Effects of combination modes of favorable growth unit of Al(OH)3 crystals precipitating on Van der Waals and chemical bond force
WU Zheng-ping(吴争平), CHEN Qi-yuan(陈启元), YIN Zhou-lan(尹周澜), LI Jie(李 洁)
(School of Chemistry and Chemical Engineering, Central South University,Changsha 410083, China)
Abstract: The dipole moment, total energy, atomic charge, orbital population and orbital energy of four representative combination models of the favorable growth unit Al6(OH)18(H2O)6 of Al(OH)3 crystals precipitating are calculated by ab initio at RHF/STO-3G, RHF/3-21G, RHF/6-31G levels and DFT at RB3LYP/STO-3G, RB3LYP/3-21G, RB3LYP/6-31G levels with Dipole & Sphere solvent model. The effect of various combination models on Van der Waals force is analyzed using dipole moment and molecular radius, and that on chemical bond force is analyzed using total energy, orbital population and orbital energy.
Key words: gibbsite; combination; ab initio; DFT; chemical bond force; Van der Waals force CLC number: O641.12
Document code: A
1 INTRODUCTION
A lot of studies on the crystallization of Al(OH)3 from supersaturated sodium aluminate solution were carried out, but there are not many reports on the crystal strength[1-3]. The interrelated research indicated that strength of alumina was mainly related to strength of Al(OH)3 precipitated from sodium aluminate solution[4, 5]. The nucleation, agglomeration and growth of Al(OH)3 result in the combination of growth unit. Li et al[6-13] studied the structural characteristics of supersaturated sodium aluminate solution and growth units of Al(OH)3 systematically. They brought forward and proved that the growth units of gibbsite were Al(OH)3-6 and Al(OH)3-6 polymer and Al6(OH)18(H2O)6 with hexagon face shape was the favorable growth unit.
On the base of the investigation by Li et al[6-13], the ab intio and DFT analyses on the structure of the favorable growth unit Al6(OH)18-(H2O)6 were studied[14]. In this paper, effect of the combination mode of the favorable growth unit Al6(OH)18(H2O)6 on the Van der Waals and chemical bond force will be carried on.
2 CALCULATION METHODS AND THEORY
Based on ab initio Self Consistent Field molecular orbital theory and Density Function Theory method, the total energy, dipole moment, orbital population and atomic charge are calculated at STO-3G, 3-21G, 6-31G levels with Dipole & Sphere solvent model. Density Function Theory method adopts B3LYP Becke model with three parameters[15-17]. Calculations are performed at C2 workstation in Central South University by Gaussian98 program.
Based on the Molecular Mechanics Force Field, the geometry optimization is implemented by MM+ method using conjugation gradient Polak-Ribiere algorithm and the terminal condition is RMS gradient of 0.42kJ/mol or the maximum cycles of 1800.
Van der Waals force consists of action of inter moleculae. Although the force is quite infirm and the bond energy is very low, the physical properties such as boiling point, melting point, surface tension and viscosity, are influenced directly by this force. The orientation, abduction and dispersion forces are three kinds of Van der Waals force. Total Van der Waals action energy is[18]:
where 
is the orientation force (intermolecular average potential energy), 
is the abduction force (intermolecular abduction action energy), 
is the dispersion force (intermolecular attractable energy), μ is dipole moment, R is intermolecular distance, k is Boltzmann constant, T is thermodynamics temperature, α is polarization rate, and I is absolute value of ionization potential.
For the same molecular, total Van der Waals action energy is
In this paper, two Al6(OH)18(H2O)6 units with four kinds of typical combination modes are studied, and the two Al6(OH)18(H2O)6 units are regarded as a large molecular system. Using parameters of dipole moment and molecular radius, the effect of various combination modes on Van der Waals force is analyzed.
3 COMBINATION MODES OF Al6(OH)18(H2O)6 AND CALCULATION MODEL
Four kinds of typical combination modes of the favorable growth unit Al6(OH)18(H2O)6 with hexagon face shape are designed. Regarding six Al as structure framework, there are side-uprightness-combination-A, side-face-combination-B, obverse-uprightness-combination-C and obverse-face-combination-D (Fig.1). Fig.2 shows the calculation models of four typical combination modes.
4 CALCULATION RESULTS AND DISCUSSION
4.1 Dipole moment and molecular radius
The molecular radius is calculated using Monte-Carlo method by ab initio and DFT at RHF/STO-3G, RHF/3-21G, RHF/6-31G, RB3LYP/STO-3G, RB3LYP/3-21G, RB3LYP/6-31G levels. Fig.3 shows the calculated molecular radius. By the same methods of ab initio and DFT, using Self Consistent Field Onsager model, the dipole moment is calculated in the reaction field with dielectric constant of 78.39. Fig.4 shows the calculated dipole moment.
Based on Equation(2), the orientation, inducement, and dispersion energies are proportional to quartic of dipole moment, square of polarization rate and dipole moment, square of polarization rate, respectively. The polarization rate is in direct proportion to cube of average molecular radius[18]. The molecular radii of four typical combination modes are nearly equal, and the difference is very small when calculating at 6-31G that is the most accurate level compared with STO-3G and 3-21G levels. Therefore, the difference of four systems polarization rate is so small that it could be supposed that the polarization rate and intermolecular distance are equal approximately. Under this con-
Fig.1 Sketch map of four combination modes of Al6(OH)18(H2O)6
Fig.2 Calculation models for four combination modes of Al6(OH)18(H2O)6
Fig.3 Calculation results of molecular radius
Fig.4 Calculation results of dipole moment
dition, the most effective factor on Van der Waals force is dipole moment. In other word, if the dipole moment becomes higher and higher, the Van der Waals force will be bigger and bigger, and this will be favorable to the combination of the growth units of gibbsite. From Fig.4, it can be seen that the numerical relation of dipole moment is D>C>B>A, and Van der Waals force of the obverse-face combination mode may be the strongest and firmest.
4.2 Total energy
Using Self Consistent Field Onsager model with dielectric constant of 78.39, total energy is calculated by ab initio and DFT methods. The calculation results are listed in Table 1. Total energy of obverse-face-combination-D mode is relatively lower, and from the viewpoint of energy, this combination mode exhibits more possibility than the other combination modes.
4.3 Orbital energy
Energies of 300 bonding molecular orbits and 108 antibonding molecular orbits are acquired. The 300th orbit is HUMO and the 301st is LUMO. The energies of some frontier molecular orbits of the four combination modes are listed in Table 2. It can be seen that energy difference of LUMO and HUMO of the obverse-face-combination-D mode is larger, and the bonding is firmer than the other combination modes.
In addition, the difference of the results calculated by ab initio and DFT methods is very dis-tinct. Energy calculated by DFT is higher than
Table 1 Calculation results of total energy
Table 2 Calculation results of orbital energy10-18J
that by ab initio. The reason for this is that on the base of Non-Relativity, Oppenheimer and Orbital Approximations, ab intio is a method of Hartree-Fock equation by Self Consistent Field, never-theless, DFT is to use the electronic density to gain the properties of system.
4.4 Analysis of orbital population
Orbital populations of 708 bonding and antibonding orbits of four systems are calculated by ab initio and DFT methods at RHF/STO-3G, RHF/3-21G, RHF/6-31G, RB3LYP/STO-3G, RB3LYP/3-21G, RB3LYP/6-31G levels using Self Consistent Field Onsager model with dielectric constant of 78.39. Some orbital populations calculated at RHF/6-31G and RB3LYP/6-31G levels and the average populations of 3PX, 3PY, 3PZ orbits are listed in Table 3. It can be seen that except for Al 7 and Al 8, the numerical relation of 3S or-bital population of the other ten Al is D>C>A>
Table 3 Calculation results of some orbital populations
B, and 3PX, 3PY, 3PZ orbital average population of the obverse-face-combination-D is the largest. The calculation results show that the bonding of the obverse-face-combination-D mode is firmer than the other combination modes.
The calculation results of total energy, atomic charge, orbital population and orbital energy all accord with the prediction about bonding orientation of the favorable growth unit Al6(OH)18-(H2O)6 in Ref.[14].
5 CONCLUSIONS
1) The calculation results of dipole moment and molecular radius speculate that Van der Waals force of the obverse-face combination mode is the strongest and the firmest, and this combination mode seems more possible than the others.
2) The calculation results of total energy, orbital population and orbital energy indicate that the bonding of the obverse-face combination mode is the firmest because of the lower total energy, the largest energy difference of LUMO and HUMO and the higher orbital average populations.
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(Edited by YANG Bing)
Foundation item: Project(50374078) supported by the National Natural Science Foundation of China; Project(G1999064902) supported by the National Basic Research Program of China
Received date: 2004-04-20; Accepted date:2004-12-30
Correspondence: WU Zheng-ping, PhD; Tel: + 86-731-8877364-315; E-mail: wzp@mail.csu.edu.cn
