1P065

The relations of bond length and force constant with the potential acting on
an electron in a molecule
Dong-Xia Zhao, Li-Dong Gong, Zhong-Zhi Yang*
Department of Chemistry, Liaoning Normal University, Dalian 116029, P. R. China

The potential acting on an electron in a molecule (PAEM) is defined as the interactionenergy of a local electron with the rest particles, i.e. all nuclei and remaining electrons. The
substantial difference of the PAEM from the molecular electrostatic potential (MEP) is
analyzed and discussed. PAEM has been introduced and used in the previous studies,1-4 forG
describing and defining a kind of molecular intrinsic characteristic contour. PAEM at r1 in amolecule can be expressed as

G GZAρ 2 (r1 , r2 ) GG1
V (r1 ) = −∑ G G + G ∫ G G dr2
ρ (r1 ) r1 − r2
A r1 − RAGG= Vne (r1 ) + Vee (r1 )(1)

The SDCI calculations were performed by the MELD5 program package developed byDavidson et al. and a program of our own, and then the PAEM was obtained with the near
Hartree-Fock quality Gaussian-type orbital basis sets6. The PAEMs for a series of diatomic
halides, HX, LiX, NaX and X2 (X=F, Cl, Br, and I), as well as H2O and NH3 and someorganic molecules have been studied. The 3D graph of the PAEM for HBr on XY plane(Molecular Plane) is depicted in Figure 1.
We have illustrated and compared the 3D topological graphs of the PAEMs. All these 3Dgraphs of the PAEMs are topologically similar along the chemical bond axes, which are
divided into three regions, the near-nucleus, bond and out bond regions. However, it should
be noted that we can distinguish them from each other by two points: one is the well width
which mainly reflects the nuclear charge, and the other is the height of the PAEM barrier
1along the bond axis around the bond region, or equivalently the depth Dpb of the PAEM curveon the plane that passes through the saddle point and perpendicular to the bond axis. We havefound that the Dpb inherently correlates with the bond length and force constant, which are
two fundamental bond properties characterizing the strength of a chemical bond. Figure 2
shows the linear relationship between the Dpb and bond lengths for H-X (X=F, Cl, Br, I)
chemical bond. Thus, it is demonstrated that the PAEM value Dpb at the saddle point
characterizes the strength of the chemical bond.
2.8

HX(X=F, Cl, Br and I)PAEM=-0.8048Re+3.9756

2.6

2

R =0.9854
2.4

Dpb(hartree)

2.2
2.0
1.8
1.6
1.4
1.6

2.0

2.4

2.8

3.2

Bond Length (Re)(a.u.)

Figure 1 The three-dimensional graph of the
Figure 2. The linear relationship between the
PAEM for HBr on XY plane (Molecular Plane).
Dpb and bond lengths for H-X (X=F,
Cl, Br, I) chemical bond

Reference
(1).
(2).
(3).
(4).
(5).
(6).

Yang, Z. Z.; Davidson, E. R. Int. J. Quantum Chem. 1996, 62, 47.
Yang, Z. Z.; Zhao, D. X.; Chem. Phys. Letters 1998, 292, 387.
Yang, Z. Z.; Zhao, D. X.; Wu, Y. J. Chem. Phys. 2004, 121, 3452.
Yang, Z. Z.; Gong, L. D.; Zhao, D. X.; Zhang, M. B. J. Comput. Chem. 2005, 26, 35.
Davidson, E. R. MELD Program, MELD Program Description in MOTECC; ESCOM: New York,
1990.
Partridge, H. J. J Chem. Phys. 1987, 87, 6643.

The authors are very grateful to Professor E. R. Davidson for providing us the MELD package andother kinds of helps. The research is supported by the grants (No.: 20403007 and 20073018) from National
Science Foundation of China.

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