Pteridines 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]pyrimidine, 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 pteridine 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 ∂∂xy∂z 2 1 8a 7 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.