4E05
電子状態シミュレーションによる分子形状解析（熊本大院・自然科学）杉本 学
Introduction: Molecular recognition is a process of forming a specific pair of molecules. This process is a
key step in e.g. biological ligand-receptor binding. The driving force to yield the complex is due tointermolecular interactions. Although they arise from quantum mechanical nature of electrons in molecules,
empirical potential energy functions are frequently employed for large systems where positions of atoms
are their variables.
When a docking geometry is computationally optimized or is experimentally elucidated, the easiest wayof quantitative interpretation would be to introduce the concept of molecular shape. Usually the shape isdefined by van der Waals radii of atoms. It is further used
to define molecular volume, which can be a good measureinvestigating chemical nature of pores in porous materials.
Conceptual importance of molecular shape is wellknown in biochemistry: the lock-and-key model is afundamental model for understanding ligand-receptor
interactions. A simple but fundamentally importantquestion about molecular shape is “how the quantum
mechanical intermolecular interactions can be modeled bymolecular shape”. This issue seems important because theconcept of molecular shape can be regarded as one of thecoarse-grained pictures of complicated quantum
mechanical interactions. In this paper, we develop a
computational scheme of defining molecular shape withthe use of ab initio electronic structure calculations. Our
objectives are to investigate chemically importantFigure 1: Illustration of the computational
topological features of molecular shapes and tosurface-probing method.
characterize them quantitatively.
Computational Algorithm and Method: Molecular shape can be regarded as one of the molecularproperties. It is well known that an electronic property such as electric dipole moment, electricsusceptibility, etc. is defined as a response to an applied external field. For a given perturbation (λ), theenergy is expressed by the Taylor series such as⎡ ∂E ⎤1 N N ⎡ ∂2E ⎤E ( λ1 , λ2 ," , λN ) = E ( 0 ) + ∑ ⎢⎥ λi λ j + ""⎥ λi + ∑∑ ⎢2! i =1 j =1 ⎣⎢ ∂λi ∂λ j ⎦⎥i =1 ⎣ ∂λi ⎦ λ = 0λ =0N(1)where E(0) is the energy without perturbation. For example, dipole moment corresponds to the first order
response of molecular energy to the electric perturbation. Therefore a consistent definition of molecularshape would be to consider energy response to an appropriate perturbation.
Here we propose to define molecular shape by computing quantum mechanical energy for interaction
between a target molecule and a probe atom (see Fig. 1). From the interest in biological systems andchemistries in aqueous solution, we focus on interaction related to the hydrogen bond. This is done bychoosing H+ and O2- as probe atoms. For a target molecule fixed in the 3D space, electronic-structure
calculations are repeatedly carried out for a probe atom on each grid in the same space. By displacing it in
the predefined 3D box, energy mapping can be achieved. By extracting an isoenergy contour for an
appropriate threshold, we can obtain a surface defining molecular shape. The present method can be called“the computational surface-probing method”.

In the present study, interaction energies were calculated by using the MP2 method with the cc-pVDZ
basis set. Geometries of target molecules (H2O, CO2 and C2H2 in this paper) were firstly optimized, andthen calculations were repeated for the ”target + probe” system where a probe atom was displaced on theuniform 3D grids. The 2 dimensional contours shown below were obtained for the 50×50 grids on themolecular plane of each target. As a probe, we considered H+ and F-. The latter ion was used as analternative to O2-. This is because convergence difficulty was encountered in SCF calculations in case of theO2- probing. The energy contour map was drawn by calculating binding energies (stabilization energies)
where the separated limit was referred to.
Results and Discussion: Fig. 2 shows isoenergy contour
map of H2O. The result indicates that the space can bedivided into two parts: one is a region of positive energy
corresponding to repulsive interaction. It roughly
corresponds to a while region in Fig. 2. This region may
be called “repulsive shape”. It may be approximately
represented as superposition of circles centered on atoms
when H+ is used as a probe: three circles on O and two HFigure 2: Isoenergy contour of H2O probed
atoms can be distinguished. For the F- probe, theby the H+ (left) and F- (right) ions.
repulsive shape is an ellipsoid rather than a circle. The
area of the repulsive region is larger for the F- probe than for the H+ probe. This may be interpreted asreflecting a difference between ionic radii of H+ and F-.
Another part of the energy contour is a region of negative energy (the colored region). This may becalled “attractive shape” of the target molecule. An interesting feature of the attractive shape of H2O isexistence of an interaction site near the oxygen atom. From its topological feature, it appears assignable tothe oxygen lone pair orbital. This supports that, when interaction sites are determined for deriving empiricalpotential energy functions, they should be centered on, at least, three atoms (O and two H) and a site
corresponding to a lone pair. In the attractive region probed by F-, we see two energy minima near thehydrogen atoms. This is reasonable to represent an interaction in hydrogen bonding between theelectropositive (H) and electronegative atoms (F).
Fig. 3 shows contour maps of CO2. Similar to H2O, we see interaction sites around two oxygen atoms
for the H+ probe. Reflecting differences of chemical interaction between the C-H+ and O-H+ pairs, the radiiof the carbon and oxygen atoms are different. The energy contour probed by F- indicates that CO2 has noclosed energy minima. Thus its shape consists of only repulsive region.
Fig. 4 depicts energy contours for acetylene. When it is probed by H+, energy minima appear on bothsides of molecular axis. This seems to be related to the π orbital of acetylene. This feature implies that
topological shape of a chemically important orbital can be extracted by the present computationalprocedure. For the F-probed contour, we see two interaction sites near two hydrogen atoms although theenergy stabilization is appreciably small in comparison with that obtained for the H-probed contour.
As seen in the above examples, it is evident that molecular shapes probed by ions show interesting
topological features of molecules and look chemically important. The contour is nothing but a potential
energy surface, which has clear physical meaning and quantitatively reflects chemical interactions: locationand depth of energy minima directly reflect the nature of the ion-molecule interaction. For furtherapplications, numerical analyses of molecular shapes need to be developed.

Figure 3: Isoenergy contour of CO2 probed by the H+(left) and F- (right) ions.

Figure 4: Isoenergy contour of C2H2 probed by theH+ (left) and F- (right) ions.