2014; 25(2): 41–48

Gilbert Reibnegger* QT-AIM analysis of neutral pterin and its anionic and cationic forms

Abstract: Quantum theory of atoms in molecules (QT-AIM) pyrazino[2,3-d], containing four ring nitrogen allows detailed insight into the electronic structure of atoms, leads to remarkably complex chemical behavior. molecules by analysis of the gradient vector field of the Thus, they have early attracted the interest of theoretically electronic density distribution function. First results of a minded chemists, and during the last two decades of the QT-AIM analysis of neutral pterin as well as its anionic and 20th century, quite a number of papers described results cationic forms in aqueous solution are reported based on of quantum chemical work on various biologically and/or density functional theory using B3LYP/6–311+G(2d,p)//6– chemically interesting derivatives [1–10]. Given 31G(d) level of theory. Besides reporting QT-AIM results the state of theoretical chemistry and particularly the of the atomic partial charges and bond orders of the availability of computing power during those times, it is molecules, their electron density functions, Laplacians not surprising that most of these earlier papers employed and electrostatic potential functions are also shown. The ab initio quantum chemical procedures confined to the results demonstrate the rather extensive delocalization of Hartee-Fock method using rather small basis function sets both negative and positive extra charges predominantly or even resorting to using semi-empirical methods. over the pyrimidine moiety of the pterin ring system and More recently, studies employing Density Functional allow a precise quantitation of the effects of addition or Theory with moderately large basis function sets reported elimination of a proton on the bonding structure. Quan- on spectroscopic properties of pterin in aqueous environ- tum chemical techniques in combination with QT-AIM ments [11] and investigated the energetics of the plethora procedures are thus well-suited to describing the bonding of possible tautomeric structures of neutral 6-methyl- structure as well as the major atomic and bonding features pterin and its anionic and cationic forms in aqueous solu- of neutral pterin and its cationic and anionic forms. More- tions [12–14]. over, the data demonstrate that the chosen level of theory Using pterin structures concordant with the most stable yields chemically reasonable results while not being com- tautomeric forms of 6-methyl-pterin according to [12–14], putationally too expensive, thus providing a sound basis I report here on detailed analyses of the neutral as well as the for further theoretical chemical work on pteridines. anionic and the cationic forms of pterin (2-aminopteridine- 4(3H)-one, [15]), obtained at the B3LYP/6–311+G(2d,p)//6- Keywords: atoms in molecules; density functional theory; 31G(d) level of theory for the gas phase as well as for electronic structure. aqueous solutions (B3LYP is Becke’s 3-parametric density exchange functional using the correlation function by Lee, Yang and Parr) [16, 17]. Specifically, the Quantum Theory of DOI 10.1515/pteridines-2014-0005 Received March 21, 2014; accepted April 8, 2014 Atoms in Molecules (QT-AIM) [18] is applied to the result- ing wave functions yielding, among others, realistic atomic partial charges and bond orders. Additionally, for each of the three forms of pterin, I present visualizations of the Introduction electron density function, its gradient vector field topol- ogy and its Laplacian along with the electrostatic potential Pteridine derivatives are widespread in biological (ESP) function, in order to provide enhanced insights into systems, exhibiting a broad spectrum of interesting func- the intimate bonding structures of the molecules. tions. From a chemical point of view, their character as This aim of this study is to evaluate, for the first time, the application of QT-AIM analysis on good quality density functional theory wave functions of pteridine *Corresponding author: Prof. Dr. Gilbert Reibnegger, Institut für systems with particular focus on binding characteristics Physiologische Chemie, Zentrum für Physiologische Medizin, Medizinische Universität Graz, Harrachgasse 21/II, A-8010 Graz, of such molecules and to lay a firm foundation for further Austria, Phone: +43-316 380 4160, Fax: +43-316 380 9610, theoretical work on biologically and chemically interest- E-mail: [email protected] ing pteridine derivatives. 42 Reibnegger: Electronic structures of pterin and its ions

defined by a “zero-flux” condition. This means that no gradient path Materials and methods can cross such a surface, and this condition guarantees the identifi- cation of the unequivocally defined basins of attractions as “atoms in a molecule” in a strictly physical sense, allowing the computation QT-AIM – a brief outline of many atomic properties. For example, the electronic charge of an Traditional quantum chemistry faced some difficulty with the con- atom can be obtained by integrating the electronic density function cept of “an atom within the context of a molecule”, i.e., neither the over the whole basin of attraction of that atom. Similarly, integration molecular wave function nor the electron density function computed of the electron density function over the interatomic surface yields from the latter yield a direct perception of “atoms” or of such age- a physically sound measure of the bond order between the involved honoured and incredibly important and fruitful chemical ideas as atoms. Importantly, QT-AIM properties of an atom in a molecule are “electron pairs” (bonding as well as lone pairs). It was the outstand- derived from the electron density function (which is obtainable either ing work of Richard WF Bader and his co-workers over decades, by quantum chemistry or by X-ray diffraction experiments) and are excellently summarized in [18], that paved the way for a physically not, in contrast to other quantum chemical techniques, estimated by correct and unique quantum mechanical description of “atoms in more or less arbitrary partitioning schemes between atoms applied molecules” and their properties. Briefly, an atom within the context to molecular orbitals (which are not “observables” in a strict sense). of a molecular system is defined in QT-AIM on the basis of a topologi- QT-AIM also emphasizes the importance of the so-called Lapla- Δ ρ cal analysis of the gradient vector field associated with the electron cian ( ), which is obtained by computing, at each point of space, density function ρ(x, y, z), a scalar function in physical space which is the sum of the diagonal elements of the diagonalized Hessian matrix: an “observable” in the strict sense of quantum mechanics. The major topological feature of this function is that its local maximum values occur at the nuclear positions. All gradient paths of the associated gradient vector field ∇ρ(x, y, z) (the “nabla” operator ∇ is defined as: 3 4 4a 5 6 RCP ∂∂ ∂ (1) BCP ∇= ij++k. 8 ∂∂∂ 2 1 8a 7 xyz ACP with unit vectors i , j , and k ), with very few and special excep- tions, are “attracted” by these maximum positions where, of course, the gradient vectors become zero. Moreover, besides the nuclear posi- tions (atomic critical points), there are also other “critical points” at which the gradient vector vanishes ( ∇=ρ 0 ). The true nature of such a critical point is determined by the behavior of the tensor ∇∇ρ lead- ing to the so-called “Hessian matrix” of the nine possible second derivatives of ρ. The latter can be diagonalized and their “eigenval- ues” λ1, λ2 and λ3 can be determined. In 3D space, four types of critical points can be distinguished and characterized as pair (rank, signa- ture), according to their rank (the number of the non-zero “curva- Isodensity line tures”, i.e., the non-zero second derivatives) and signature (the sum Gradient path of the signs of the eigenvalues): –– (3, -3): atomic critical points (ACP): local maximum points of ρ (three negative curvatures) –– (3, -1): bond critical points (BCP): saddle points between ACP (two negative curvatures, one positive) –– (3, +1): ring critical points (RCP): saddle points characteristic for ring system (one negative, two positive curvatures) –– (3, +3): cage critical points (CCP): local minimum points, characteristic for caged molecules (three positive curvatures). Figure 1 Chemical formulae (left column) and plots of the electron density as well as the gradient paths (right column) of neutral (top), Each gradient path originates or terminates either at a critical point, cationic (middle) and anionic (bottom) pterin. The formula for neutral or at infinity. There are “special” gradient paths; for example, those pterin also shows the conventional numbering of the ring atoms. originating at a BCP and terminating at the two neighboring ACPs. “Normal” gradient paths are shown as thin lines perpendicular to the Their entirety defines the framework of the chemical bonds of a mol- isodensity lines and are coloured according to their respective atoms ecule. Other special gradient paths originate at infinity and terminate (red, oxygen; blue, nitrogen; dark gray, carbon; light gray, hydrogen). at one BCP, or they connect an RCP with a BCP; in their entirety, these “Special” paths such as bond paths (connecting ACP and BCP) and paths define the interatomic surfaces. ring paths (connecting BCP and RCP) are shown as thick red lines. The In QT-AIM, the topological analysis of ρ(x, y, z) provides a means outermost isodensity contour is at 0.001 a.u. Other lines are at 0.002, of partitioning the physical space of a molecule into non-overlapping 0.004, 0.008, 0.02, 0.04, 0.08 … a.u. of electron density. domains (“basins of attraction”) which consist of the entirety of all ACP, atomic critical points (larger dots coloured according to the gradient paths terminating at one specific ACP, i.e., at one specific respective atom); BCP, bond critical points (red dots); RCP, ring criti- nucleus. The surfaces between adjacent basins of attraction are cal points (yellow dots). Reibnegger: Electronic structures of pterin and its ions 43

∂∂∂222ρρρ not strictly planar in a true minimum geometry (the two hydrogen ∆=ρλ++=+λλ+ (2) () 222 123 atoms are slightly bent off the molecular plane). In contrast, in the ∂∂∂xyz cationic form, even when starting with a non-planar geometry, the a scalar field which is useful for visualizing the local concentration optimum geometry obtained is strictly planar; obviously a result of (Δ(ρ) < 0) or depletion of electron density (Δ(ρ) > 0) thus providing the positive charge, the delocalization of the lone pair at the nitrogen chemically meaningful information regarding chemical bonds and/ atom is substantially stronger, thus favouring the planar structure. or nonbonding electron pairs. All results shown in this paper refer to the true minimum energy geometries according to frequency analysis. The remaining computations of the final electronic energy, the molecular wave function, the electron density distribution, the elec- Computational strategy and computer trostatic potential (ESP), and the atomic partial charges and bond software orders according to QT-AIM, for each structure were done using G09W software at the B3LYP/6–311+G(2d,p) level of theory. As shown Of the many possible tautomeric structures of neutral, cationic and in [20], the B3LYP/6–311+G(2d,p)//6–31G(d) level of theory yields anionic pterin, I choose analogous structures according to the mini- quite accurate results while at the same time being computationally mum energy tautomers of 6-methyl-pterin [12–14]. (Note: In [12, 13] feasible for medium-sized molecules as well. The choice of a rela- 6-methyl-pterin erroneously is designated as “pterin”.) For each of the tively extended basis set including polarization and diffuse functions three studied structures, a reasonable starting geometry is obtained for the final computations is motivated by the aim to also get reliable by Avogadro software [19]. These structures are then employed as results for the anionic form of pterin. Notably, all quantum chemical input geometries for a geometry optimization at the B3LYP/6–31G(d) computations were performed in the gas phase as well as in solu- level of theory, using the GAUSSIAN suite of quantum chemistry pro- tion phase. In this work, the SMD model [21] is employed. The SMD grams (Gaussian G09W, version 9.5, Gaussian Inc., Pittsburgh, PA, model is a continuum solvation model based on quantum mechani- USA). In order to ensure that the geometries found are indeed mini- cal charge density of a solute molecule interacting with a continuum mum energy structures, a frequency calculation is then performed description of the solvent. Full electron density is employed without at the same level of theory. Notably, when strictly planar starting defining partial atomic charges. The model is universally applicable geometries are used, in the case of neutral and anionic pterin, the to charged or uncharged solute molecules in any solvent for which first of these two steps indeed yields planar optimized structures a few key descriptors such as the dielectric constant, the refrac- which, however, by the second step are recognized as transition tive index, the bulk surface tension and the acidity and basicity states. The frequency analysis reveals that the amino group at C2 is parameters are known.

Figure 2 Molecular graph for neutral pterin and visualizations of selected atomic basins of attraction of oxygen (left top; red), nitrogens (left bottom; blue), carbons (right top; black) and hydrogens (right bottom; light grey). For clarity, only selected carbons are shown. 44 Reibnegger: Electronic structures of pterin and its ions

-1.184

0.463 1.292 -0.986 0.409 0.096 -1.025 0.444

0.445 1.290 0.461 -1.039 0.785 -1.011 -0.987 0.100 0.446

-1.140

1.323 0.491 -0.953 0.451 0.117 -1.000 0.464 0.487 1.385

-1.033 0.813 0.470 -1.025 -0.963 0.126 0.487 0.497

-1.257

1.218 -1.008 0.391 -1.053 0.078

0.413 0.408 1.194

0.441 -1.037 0.774 -1.043 -1.008 0.082 0.408

-0.12 +0.75

Figure 3 QT-AIM atomic partial charges (left column) and visualizations of the electron density functions and the ESP of neutral (top), cationic (middle) and anionic (bottom) pterin (right column). The molecules are represented by the isodensity surfaces at 0.10 a.u. of elec- tron density function, coloured according to the local ESP (for color code see bottom of the Figure). Blue ESP contours: negative ESP from –0.01 a.u. (outermost contour) in steps decreasing in –0.01 a.u. steps. Red ESP contours: positive ESP from +0.01 a.u. (outermost contour) increasing in +0.01 a.u. steps. For these plots, electron density functions and ESP functions are evaluated by program G09W using regular 192 × 192 × 192 cubes surrounding the molecular structures. Reibnegger: Electronic structures of pterin and its ions 45

In-depth QT-AIM analysis (computation of the critical points Table 1 Comparison of atomic partial charges obtained by different of the electron density function as well as the molecular graph and methods at B3LYP/6–311+G(2d,p) level of theory (see also Figure 3). the gradient paths) and visualization of these results as well as of the atomic basins of attraction is done using the programs AIM2000 Atom Mulliken Natural QT-AIM version 2.0 (Innovative Software, F. Biegler-König, J. Schönbohm, charge charge charge Bielefeld, Germany) and AIMStudio Version 13.11.04 Professional (TK N –0.627 –0.613 –1.011 Gristmill Software, Todd A. Keith, Overland Park, KS, USA). These 1 C 0.548 0.659 1.290 programs are also used to verify the QT-AIM charges obtained with 2 N –0.468 –0.598 –1.025 G09W. Finally, visualizations of the electron density function, the 3 C 0.653 0.679 1.292 Laplacian and the ESP of the molecules are done using AVS Express 4 5.3 software (Advanced Visual Systems Inc., Waltham, MA, USA). O –0.648 –0.692 –1.184 C4a 0.215 0.024 0.409

N5 –0.391 –0.408 –0.986

C6 –0.031 0.001 0.444

C7 0.155 0.069 0.461 N –0.398 –0.474 –0.987 Results 8 C8a 0.195 0.381 0.785 N –0.471 –0.770 –1.039 Figure 1 shows the chemical formulae of the three molecu- 2′ H at N 0.352 0.449 0.463 lar systems studied (left column) and first results of the 3 H at C6 0.151 0.216 0.096 QT-AIM analyses (right column). The electron density H at C7 0.155 0.216 0.100 a functions, computed in the molecular planes, are H at N2′ (N1) 0.305 0.432 0.446 a depicted as isodensity lines. Perpendicular to these, some H at N2′ (N3) 0.305 0.428 0.445 gradient paths are shown. There are three types of critical a The two hydrogens of the NH2-group are oriented towards N1 and points (ACP, BCP and RCP); the “special” gradient paths N3, respectively. ­connecting these are emphasized in red color. The set of the critical points together with these special gradient paths define the “molecular graph”. Notably, the molecu- distribution among the ring atoms occur in the pyrimi- lar graphs are calculated exclusively from the properties dine moiety of the pterin ring system. In contrast, the of the electron density functions; however, as the pictures pyrazine part remains nearly unaffected from addition or demonstrate, they show perfect analogy with the chemi- elimination of a proton. The strongest changes occur – in cal formulae. this order and with the expected direction – at carbon C2,

In order to visualize the 3-dimensional “basins of oxygen and carbon C4 (observe Figure 1, top, for the num- attraction” which one can identify as “atoms” in the bering scheme). sense of QT-AIM, Figure 2 shows selected atoms for the Figure 3 (right column) shows isosurfaces of the elec- case of pterin. Obviously the shapes of these basins of tron density functions of pterin and its cation and anion attraction are quite different for different elements. For mapping, by colors, of the local ESP. Additionally, the ESP example, the strongly electronegative oxygen and nitro- functions obtained in the molecular planes are visualized gen atoms appear more bulky than the positively charged as contour diagrams in order to demonstrate how the mol- carbon atoms, and the hydrogen atoms appear as “caps” ecules would interact with a positive probe charge. Red sitting on their respective bond partners. Importantly, all contour lines (positive ESP) define parts of the molecules’­ atomic properties according to the QT-AIM framework are neighborhoods where a positive probe charge would be obtained by integration over the respective atomic basin repelled, and blue contour lines (negative ESP) denote of attraction. regions where a positive probe charge would be attracted. Thus, by integrating the electron density function of While neutral pterin shows negative ESP along the axis of the atomic basins of attraction, one obtains the atomic the oxygen atom and nitrogen atom N5, and along nitro- partial charges (Figure 3, left column). Notably, charges gen atoms N3 and N8, a pterin cation is surrounded nearly obtained by QT-AIM are generally considerably larger (in exclusively by positive ESP. In contrast, a pterin anion is terms of absolute values) than the charges obtained by surrounded by negative ESP. other quantum chemical techniques, including Mulliken Similarly, Figure 4 (left column) shows the bond as well as natural bond orbital (NBO) population analy- orders obtained by integrating the electron density along ses (Table 1 shows the comparison of the atomic partial the interatomic surfaces and visualizations of the Lapla- charges obtained by the three methods for the atoms of cian functions of the molecules, overlaid on an electron neutral pterin). It is obvious from a comparison of the density isosurface (right column). When comparing the three forms of pterin that the largest changes of the charge cation as well as the anion with the neutral form of pterin, 46 Reibnegger: Electronic structures of pterin and its ions

1.342 1.075 1.059 0.791 1.630 1.170 0.952 1.096 1.228 1.310 1.119 0.798 1.182 1.421 1.183 0.945 1.523 0.794

1.390 1.025 1.039 0.741 1.171 1.604 1.164 0.945 1.341 1.344 1.117 0.758 1.194 1.243 1.021 0.938 0.758 1.473 0.735

1.261

1.257 1.048 1.650 1.171 0.958 1.297 1.146 1.282 1.132 0.826 1.343 1.238 1.174 0.949 0.826 1.528

Figure 4 QT-AIM bond orders (left column) and visualizations of the electron density functions and their Laplacians for neutral (top), cati- onic (middle) and anionic (bottom) pterin (right column). The molecules are represented by the isodensity surfaces at 0.15 a.u. of electron density function (transparent light-blue). Regions of electronic charge depletion (positive Laplacian) are shown as red isosurfaces at an isovalue of 1.0; regions of electronic charge accumulation (negative Laplacian) are shown as yellow isosurfaces at an isovalue of –2.6. For these visualizations, electron density function values are provided by program G09W using regular 192 × 192 × 192 cubes surrounding the molecular structures. The computation of the Laplacian functions is accomplished by the graphical visualization software AVS Express 5.3, acting directly on the data of the electron density cube.

it is obvious that the largest differences are again seen from the cation via neutral pterin to the anion, and for the in the bonding situation of the pyrimidine moiety, i.e., C4–O and the C2–NH2 bond, bond order decreases in that the pyrazine part remains essentially unchanged. The direction. These changes are compatible with the formu- strongest variation occurs along the N1–C2 bond, and, lation of mesomeric resonance structures that are shown interestingly, bond order (and, thus, the partial double in Figure 5. In the cationic form, strong delocalization of bond character) decreases for the cation as well as for the positive charge between the nitrogen atoms bonded the anion, when compared to neutral pterin. The second- to C2 is found, thus increasing bond strengths along the largest changes occur along the C2–N3 bond, where bond C2–N3 and the C2–NH2 bonds and decreasing bond strength order increases for both the cation and the anion. For the along the N1–C2 bond. In the anion, delocalization of the bonds between N3–C4 and N1–C8a, bond order increases extra negative charge is observed mainly from N3 to the Reibnegger: Electronic structures of pterin and its ions 47

A Particularly for the more electropositive carbon atoms, at the chosen isovalue of –2.6 “holes” in the yellow sur- faces at the atomic positions allow a glance at the “core” regions of electronic charge depletion (in red) which mark the “gap” in electronic density between the core and the valence regions of the respective atoms. Inside these core depletion regions one finds even smaller yellow regions of the core regions of electronic charge accumulation, cor- responding in principle to the 1s2 electrons. All results shown above are obtained using the SMD model simulating solution of the molecules in water. As stated in the Methods section, all molecules were also treated by the same quantum chemical procedures in the gas phase. There are no large differences in the QT-AIM B atomic charges, which may be best summarized by the molecular dipole moments. While for neutral pterin, sol- vation caused an increase of the dipole moment from 1.555 to 1.678 D (debye), for cationic pterin (1.656 in gas phase vs. 1.633 D in solution) and for anionic pterin (1.240 vs. 1.226 D, respectively) solvation in water does not alter the polarisation markedly. In contrast, the solvation enthalpy

change (ΔHsolv) is markedly larger in absolute size for the

two charged species: ΔHsolv for neutral pterin is –25.2 kcal/ mol; for cationic pterin, – 76.7 kcal/mol; and for anionic pterin, –69.1 kcal/mol. Figure 5 “Traditional” interpretation of the results shown in Figures 3 and 4 in terms of mesomeric resonance structures for the pterin cation (top) and anion (bottom). Discussion

In this paper I analyse the electronic structure of neutral as oxygen atom, thus increasing the aromatic character of well as cationic and anionic pterin using quantum chem- the pyrimidine part of the system. istry at the Density Functional level of theory, combined These changes of the bond orders are nicely reflected with – to the best of my knowledge – the first application by the Laplacian functions also shown in Figure 4. As of QT-AIM analysis in the field of pteridine research. In an example, at the chosen isovalue of –2.6 a.u. the nega- order to get a reliable description of the electronic struc- tive charge concentration (yellow isosurfaces) in neutral ture, I employ geometry optimization with the 6–31G(d) pterin is interrupted along the C2-N3 bond, and a contigu- basis set and computation of the final wave function with ous isosurface is found along this bond in the cation as the extended 6–311+G(2d,p) basis set. The use of polariza- well as in the anion. On the other hand, in the cation, tion functions as well as diffuse functions is mainly dic- an interruption of this isosurface is seen along the N1-C8a tated by the desire to also get a good representation of the bond, while in the anion a nearly contiguous charge con- electron-rich anion of pterin. centration in the whole pyrimidine moiety is found. Only One might criticize that I have not considered all the between C4 and C4a is there a gap in the respective isosur- possible tautomeric forms of neutral, cationic and anionic face. In contrast, the negative charge density along the pterin. However, here I aim to demonstrate the basic use-

C2-NH2 bond is markedly “thinner” in the anion, pointing fulness of QT-AIM for the analysis of the electronic struc- to a decrease of the delocalization of the lone pair at the tures of pteridines in general, and I have chosen starting

NH2 nitrogen atom. In accordance with the atomic partial molecular geometries which are in accordance with charges as well as the bond orders, in the pyrazine ring, in “chemical” knowledge as well as with recent results of all cases a contiguous isosurface is observed, demonstrat- quantum chemical calculations on 6-methyl pterin using ing its rather undisturbed aromatic character in all three density functional level of theory, albeit at smaller basis forms of the molecule. set sizes [12–14]. 48 Reibnegger: Electronic structures of pterin and its ions

QT-AIM in combination with high-level ab initio quantum 5. Uchimaru T, Tsuzuki S, Tanabe K, Benkovic SJ, Furukawa K, chemistry enables detailed insight into the electronic struc- Taira K. Computational studies on pterins and speculations on the mechanism of action of dihydrofolate reductase. Biochem ture and the bonding situation of neutral as well as charged Biophys Res Commun 1989;161:64–8. forms of pterin. In particular, the changes occurring when 6. Katoh S, Sueoka T, Kurihara T. Computer studies on the ste- adding or eliminating a proton are well described and are in reostructure and quantum chemical properties of 6-pyruvoyl excellent accordance with conventional chemical wisdom tetrahydropterin, the key intermediate of and concepts. The particular charm of QT-AIM is the ready biosynthesis. Biochem Biophys Res Commun 1991;176:52–8. transformation of more abstract quantum chemical con- 7. Reibnegger G, Denny BJ, Wachter H. Ab initio quantum chemical calculations on the stability of different tautomers of 6- and structs, such as molecular orbitals, into a picture of the bond 7-phenacetyl pterins. Pteridines 1993;4:23–6. structures which is much more similar to traditional chemical 8. Estelberger W, Fuchs D, Murr C, Wachter H, Reibnegger G. Con- concepts such as bonding or non-bonding localized electron formational investigation of the (6R,1′R,2′S-)-5,6,7,8- pairs according to Lewis’ classical model [22]. In the particu- tetrahydrobiopterin. BBA 1995;1249:23–8. lar investigated forms of pterin, these classical ideas can be 9. Reibnegger G, Horejsi R, Oettl K, Mlekusch W. Electronic charge density and electrostatic potential of pterin, 7,8-dihydropterin nicely identified, employing – in a physically correct way – and 5,6,7,8-tetrahydropterin – an ab initio quantum chemical only the topological properties of the electron density func- study. Pteridines 1998;9:85–90. tion which by itself is an observable in the strict sense of 10. Reibnegger G, Pauschenwein J, Werner ER. Electronic structure quantum mechanics. of tetrahydropteridine derivatives. Pteridines 2000;10:91–4. The present results are encouraging with regards to 11. Jaramillo P, Coutinho K, Canuto S. Continuum, discrete and further work on interesting aspects of pteridine chemis- explicit solvation models for describing the low-lying absorp- tion spectrum of the pterin acid in aqueous environment. Int J try and biochemistry. Theoretical studies of this type may Quantum Chem 2010;110:2371–7. provide deeper insight into, for instance, the field of spec- 12. Soniat M, Martin CB. Theoretical study on the relative energies troscopic properties of pteridines or even the quite com- of neutral pterin tautomers. Pteridines 2008;19:120–4. plicated and by no means fully understood interactions 13. Soniat M, Martin CB. Theoretical study on the relative energies of various pteridine derivatives with free radicals – a topic of anionic pterin tautomers. Pteridines 2009;20:124–9. 14. Soniat M, Martin CB. Theoretical study on the relative energies most relevant to the plethora of biological roles and func- of cationic pterin tautomers. Pteridines, in press. tions of these fascinating molecules. 15. Ferré J, Jacobson KB, Pfleiderer W. Proposal towards a normali- zation of pteridine nomenclature. Pteridines 1990;2:129–32. 16. Becke AD. A new mixing of Hartree-Fock and local density-­ functional theories. J Chem Phys 1993;98:1372–7. 17. Lee C, Yang W, Parr RG. Development of the Colle-Salvetti References correlation-energy formula into a functional of the electron density. Phys Rev B 1988;37:785–9. 1. Bieri J, Geiger RE. Über Pterinchemie. 51. Mitteilung. CNDO- 18. Bader RW. Atoms in molecules: a quantum theory. Oxford, UK: Rechnungen an pterin, 6,7-dimethyl-7,8-dihydropterin and Oxford University Press, 1990. 5-formyl-6,7-dimethyl-5,6,7,8-tetrahydropterin. Helv Chim Acta 19. Hanwell MD, Curtis DE. Lonie DC, Vandermeersch T, Zurek E, 1975;58:1201–5. Hutchison GR. Avogadro: an advanced semantic chemical 2. Gready JE. The value of the π-bond order – bond length relation- editor, visualization and analysis platform. J Cheminformatics ship in geometry prediction and chemical bonding interpretation. 2012;4:17. http://www.jcheminf.com/content/4/1/17. J Comput Chem 1984;5:411–26. 20. Foresman JB, Frisch AE. Exploring chemistry with electronic 3. Gready JE. Theoretical studies on pteridines. 2. Geometries, structure methods, 2nd Ed. Pittsburgh, PA: Gaussian Inc., 1996. tautomers, ionization and reduction energies of substrates 21. Marenich AV, Cramer CJ, Truhlar DG. Universal solvation model and inhibitors of dihydrofolate reductase. J Comput Chem based on solute electron density and on a continuum model of 1985;6:377–400. the solvent defined by the bulk dielectric constant and atomic 4. Gready JE. Analysis of the inter-ring coupling effects in surface tensions. J Phys Chem B 2009;113:6378–96. ­N-heterobicyclic π-systems using a structural definition of 22. Lewis GN. The atom and the molecule. J Am Chem Soc ­aromaticity. Int J Quant Chem 1987;31:369–82. 1916;38:762–85.