Positron Binding Properties of Glycine and Its Aqueous Complexes

May 27, 2016 - Department of Applied Physics, Aalto University School of Science, 02150 ... Graduate School of NanoBioScience, Yokohama City Universit...
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Positron Binding Properties of Glycine and Its Aqueous Complexes Mikko Nummela,†,‡ Hannes Raebiger,*,† Daisuke Yoshida,† and Masanori Tachikawa¶ †

Department of Physics, Graduate School of Engineering, Yokohama National University, Yokohama 240-8501, Japan Department of Applied Physics, Aalto University School of Science, 02150 Espoo, Finland ¶ Quantum Chemistry Division, Graduate School of NanoBioScience, Yokohama City University, Yokohama 236-0027, Japan ‡

ABSTRACT: We investigate positron binding to glycine and its aqueous complexes by first-principles calculation. We show that while glycine in its ground state (Gly) does not bind positrons, several of its strongly polar conformers do, and in particular, its zwitterion form (GlyZI) binds positrons strongly. Aqueous complexes Gly·nH2O and GlyZI·nH2O also bind positrons, if their dipole moment μ > μcr. However, μ is not a sufficient quantity to describe positron binding to these complexes. We show that in addition to μ, positron binding strongly depends on the intramolecular bonding of glycine. In Gly·nH2O, positrons are weakly bound to the nitrogen in Gly, whereas in GlyZI·nH2O, the ionic oxygen in GlyZI is a strong “positron attractor”.

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INTRODUCTION Positrons have become a versatile tool to probe various properties of a wide range of materials. In bulk materials, positrons are trapped by negatively charged defects or vacancytype defects associated with an open volume, which allows for a very detailed and noninvasive characterization of the bulk defects in question.1 Similar characterization is possible for molecules that trap positrons: in addition to negative ions, such trapping also occurs in the dipole field of a neutral molecule with a sufficiently large dipole moment.2 Such positron trapping by individual molecules, and even individual positron binding energies, can be experimentally measured,3−9 but theoretical analyses10−18 are indispensable to elucidate the mechanisms that underlie the positron trapping by molecules. Apart from the study of fundamental properties of solid and molecular materials, positron emission tomography (PET) is a medical application used for studies of cerebral metabolism and cancer detection, based on the detection of the two photons simultaneously emitted upon electron−positron annihilation.19 Despite such widespread medical and biological applications, the positron binding properties in biological molecules remain poorly known.17,18 To this end, we investigate positron binding to the simplest amino acid glycine (Gly) and its highly polar zwitterion form (GlyZI) in aqueous environments. Our approach is purely theoretical, with the objective to guide future positron experiment of amino acids and other biological molecules in aqueous environments. A recent study of positron binding to a variety amino acids shows that, as isolated molecules in their global minimum structure, only three amino acids (Trp, His, and Gln) trap positrons.17 However, the conformers that include an intramolecular hydrogen bond of the same amino acids all have dipole moments well above Crawford’s critical value of 1.65 D, © XXXX American Chemical Society

large enough to bind positrons. Gly has a total of 8 known conformers and the zwitterion (ZI) form, of which the ZI should be highly polar and bind a positron, but other conformers may also exceed Crawford’s threshold. However, e.g., GlyZI is stable only in an aqueous solution, which still leaves open the question of what is the effect of such environments on positron affinities. In particular, aqueous complexes, where Gly forms hydrogen bonds with nearby water molecules could have large enough dipole moments to bind a positron. In this work, we focus on Gly and GlyZI and the complexes Gly·nH2O and GlyZI·nH2O containing up to n = 4 water molecules. The simple expectation would be that only the GlyZI and GlyZI·nH2O can bind positrons, and indeed, GlyZI and all GlyZI·nH2O are found to bind positrons. However, we also find many stable Gly·nH2O that can trap a positron, which suggests that positron binding properties of molecules can be strongly altered by aqueous and other environments. This paper is organized as follows. First we describe the computational details, followed by a section with the calculated results and discussion. The final section summarizes this work.

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COMPUTATIONAL DETAILS Molecular structures, their stabilities, and total energies are calculated using the multicomponent molecular orbital (MC_MO) method. With this method, the multicomponent wave function containing the electronic Slater determinant and the positronic orbitals can be obtained by solving the electronic Received: February 22, 2016 Revised: May 13, 2016

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DOI: 10.1021/acs.jpca.6b01780 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Total energies and dipole moments of (a) Gly and Gly·nH2O and (b) GlyZI and GlyZI·nH2O. Energies of different stable structures are given with respect to the lowest energy structure of a particular stoichiometry. Structures with positive PA values are indicated by red lines. (c) Reaction enthalpies of formation of Gly·nH2O and GlyZI·nH2O.

In order to unveil the bonding mechanism of positrons to amino acids in aqueous environments, we consider a wide variety of system sizes and isomers. For Gly, we calculate all eight conformers and GlyZI. Aqueous complexes are constructed only of Gly and GlyZI. Stable structures of Gly· nH2O and GlyZI·nH2O are obtained systematically by adding H2O molecules one by one at arbitrary initial positions around Gly or GlyZI, optimizing each geometry until a stable minimum is found.

and the positronic Roothan equations, simultaneously. The details of this method can be found in ref 20. For each system A, we calculate the total energy E[A] at local equilibrium nuclear configuration, and E[A; e+] for the same system containing a positron. As we will show, the positrons are rather weakly bound to the systems considered and nuclear relaxations of positron containing systems may be considered negligible. Thus, E[A; e+] is calculated at the same nuclear configuration as the isolated system A. Using these total energies, we define the positron affinity for system A as PA(A) = E[A] − E[A; e+]

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RESULTS AND DISCUSSION Stability and Polarity. The total energy and dipole moment of the eight Gly conformers, GlyZI, Gly·nH2O and GlyZI·nH2O with up to n = 4, are given in Figure 1a,b. Both Gly and GlyZI bind strongly H2O molecules, as indicated by the exothermic reaction enthalpies corresponding to reactions where H2O molecules are added one by one or all at once shown in Figure 1c. Clearly GlyZI is more hydrophilic than Gly, which explains why the energy of GlyZI·nH2O given with respect to the lowest energy Gly·nH2O structure systematically decreases as n increases. This is well in agreement with earlier works, which suggest that for n ≥ 5···7, GlyZI·nH2O and Gly· nH2O become isoenergetic.34−37 The bonding of Gly and GlyZI with H2O is quite strong, as evidenced by Figure 1c. However, neither covalent nor ionic bonds are formed. Gly, GlyZI, and H2O all are polar molecules, and the main

(1)

E[A] and E[A; e+] are calculated at the Hartree−Fock (HF) level using a modified version of Gaussian03.21 We used the 631G* basis set for electrons and the [11s9p4d2f] Gaussian type functions for positrons. While HF may severely underestimate positron binding energies,15,16,22−24 it well reproduces chemical trends for varying system sizes and/or chemical species.10,16−18,25 These positron binding energies can be systematically improved, for example, by configuration interaction methods,10−14,16,20,24 explicitly correlated methods,26−31 quantum Monte Carlo,15,23,32 or quasiparticle thoeries.33 However, such more accurate methods are computationally very heavy, and can only be applied for rather small systems, which precludes systematic studies of chemical trends and binding mechanisms, such as the present. B

DOI: 10.1021/acs.jpca.6b01780 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Table 1. Total Energies E in eV, Dipole Moments μ in Debye, and Positron Affinities PA in meV for Gly, GlyZI, Gly·nH2O and GlyZI·nH2O with n = 1,2a

interaction among them is thus the dipole−dipole interaction, which also leads to hydrogen bond formation. The Gly·nH2O and GlyZI·nH2O complexes are thus networks of dipole−dipole and/or hydrogen bonds, and may exhibit quite large dipole moments. Figure 1a,b shows no universal trend correlating total energies with dipole moments. For the isolated Gly, the dipole moment correlates fairly well with total energy, i.e., low total energy implies low dipole moment and vice versa. The only exception is the conformer with an intramolecular hydrogen bond, with positron binding properties discussed recently.17 Gly·nH2O and GlyZI·nH2O, however, exhibit no correlation between dipole moment and total energy. In fact, for Gly·nH2O the global minimum structures have rather large dipole moments. GlyZI has a very large dipole moment as expected, which reduces for GlyZI·nH2O upon increasing n. However, for any given n, there is no obvious correlation between total energies and dipole moment for the different GlyZI·nH2O structures. Positron Binding Properties. The positron affinities (PA) calculated for each geometry are given in Tables 1, 2 and 3. Structures that bind positrons, i.e., have positive PA values, are indicated by red lines in Figure 1a,b. For Gly, all but the three lowest energy conformers can bind a positron. For Gly·nH2O, the lowest energy structure never binds a positron, but roughly half of the structures calculated can bind a positron. The total energies of Gly·nH2O have no obvious correlation with the PA of a given structure, because of the lack of correlation of total energy and μ discussed above. GlyZI and all GlyZI·nH2O complexes can bind a positron. The positive PA values are always associated with a dipole moment μ > 3···4 D; the smallest μ associated with a positive PA is only 2.75 D (Table 1, Gly, Structure 5), while other structures with μ up to 3.265 D (see, e.g., Table 3, GlyZI·4H2O, Structure 16) have negative PA values. The correlation between dipole moment μ and positron affinity PA is shown in Figure 2. A least-squares fit of the entire data (indicated by the solid line) seems somewhat reasonable; the correlation coefficient is R2 = 0.896. The fitted line intersects the PA = 0 axis at the critical dipole moment of μcr = 3.71 D, which also seems reasonable in comparison with an earlier study of positron binding in amino acids that suggested a critical value of μcr = 3.46 D.17 However, the lowest dipole moment found to bind a positron is only 2.75 D, and in total, 8 out of the 30 structures with PA > 0 have a dipole moment μ < 3.71 D. Moreover, the data is clearly scattered in two regions: the Gly and Gly·nH2O data are clustered in the low-PA and low-μ region, whereas the GlyZI and GlyZI·nH2O data are distributed in the high-PA and high-μ region, and the GlyZI and GlyZI·nH2O data clearly has a steeper slope than the Gly and Gly·nH2O data, as shown by their respective fitted lines. These individual data sets are less correlated: the Gly and Gly· nH2O data suggests a critical dipole moment of μcr = 3.14 D and has a correlation coefficient of R2 = 0.623, and the GlyZI and GlyZI·nH2O data has a critical dipole moment of μcr= 3.05 D and R2= 0.818. The above discussion suggests that the rather large R2 = 0.896 for the entire data set is likely an artifact due to the large distribution and strong clustering of the data in the low-PA and low-μ region, and that linear relations between PA and μ are not reliable even to extrapolate the critical μcr for positron binding. To understand the origin of the poor correlation of PA and μ, we investigate the spatial distribution of positrons bound by

system Gly

GlyZI Gly·H2O

GlyZI·H2O

Gly·2H2O

GlyZI·2H2O

structure 1 2 3 4 5 6 7 8 1 1 2 3 4 5 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5

E (eV) 0.000 0.082 0.090 0.127 0.133 0.303 0.402 0.404 1.226 0.000 0.177 0.182 0.206 0.312 1.014 1.112 1.219 1.254 0.000 0.198 0.207 0.250 0.276 0.297 0.302 0.363 0.368 0.455 0.498 0.796 0.799 0.825 0.849 1.264

μ (Debye) 1.331 2.040 2.303 5.689 2.746 3.284 4.480 4.734 10.075 1.871 2.499 3.272 2.130 2.774 8.761 8.530 8.584 13.458 2.804 4.052 3.981 2.604 1.572 4.661 3.725 3.194 3.704 3.242 2.466 7.130 8.867 6.619 8.107 11.623

PA (meV) − − − 54.282 0.128 2.266 23.326 21.844 313.878 − − 0.503 − − 257.507 238.186 193.497 288.492 − 1.863 1.437 − − 11.798 1.016 0.080 0.575 0.040 − 161.923 133.497 115.310 224.628 218.211

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PA is given only for structures that bind positrons. Structures for each system are numbered starting from lowest energy.

the various complexes. Figures 3−5 show the molecular structures, dipole moments, electrostatic potentials, and positronic orbitals of representative isolated molecules and aqueous complexes. Let us first investigate the isolated molecules shown in Figure 3. The ground state conformer of Gly (Figure 3a) has a very small dipole moment, pointing toward the unhydrogenated oxygen atom, but this dipole moment is too small to bind a positron. Gly with an intramolecular hydrogen bond Figure 3b), and GlyZI have large dipole moments, roughly aligned along the C−C bond from oxygen atoms toward N, i.e., opposite to μ of Gly in its ground state structure. The positronic orbital appears close to the oxygen atoms, as can be expected based on the direction of the dipole moment vector μ⃗ . The positronic orbital clearly is nodeless (s-like), but has a “dent”, which is similar to the negative isosurface of the electrostatic potential. Figures 4 and 5 show the molecular structures, dipole moments, electrostatic potentials, and positronic orbitals of aqueous complexes of Gly and GlyZI, respectively. The dipole moments and electrostatic potentials of the aqueous complexes of Gly and GlyZI are strikingly different: the direction of the C

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The Journal of Physical Chemistry A Table 2. Total Energies E in eV, Dipole Moments μ in Debye, and Positron Affinities PA in meV for Gly·nH2O and GlyZI·nH2O with n = 3a system Gly·3H2O

GlyZI·3H2O

structure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3

E (eV) 0.000 0.055 0.065 0.137 0.141 0.147 0.197 0.211 0.244 0.246 0.259 0.316 0.343 0.358 0.366 0.384 0.461 0.505 0.564 0.662 0.686 0.705

μ (Debye) 2.166 3.166 2.949 2.325 2.086 1.062 1.534 5.531 3.552 2.278 4.320 2.234 5.266 4.263 2.650 4.775 5.234 4.845 3.203 5.007 5.350 10.254

PA (meV) − 0.091 − − − − − 15.802 0.912 − 2.123 − 6.402 4.986 − 6.200 18.512 11.242 − 109.794 41.233 172.323

Figure 2. Correlation of positron affinity PA (meV) with dipole moment μ (Debye). Data for Gly and Gly·nH2O are shown by filled symbols, GlyZI and GlyZI·nH2O by open symbols. The squares, circles, upward triangles, downward triangles, and diamonds indicate Gly or GlyZI with 0, 1, 2, 3, or 4 H2O molecules, respectively. The solid line is a least-squares fit for all the data, the dashed line is for Gly and Gly·nH2O, and the dotted line is for GlyZI and GlyZI·nH2O.

a

PA is given only for structures that bind positrons. Structures for each system are numbered starting from lowest energy.

Table 3. Total Energies E in eV, Dipole Moments μ in Debye, and Positron Affinities PA in meV for Gly·nH2O and GlyZI·nH2O with n = 4a system Gly·4H2O

GlyZI·4H2O

structure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4

E (eV) 0.000 0.145 0.164 0.243 0.256 0.288 0.289 0.289 0.351 0.369 0.379 0.431 0.472 0.492 0.591 0.619 0.627 0.671 0.674 0.429 0.476 0.567 0.578

μ (Debye) 2.412 1.077 5.247 1.823 2.991 3.355 0.966 4.599 2.846 2.437 3.555 2.524 1.862 4.476 3.265 1.633 5.848 4.397 3.521 7.371 4.782 5.520 3.907

Figure 3. Dipole moment, electrostatic potential, and positronic orbital bound to (a) Gly, (b) Gly with an intramolecular hydrogen bond, and (c) GlyZI. The upper figures show the electrostatic potential at isosurfaces ±0.05 V, red for positive and blue for negative. The arrows in the lower molecules indicate the dipole moment (magnitude is proportional to length), and the yellow isosurfaces indicate the positronic orbitals [at isosurface values 0.007 e/bohr3 in (b) and 0.012 e/bohr3 in (c)].

PA (meV) − − 8.311 − − − − 3.769 − − 0.264 − − 11.788 − − 9.570 2.328 0.091 32.422 14.019 47.873 3.050

and for GlyZI·nH2O (Figure 5), μ⃗ points from O toward N. Again, the positronic orbital aligns with the dipole moment vectors, i.e., the positronic orbital appears nearby N for Gly· nH2O and nearby O for GlyZI·nH2O. We observe also that the positrons bound by GlyZI·nH2O exhibit a “dent” similar to the one seen in the negative electrostatic potential isosurface, and the positronic orbitals are much closer to the O than they are to N in the Gly·nH2O. The electrostatic potentials around Gly· nH2O and GlyZI·nH2O also are quite different: for Gly·nH2O, there are equally large regions negative electrostatic potential both around N and some of the H2O molecules, whereas for GlyZI·nH2O, there is a distinct and large region of negative electrostatic potential around the O atoms of GlyZI. The striking differences in positron orbitals next to Gly· nH2O and GlyZI·nH2O suggest a fundamental difference in the positron binding mechanisms, which depend not only on dipole moment, but also on the nature of the atoms nearby the negative dipole moment direction. Here, even though the molecules and their aqueous complexes are neutral, a major difference is the ionic nature of oxygen in the zwitterion forms of glycine. Thus, it is not only the magnitude of the dipole moment, but also the nature of intramolecular bonding, ionic versus covalent, which determines how positrons are bound to

a

PA is given only for structures that bind positrons. Structures for each system are numbered starting from lowest energy.

dipole moment vector μ⃗ is opposite for Gly·nH2O and GlyZI· nH2O. For Gly·nH2O (Figure 4), μ⃗ points from N toward O, D

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Figure 5. Dipole moment, electrostatic potential, and positronic orbital bound to GlyZI·nH2O. (a) GlyZI·1H2O structure 3; (b) GlyZI· 2H2O structure 3; (c) GlyZI·3H2O structure 2; and (d) GlyZI·4H2O structure 3. See Figure 3 for legend. Positron orbital isosurface values are 0.012 e/bohr3 in (a−d).

Figure 4. Dipole moment, electrostatic potential, and positronic orbital bound to Gly·nH2O. (a) Gly·1H2O structure 3; (b) Gly·2H2O structure 6; (c) Gly·3H2O structure 17; and (d) Gly·4H2O structure 14. See Figure 3 for legend. Positron orbital isosurface values are 0.001 e/bohr3 in (a) and 0.007 e/bohr3 in (b−d).

a given complex. This sheds also some light on the poor correlations of μ versus PA discussed above. For the GlyZI· nH2O systems, positrons are strongly bound by the ionic oxygen in GlyZI. For the Gly·nH2O, however, Gly and the nH2O molecules may form strongly polar complexes by different types of bondings, but there is no distinct “positronattractor” like the ionic oxygen, and poor correlation is due to the diversity of interactions within the Gly·nH2O. Our complexes containing up to 4 H2O are far from an aqueous solution, but the results presented above offer some insight in what to expect from glycine in water. Even the ground state conformer of Gly forms strongly polar Gly·nH2O complexes which bind positrons, and the same holds for GlyZI. Interestingly, the positron binding of Gly·nH2O and GlyZI· nH2O is different: the positron prefers a location nearby N and O, respectively. Thus, if positron binding in aqueous solutions of glycine can be verified, Doppler broadening spectroscopy1 could be used to distinguish whether the positron is bound to Gly or GlyZI.

complex systems, which may exhibit a variety of different mechanisms for positron binding. We find that the positron binding mechanism is quite different for Gly·nH2O and GlyZI· nH2O due to the different types of bondings in these complexes; the ionic oxygen in GlyZI is a particularly strong “positron attractor”, whereas in Gly·nH2O the positron is weakly bound to the nitrogen of Gly. Our results suggest that glycine in water could bind positrons, and due to the different binding by Gly and GlyZI, positron annihilation spectroscopy could be used to identify Gly and GlyZI in aqueous solution.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81 (45) 339 4149. Fax: +81 (45) 338 3020. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Y. Kita, U. Nagashima, and T. Oyamada for support and discussions. M.N. and H.R. are grateful for financial support from the Scandinavia−Japan Sasakawa Foundation.

CONCLUSION We have predicted positron binding properties for glycine (Gly) in its various conformers, including the zwitterion form (GlyZI), and various aqueous complexes Gly·nH2O and GlyZI· nH2O. We show that Gly and GlyZI systems with a dipole moment μ > μcr, where μcr lies in the range of 3.05 and 3.71 D, bind positrons. The correlation of positron affinity versus μ is rather poor, and thus, μcr cannot be defined accurately. Clearly, μ is not a sufficient measure to classify positron binding to

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