 5.89 �0.20c4 4.90 0.47 2.78 3.06 6.59 1.61c5 6.38 8.11 8.56 6.25 6.94 9.43c6 6.40 5.93 6.36 11.55 10.56 8.91c7 7.16 1.25 3.57 7.08 10.98 3.59c8 7.25 10.47 10.70 11.66 10.26 14.39c9 7.52 5.61 5.79 8.30 9.09 5.65c10 7.55 4.61 5.37 11.88 11.89 6.98c11 8.03 4.37 4.73 9.63 10.71 4.52c12 8.04 8.01 8.16 11.41 10.50 9.86c13 8.54 9.67 9.92 12.76 11.18 11.86c14 9.16 12.13 10.95 14.84 12.29 13.67c15 9.59 2.91 3.40 8.45 11.16 1.72c16 10.71 9.04 7.61 15.18 13.84 9.09c17 11.44 6.95 7.65 16.96 16.70 8.84c18 13.07 11.05 11.14 13.39 14.65 11.10c19 13.09 8.64 11.54 10.66 14.47 9.56c20 13.18 12.77 11.49 16.58 15.44 13.30c21 14.22 8.72 8.64 14.44 16.79 7.68

with the basis set of 6-311++G(2df,2pd) are denoted as EBH, EB3LYP,EMP2 and EB97D and EM062X in Table 1. These symbols are also usedbelow to denote the corresponding results for the dipole momentsas well as enthalpies and free energies, even though the ZPVE andentropic contributions are always determined at the BHandHLYP/6-311++G⁄⁄ level. The conformations are denoted as cn, where nis a numeral denoting the conformational stability ordered byECCSD0.

As shown in Table 1, the relative energies are dependent on thecomputational method and it is nontrivial to determine the mosttrustworthy results. Fortunately, the overall trends for the relativeconformational energies are similar for these methods. Therefore,it is reasonable to believe that all the important low energyconformers are included in Table 1. Another feature displayed inTable 1 is that the basis set convergence on the relative electronicenergy is slow even for the DFT method, e.g., the relative c2 and c7energy is 0.3 kJ/mol for EBH0 and 3.6 kJ/mol for EBH. It is preferableto use the results obtained with the larger basis set, i.e., 6-311++G(2df,2pd), and EBH, EB3LYP, EMP2, EB97D and EM062X are usedin the following discussion, unless explicitly stated otherwise.

Even though the relative conformational energies are sensitiveto the basis set, the influence of the basis set on the conformationalgeometries is rather limited. The structures optimized with the 6-311++G⁄⁄ and cc-PVTZ basis sets are essentially the same. The max-imal change in the conformational energies was only 0.4 kJ/moland negligible. Re-optimizations with the M062X and B97D func-tionals bring about somewhat larger changes. With the B97D opti-mization, both c10 and c14 are transformed to become c2, whilec11 becomes c1. For the remaining 18 conformers, however, therelative energies are only marginally affected. The largest change

energy at the standard state (DG) and rotational constants (in GHz) for low energy

DVE DG Rotational constants

EB97D EM062X A B C

0.00 0.00 0.00 0.00 2.23 0.88 0.736.13 5.43 �1.76 �3.97 2.55 0.72 0.654.05 3.97 �1.85 �5.46 2.05 0.86 0.790.26 1.71 �0.74 0.45 2.31 0.87 0.757.85 4.57 �0.26 0.74 1.79 1.13 1.01

12.83 8.15 �3.62 �6.26 3.00 0.67 0.636.36 2.88 �1.89 �1.60 2.43 0.82 0.67

14.23 7.74 �1.65 �1.57 1.85 1.11 0.967.23 6.78 �1.34 �3.15 2.60 0.72 0.65

12.31 9.63 �4.99 �11.00 2.74 0.69 0.629.18 8.64 �2.61 �7.11 2.26 0.80 0.689.99 9.22 �1.80 �2.76 2.19 0.87 0.73

12.28 10.77 �1.93 �2.59 2.19 0.88 0.7413.76 12.54 �2.10 �5.86 2.54 0.71 0.65

7.67 8.05 �2.62 �6.62 3.26 0.64 0.5712.13 13.51 �2.17 �6.25 3.01 0.64 0.5716.58 14.12 �5.82 �13.61 2.87 0.57 0.5312.31 11.24 �0.92 �1.58 2.40 0.80 0.66

8.98 9.38 �1.22 0.12 2.33 0.87 0.7514.79 14.54 �2.18 �5.30 2.56 0.72 0.6613.25 13.29 �1.31 �5.01 3.12 0.67 0.58

Table 2Vertical ionization energies (VIE) and dipole moments (dipole) of low energyconformers of Gln.

Conf. VIE (eV) Dipole (Debye)

OVGF EBH EB3LYP EMP2 EBH EB3LYP EB97D

c1 9.91 9.36 9.24 3.89 3.69 3.56 3.46c2 9.85 9.29 9.20 3.20 3.13 3.07 3.00c3 9.52 9.53 8.98 4.21 4.16 4.10 4.03c4 9.42 9.40 9.09 7.19 7.00 6.85 6.73c5 9.68 9.65 9.06 5.23 4.95 4.71 4.49c6 9.60 9.51 9.03 4.28 4.04 3.87 3.75c7 9.42 9.45 9.08 8.15 7.90 7.70 7.53c8 9.14 9.10 8.78 2.24 2.17 2.10 2.03c9 9.76 9.72 9.12 5.98 5.82 5.67 5.51c10 9.66 9.58 9.06 2.86 2.71 2.60 2.52c11 9.91 9.79 9.13 2.76 2.68 2.60 2.50c12 9.79 9.25 8.91 5.40 5.20 5.08 4.97c13 9.73 9.63 8.99 3.85 3.66 3.54 3.47c14 9.83 9.26 9.07 5.50 5.33 5.21 5.13c15 9.50 9.47 8.98 7.70 7.55 7.41 7.28c16 9.72 9.07 8.94 5.06 4.94 4.85 4.75c17 9.76 9.76 9.08 4.29 4.07 3.92 3.81c18 9.93 9.29 9.20 5.29 4.98 4.77 4.60c19 9.35 9.20 9.04 8.91 8.67 8.46 8.27c20 9.68 9.06 8.96 5.70 5.53 5.41 5.29c21 9.66 9.65 9.03 6.88 6.74 6.61 6.47

R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21 17

in the relative energies is only 2.1 kJ/mol observed for c21, whilethe mean absolute change is 0.5 kJ/mol. With the M062X optimiza-tion, all the 21 low energy conformers remain unique conformers.A rather large increase of 6.6 kJ/mol in the relative energy is ob-served for c3. But the energies of other conformers are changedby 1.5 kJ/mol or less, and the mean absolute change is only0.7 kJ/mol. More details are shown in the Supplementary material.Overall speaking, the influence of the structural change on the val-ues of PA, GB, PDE and GA is limited, as to be seen in Section 3.3below.

Among the conformers shown in Table 1, c6 was identified byDinadayalane et al. [29], c3 was located by Jones et al. [10], whilec1, c2, c10, c6 and c4 were reported by Bouchoux [23]. Several con-formations such as c17 and c11 which are important for determin-ing the conformational distributions were missed by all theseprevious studies, illustrating the necessity of the thorough searchperformed in this work.

Fig. 3 shows the structures of 9 representative low energy con-formers of neutral Gln. The low energy conformers usually havecompact structures that are helpful for forming multiple hydrogenbonds (H-bonds) with the lowered electronic energies. The H-bondlengths (in Å) are also indicated in Fig. 3. The existence of H-bond isdetermined here by a geometric criterion of taking a cutoffdistance of 2.8 Å between the H-bond donor and acceptor [18].Though a compact structure with strong H-bonds is helpful forlowering the electronic energy, it is often associated with a highZPVE and low entropy that are unfavorable for the free energy.Consequently, the global electronic energy minimum is notnecessarily the most important conformer at the temperature ofinterest. In the other hand, conformers with modestly lowelectronic energies and extended configurations such as c17 andc10 are advantageous for having low ZPVEs and high entropies.Their importance increases with the increased temperature, as tobe seen below.

Table 2 shows the VIEs and dipole moments of the low energyconformers. As seen in Table 2, the BHandHLYP and OVGF resultsfor VIEs agree with each other very well for most Gln conformers,mutually validating each other. For c1, c2, c16, c18 and c20, theOVGF results are higher than that of BHandHLYP by 0.5 eV or more.A close look at the orbitals of these conformers reveals the cause

c1 c2

c4 c5

c10 c11

1.94

2.17

2.43

2.29

2.69

2.44

1.76 2.461.97 2

2.252.43

1.97

Fig. 3. Structures of representative low energy conformers of Gln. The dash lines in

for the large discrepancy. A common feature for the five conform-ers is that their second HOMO ionization energies are very close totheir HOMO ones. In such cases, the perturbation approach used inOVGF is expected to produce poor results. Therefore, the BHandH-LYP results are more trustworthy. Incidentally, the B3LYP resultsfor VIEs of these conformers are very close to the BHandHLYP ones.For the other conformers, the B3LYP VIEs are substantially smallerthan the BHandHLYP or OVGF ones. On average, the B3LYP VIEs aresmaller than the BHandHLYP results by about 0.40 eV. Coinci-dently, previous studies have shown that the B3LYP results under-estimate the experimental VIEs for histidine and phenylalanine byabout 0.3 eV [20,19]. Taking all these facts into consideration, it isreasonable to conclude that BHandHLYP is the method of choice forcomputing VIEs.

c3

c6

c17

2.48

1.88 1.962.46

.17

2.462.28

2.66 2.462.59

2.472.23

2.61

2.47

dicate H-bonds and the numbers in parentheses are the H-bond lengths (in Å).

Table 3Equilibrium conformational distributions of gaseous Gln.

Conf. 298 K 498 K

ECCSD0 EMP2 EBH ECCSD0 EMP2 EBH

c1 7.2 17.7 2.0 2.7 5.7 1.2c2 13.7 4.1 1.4 6.9 4.2 1.7c3 9.9 31.5 16.5 6.7 16.6 8.7c4 0.8 4.3 1.4 0.6 2.1 0.8c6 6.8 2.1 2.3 5.5 3.4 2.8c10 28.9 12.4 26.5 27.3 20.5 24.9c11 4.9 6.4 6.1 5.6 8.2 6.1c15 2.2 8.4 9.0 3.1 8.7 6.9c17 17.1 4.6 29.4 28.9 16.3 38.5

18 R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21

As shown in Table 2, the BHandHLYP dipole moments are smal-ler than the MP2 ones, by 0.17 Debye on average. The B3LYP dipolemoments are further smaller than the BHandHLYP ones by an aver-age of 0.13 Debye. The B97D dipole moments are the smallest andare below the MP2 results by 0.43 Debye on average. These resultsfollow the trend that the more the HF component is, the larger thedipole moment is. As the MP2 dipole moments are found to agreewell with the experimental measurement [49], the MP2 results arerecommendable. Meanwhile, the BHandHLYP results are also veryuseful, but the B3LYP results are less favored. The B97D dipole mo-ments are disfavored, even though the B97D method is intended tobest mimic the MP2 result [50,42]. For open shell systems that areoften treated poorly by the MP2 method, however, the BHandHLYPapproach is preferred.

Table 3 shows the equilibrium distributions of Gln conforma-tions at 298 K and 498 K, as calculated by the three methods ofCCSD, MP2 and BHandHLYP. For simplicity, only conformers withequilibrium contents over 3% as calculated by any of the threemethods are shown. As seen in Table 3, the conformationaldistributions are strongly dependent on the computationalmethods. Overall speaking, the similarity between the BHandHLYPand CCSD results is higher than that between the MP2 and CCSDresults. The BHandHLYP method seems to be an economic way toobtain reasonable conformational distributions. This is rathercomforting and is of practical importance when dealing with largerbiomolecules.

Irrespective of the computational methods used, the contents ofc11 and c17 in the equilibrium ensemble are substantial and in-crease with the temperature due to the favorable entropic effect.AT T = 498 K, both c11 and c17 are more important than c1, theglobal minimum at the electronic potential energy surface. In par-ticular, missing c17 would have notable consequence in determin-ing the properties of the ensemble at high temperature, furtherconfirming the need of performing thorough conformationalsearch reported here. Notice that, due to the structural similarityof the newly and previously found conformers and the ensembleaveraging effect, it is difficult to identify the new conformersthrough the IR spectrum. However, c17 has a higher VIE than thatof previously identified conformers and may be differentiablethrough the VIE measurement.

3.2. Conformations of protonated and deprotonated Gln

Table 4 shows the relative energies, dipole moments and rota-tional constants for the low energy conformers of protonated anddeprotonated Gln. The conformations of protonated and deproto-nated Gln are denoted respectively as pn and dn, where n is a nu-meral denoting the conformational stability ordered by ECCSD0.Their structures are shown in Fig. 4 and their Cartesian coordinatesmay be found in the Supplementary material.

In the equilibrium conformation ensemble, the protonated spe-cies is dominated by p1 and p2, while the deprotonated species is

dominated by d1 and d2. d1 is more abundant than d2, but p1 andp2 may have similar abundance. While p1, p2 and d1 have beenidentified before [23,10], d2 is reported here for the first time.The dipole moment of d2 is quite different from that of d1. d2has a content of about 20% in the equilibrium ensemble at the stan-dard state and should be observable.

As shown in Fig. 3, the structures of the two most abundantneutral Gln conformers, c10 and c17, are similar, each with an ex-tended configuration and three intramolecular H-bonds. Likewise,the structures of the dominant conformers of protonated Gln, p1and p2, are also similar, with four H-bonds each. The extra H-bondin p1 (p2) as compared with c10 (c17) is an very strong H-bond be-tween the protonated amino group and the acyl group, with a veryshort H-bond length of 1.65 (1.53) Å. The H-bond between the ami-no hydrogen and carboxyl oxygen in p1 (p2) is also substantiallystronger than that in c10 (c17). The two strong H-bonds in p1(p2) link the protonated amino group with the remaining twofunctional groups of Gln, the carboxyl and acyl groups, to form arigid ring-like configuration. Consequently, a large cyclization en-tropy effect [51]is expected in the protonation process.

By linking both the amino and acyl groups with H-bonds toform a ring-like structure, the deprotonated carboxyl in deproto-nated Gln plays a similar structural role as the protonated aminogroup in protonated Gln. The H-bond between COO� and the acylgroup is also strong, with a bond length of about 1.75 Å, but isweaker than that between the protonated amino and the acylgroup, with a bond length of around 1.6 Å. Therefore, a substantialcyclization entropy effect may be expected in the deprotonationprocess, but the cyclization entropy effect is weaker than its coun-terpart in the protonation process.

3.3. Energetics of Gln protonation and deprotonation reactions in gasphase

Table 5 shows the results of PA, GB, PDE and GA determined bydifferent computational approaches for gaseous Gln at the stan-dard state. The new symbols, EMP2TZ and EBHQZ, denote the compu-tational results of MP2/cc-PVTZ and BHandHLYP/cc-PVQZ,respectively. The results are based on the BHandHLYP/6-311++G⁄⁄ geometries, unless explicitly stated otherwise. The avail-able experimental and theoretical results in the literature are alsoshown in Table 5.

As may be seen in Table 5, there is a large spread among theexperimentally determined PA and GB. Excluding the results bysome experiments that are deemed unreliable, the difference be-tween the recent EKM result and the average of the other measure-ments on PA is more than 30 kJ/mol [23]. The difference among thecomputational results is also substantial, but all theoretical resultsare close to the high end of the experimental measurements. Thetheoretical PAs may be smaller or larger than the EKM result of988 kJ/mol, but are all larger than the largest non-EKM measure-ment of 961 kJ/mol. Moreover, it is interestingly to note that alltheoretical GBs are close to the EKM result, but substantially higherthan all non-EKM measurements. This may be a good indicationthat the EKM results for PA and GB are more reliable. This assess-ment is also consistent with the observation that there is a largeentropic change in the protonation reaction.

Due to the inherent uncertainty in the EKM measurementinvolving large reaction entropy and the large spread among differ-ent computational results, it is difficult to pinpoint the true resultsin a narrow range. However, we will risk some controversy and tryto suggest the most probable values.

As concluded by Drahoa and Vekey (D–V), the EKM determina-tion of the enthalpy change is fairly accurate even when encoun-tering large reaction entropy differences [52]. The D–Vconclusion was cautioned by Ervin and Armentrout (E–A) who

Table 4Relative electronic energies, relative thermal corrections to the free energy at the standard state (DG), relative ZPVEs (DVE), dipole moments (dipole, in Debye) and rotationalconstants (in GHz) of low energy conformers (conf.) of protonated and deprotonated Gln. The dipole moments are obtained from the MP2 calculations. All energies are in kJ/mol.

Conf. ECCSD0 EBH EMP2 DG DVE Dipole Rotational constants

p1 0.00 0.00 0.00 0.00 0.00 2.76 2.21 0.83 0.75p2 1.39 �0.74 1.84 �0.78 �0.14 2.92 3.21 0.66 0.57p3 9.94 12.01 11.87 �0.55 �0.34 3.19 2.13 0.86 0.78d1 0.00 0.00 0.00 0.00 0.00 2.95 2.30 0.88 0.75d2 3.86 3.17 2.87 0.48 0.03 4.24 2.32 0.88 0.74d3 10.89 8.78 11.21 �2.51 �0.76 3.59 2.36 0.85 0.69d4 11.61 7.68 10.71 �3.07 �1.20 3.78 2.47 0.81 0.66d5 12.15 8.45 12.08 �3.08 �1.32 4.34 2.36 0.85 0.69d6 13.16 10.08 15.23 �3.75 �0.79 3.41 2.62 0.78 0.63

2.35

2.37 2.471.65

2.35

2.17 1.53 2.45

2.35

2.121.51

2.45

2.26

1.75

2.47

2.10

1.76

2.48

2.21

1.76

2.48

2.30

1.742.43

2.09

1.77

2.482.20

1.752.49

p1 p2 p3

d1 d2 d3

d4 d5 d6

Fig. 4. Conformations of low energy conformers of protonated and deprotonated Gln.

R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21 19

proposed a somewhat increased error limit that was dependent onthe reaction entropy [53]. However, the maximum reaction entro-py calculated by all computational approaches shown in Table 5 is�36 J/mol/K at room temperature. The value is changed to �42 J/mol/K for T = 500 K, or a temperature close to the effective temper-ature in the EKM experiment [27]. The corresponding E–A errorlimit is about 6 kJ/mol for PA (2 standard deviations). Therefore,the error limit of 7.4 kJ/mol given by the EKM experiment [27] istrustable. Similarly, the experimental error limit of 11 kJ/mol forPDE [11] may be trusted.

Due to the similarity in the PA and PDE calculations, it is reason-able to expect that a suitable method producing a good result forone of the two quantities should also produce a good result forthe other quantity, except for some coincidence. Examining thedata in Table 5 shows that the computational approaches provid-ing the PDE results within the EKM determined range also happento produce the PA results in the EKM determined range, stronglysuggesting that the PA value is correctly determined in the EKMexperiment. Moreover, it is plausible to further pinpoint the PA va-lue by using the computational approaches that produce both thePA and PDE results within the experimental error limits. Basedon this assumption and the data in Table 5, the selected theoreticalapproaches are EMP2TZ, ECCSD0, EBH0, EBH, EBHQZ and EB97D. We expectthe average results of these methods to provide the best estimates

of the true values. The average PA, GB, PDE and GA given by thesemethods are 987.2, 945.1, 1385.3 and 1362.9 kJ/mol, respectively.Considering the data shown in Table 5, it appears that EBH providesthe best overall results. Moreover, the PA and PDE results given byEBH are also in excellent agreement with both the experimentalvalues, further confirming the reliability of the measured PA. Theaverage protonation and deprotonation entropies, DS+ and DS�,determined by the above data are �32.4 and 33.9 J/mol/K, respec-tively. The full ranges of PA, GB, PDE, GA, DS+ and DS� given bythese computational approaches are covered by 987.2 ± 4.0,945.1 ± 5.8, 1385.3 ± 9.0, 1362.9 ± 9.1 kJ/mol and �32.4 ± 6.2 and33.9 ± 5.1 J/mol/K, respectively. We believe that these data are reli-able reflection of the true results.

To examine the effect of structural uncertainty on the thermo-chemical data, Table 5 also shows some results obtained with thegeometries optimized using the M062X and B97D functionals.Compared to the BHandHLYP optimization, re-optimizations withthe M062X and B97D functionals may affect the values of PA, GB,PDE and GA by up to 4.9 kJ/mol. However, the difference in PA/GB/PDE/GA due to the structural change is rather small when com-pared to that obtained with different functionals and is thereforeinconsequential to the overall conclusions.

As a side note, the magnitude of DS+ computed here is clearlysmaller than that determined experimentally [27]. As DS+ is

Table 5Proton affinity (PA), gas-phase basicity (GB), proton dissociation energy (PDE) andgas-phase acidity (GA) of glutamine. All values are in kJ/mol.

Methoda PA GB PDE GA

EMP20 970.2 933.8 1372.8 1346.2EMP2 974.7 934.0 1366.4 1343.7EMP2TZ 986.2 944.3 1384.1 1362.6G3MP2B3 977.2 935.7 1371.4 1349.4EB3LYP 982.1 940.1 1372.6 1349.8ECCSD0 983.2 940.5 1388.2 1367.5EBH0 984.1 941.3 1381.4 1359.5EBHQZ 990.9 948.9 1394.2 1372.0EBH 987.6 944.5 1386.6 1364.7EBH⁄ 990.5 947.2 1386.9 1365.1EBH⁄⁄ 988.8 948.7 1387.6 1361.7EM062X 969.8 927.9 1370.0 1348.2EM062X⁄ 973.9 932.5 1370.0 1347.8EM062X⁄⁄ 970.4 932.6 1372.0 1345.7EB97D 991.1 950.8 1377.0 1354.2EB97D⁄ 994.6 955.7 1377.0 1353.7EB97D⁄⁄ 991.8 955.1 1378.0 1352.2Experiment 915–961b,

988c881–918d,939c

1385–1388e 1359e

Previoustheory

964–997f 934–938g 1368–1378e,h

1343h

a Results are based on the BHandHLYP/6-311++G⁄⁄ geometries, except for thosedenoted with ⁄ and ⁄⁄. Results denoted with ⁄ are based on the M062X/cc-PVTZgeometries, i.e., EM062X⁄, EB97D⁄ and EBH⁄ refer to the M062X/6-311++G(2df,2pd)//M062X/cc-PVTZ, B97D/6-311++G(2df,2pd)//M062X/cc-PVTZ and BHandHLYP/6-311++G(2df,2pd)//M062X/cc-PVTZ results, respectively. Results denoted with ⁄⁄ arebased on the B97D/cc-PVTZ geometries, i.e., EM062X⁄⁄, EB97D⁄⁄ and EBH⁄⁄ refer to theM062X/6-311++G(2df,2pd)//B97D/cc-PVTZ, B97D/6-311++G(2df,2pd)//B97D/cc-PVTZ and BHandHLYP/6-311++G(2df,2pd)//B97D/cc-PVTZ results, respectively.

b Refs. [4,23,22,27,54–56].c Ref. [27].d Refs. [4,23,22,54].e Refs. [10,11].f Refs. [23,28,30,29,24,57,58].g Refs. [23,24,57].h Ref. [24].

20 R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21

relatively large and temperature dependent, a large error in theEKM measurement may be expected [D–V, E–A]. Therefore, thecomputational results are deemed to be more reliable. Moreover,it should be noticed that the EKM measurement provides an over-estimate of DS+ here, instead of an underestimate commonly ob-served before [D–V, E–A]. This result supports the E–A viewpoint that the accuracy of estimating the reaction entropy cannotbe reliably improved by empirically scaling the EKM result.

By the way, the previously reported DS+ of �26.9 J/mol/K iswithin the range determined here, though the former is near thelow end of the latter. By the G3MP2B3 method used before, DS+

is calculated to be �30.2 J/mol/K, due to the new Gln conformersfound here. Overall, it is meaningful to consider the reaction entro-py in the computation of the free energy change. As noticed byBouchoux [23], the entropy of mixing can be a major componentof the reaction entropy. Here, depending on the computationalmethods used, the difference in the entropy of mixing betweenthe neutral and protonated Gln may reach 13.0 J/mol/K, or a cor-rection of �3.9 kJ/mol in the computed GB. The correction due tothe entropy of mixing on the computed GA may reach 4.5 kJ/mol.However, the majority of the entropic effect may be accountedfor by 3–4 low energy conformers. For example, the new conform-ers found here only correct the Bouchoux’s values for PA and GB by+0.3 and �0.7 kJ/mol, respectively.

3.4. Additional note on the computational results

It is widely observed that, to approach the result of the basis setlimit, an anionic system is the most difficult, a cationic system is

the easiest and a neutral system falls in between. According to thisrule of thumb, a larger basis set should generally produce a smallervalue for PA or PDE. The effect of an incomplete basis set may beapproximated by the basis set superposition error (BSSE). Thisempirical rule is followed when computing the thermochemicalproperties of glutamic acid [21], an amino acid that is very similarto Gln.

However, Table 5 shows that the computed thermochemicalquantities of Gln have a rather unusual dependence on the basisset. For BHandHLYP, the computed thermochemical quantities in-crease, rather than decrease, with the increased size of the basisset. The BSSE correction is quite misleading as it is not only havingthe wrong sign, but also too small in the magnitude. Similar behav-ior has been observed for B3LYP when the basis set is increasedfrom 6-311+G(d,p) to cc-pVTZ [29].

The thermochemical quantities computed by the MP2 methodshow a different dependence on the basis set. The value of PA (orGB) is the highest by EMP2TZ, followed by EMP2, then by EMP20. Whilefor PDE (or GA), it is the highest by EMP2TZ, followed by EMP20, thenby EMP2. In a sense, the patter of variation in the MP2 results is lessregular than that in the BHandHLYP results. Besides, the BSSE cor-rection for MP2 is quite substantial and in the order of 10 kJ/mol.However, similar to the results for BHandHLYP, the BSSE correctionfor MP2 often has a wrong sign. Inclusion of BSSE provides no helpat all.

The underlying mechanism for the peculiar basis set depen-dence of the thermochemical quantities of Gln is not properlyunderstood and requires further study.

4. Summary

We have performed thorough search on the conformationalspace of the neutral, protonated and deprotonated Gln in gasphase. Some important new conformations are found. The struc-tural and hydrogen bonding features are characterized and areconnected with their relative ZPVEs and conformational stabilities.The rotational constants, dipole moments and VIEs of the low en-ergy conformers are presented and may be helpful for explainingthe future experiments.

The relative conformational energies and the thermochemicaldata of PA, GB, PDE and GA calculated by different methods maybe substantially different and show rather unusual dependenceon the basis set. Comparison of the different theoretical resultsand the available experiments shows clearly that the EKM experi-ment gives an accurate determination of PA but overestimates theentropic effect, while all other experiments underestimate the PAof Gln. The analysis also provides the most probable values forthe PA, GB, PDE and GA of Gln. The best theoretical estimate ofthe thermochemical data are provided by the BHandHLYP andCCSD methods.

Acknowledgment

Z. Lin gratefully acknowledges the financial support of theNational Science Foundation of China (Grant No. 11074233), theNational Basic Research Program of China (973 Program Grant No.2012CB215405) and the Specialized Research Fund for the DoctoralProgram of Higher Education (Grant No. 20113402110038).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2013.07.016.

R. Pang et al. / Computational and Theoretical Chemistry 1020 (2013) 14–21 21

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