- Email: [email protected]
Orbital sizes and dipole moments in diatomic hydrides
ORBITAL
SIZES AND DIPOLE MOMENTS Peter Department
IN DIATOMIC
POLITZER
of Chemis!q. Louisiana State University Ne2c Orleans. Louisiana. USA Received
HYDRIDES
in Neu* Orleans.
17 July 1967
It is suggested that the dipole moment of AIH (recently calculated) may be anomalous. due to an unusual degree of penetration of the aluminum outer shell by the hydrogen. It is shown that the sizes of the outer shells of Mg, Al, Tl, and Pb deviate from general trends.
The dipole moments of the first- and secondrow diatomic hydrides, AH, have recently been calculated by Cade and Huo, using Hartree-FockRoothaan wave functions [l]. The graphical presentation of these data indicated a certain anomaly, of which one possible interpretation is that the dipole moment of AU3 is slightly less positive than would be expected by analogy to the results for the first-row molecules *. A possible explanation of this discrepancy lies in the anomalously large width of the outer shell of the aluminum atom, which has been pointed out previously [2]. (As a measure of the “wIdthR of the outer shell of an atom is being used the quantity (r - ye), where r and rc are the distances to the maxima of the radial probability distribution functions, 4rrY2$z (Di, corresponding respectively to the outermost occupied orbital of the atom, an 12sor np orbital, and the largest ( ?Z- 1)orbital. These orbital radii have been calculated for all of the atoms by Waber and Cromer, using relativistic self-consistent Dirac-Slater atomic wave functions [3])**. The unusual situation which prevails in the aluminum atom in regard to the width of its outer shell is seen clearly in figs. 1 and 2, in which the sizes of the outer shells of the atoms have been plotted against the positions of the atoms in the periodic table. It is observed that the points for the first, third, and fourth rows form very smooth curves. Dut in the second row there are * The directions
of the dipole moments were defined such that positive values corresponded to A-H+ and negative values to A+H-. ** The atomic wave functions were computed using the Slater approximation [4j for the exchange potentials. I would like to thank Dr.Waber for sending me some unpublished orbital radii.
deviations, at h xd 41, and in the fifth row also, at Tl and Pb”**.
Fig. 1. The widths of the outer shells of the first- and second-row atoms plotted against their positions in the periodic table. The horizonta! axes give the Group numbers of the atoms; all are A Groups. Those for the second-row atoms are given at the top. ***
It was stated in ref. [Zj on the basis of a comparison with Tl and Pb that (r-~c) is anomalously large for Bi. Consideration of the trend in this quantity for all of the fifth-row atoms shows, however, that it is rather TI and Pb which are out of line (see fig. 2). This correction does not in any way alter the ideas or numerical results presented in ref. [Z].
P.POL,ITZ,PR
228
1.7 1.5 1.3 i.l 0.9
i
il
Iii IQ i/
Vr vi1 0
Fig. 2. The widths of the outer shells of the third-. and fifth-row atoms plotted against their pofourth-, sitions in the periodic table. The horizontal axes give the Group numbers of the atoms; all are A Groups. The vertical axis ior the fourth-row atoms is at the right.
It has recently been suggested that the gaseous diatcmic hydrides can be viewed as involving a penetration, to varying extents, of the outer shell of the atom A by the hydrogen atom [2]. In terms of this mode?, the large size of the aluminum outer shell would result in an anomalously large degree of penetration by the hydrogen. This has indeed been observed to occur [2]. A large degree of penetration means that a considerable portion of the outer shell electronic density will be in the region behind the hydrogen -
that is, on the side away from the other atom. This will give a signjficant negative contribution to the dipole moment. Thus, the large outer shell of the aluminum atom, and the consequent anomalous degree of penetration by hydrogen, would be exllected to result in a dipole moment for AlB which is iess positive than would be the case if the size of the outer shell were consistent with the general trend among the second-row atoms. By the same sort ti reasoning, the dipole moment of MgH is probably somewhat more positive than this trend would imply. The analysis of the dipole moment of AlH which has been presented here does not imply any disagreement with tne conclusion of Cade and Huo that in dividing the diatomic hydrides into two groups, BH and AlH should be included with the first group of hydrides (the alkali and alkaline earth metal hydrides) rather than the second. On the contrary, very recent results tend to support, at least partially, this conclusion [5] *.
REFERENCES
’
[1] P. E. Cade and W!F. Huo, J. Chem. Phys. 45 (1966) 1063. [2] P. Politzor, J. Phys. Chem. 70 (1966) 4041. [3] J.T. Waber and D.T. Cromer, J. Chem. Phys. 42 (1965) 4llG and personal communication from J. T. Waber. [+I] J. C. Slatcr, Phys. Rev. 81 (1951) 385. [5] P. Politzer. J. Phys. Chem. 71 (1967)
* An investigation of the relationship between the diatomic hydrides and their positive ions has once more brought out the tendency of the hydrides to fall into two groups. Although there is again some uncertainty regarding the exact boundary between the groups, in terms of the properties studied in this worlc AIH belongs with the hydrides of the elements of the left side of the periodic table.
SIZES AND DIPOLE MOMENTS Peter Department
IN DIATOMIC
POLITZER
of Chemis!q. Louisiana State University Ne2c Orleans. Louisiana. USA Received
HYDRIDES
in Neu* Orleans.
17 July 1967
It is suggested that the dipole moment of AIH (recently calculated) may be anomalous. due to an unusual degree of penetration of the aluminum outer shell by the hydrogen. It is shown that the sizes of the outer shells of Mg, Al, Tl, and Pb deviate from general trends.
The dipole moments of the first- and secondrow diatomic hydrides, AH, have recently been calculated by Cade and Huo, using Hartree-FockRoothaan wave functions [l]. The graphical presentation of these data indicated a certain anomaly, of which one possible interpretation is that the dipole moment of AU3 is slightly less positive than would be expected by analogy to the results for the first-row molecules *. A possible explanation of this discrepancy lies in the anomalously large width of the outer shell of the aluminum atom, which has been pointed out previously [2]. (As a measure of the “wIdthR of the outer shell of an atom is being used the quantity (r - ye), where r and rc are the distances to the maxima of the radial probability distribution functions, 4rrY2$z (Di, corresponding respectively to the outermost occupied orbital of the atom, an 12sor np orbital, and the largest ( ?Z- 1)orbital. These orbital radii have been calculated for all of the atoms by Waber and Cromer, using relativistic self-consistent Dirac-Slater atomic wave functions [3])**. The unusual situation which prevails in the aluminum atom in regard to the width of its outer shell is seen clearly in figs. 1 and 2, in which the sizes of the outer shells of the atoms have been plotted against the positions of the atoms in the periodic table. It is observed that the points for the first, third, and fourth rows form very smooth curves. Dut in the second row there are * The directions
of the dipole moments were defined such that positive values corresponded to A-H+ and negative values to A+H-. ** The atomic wave functions were computed using the Slater approximation [4j for the exchange potentials. I would like to thank Dr.Waber for sending me some unpublished orbital radii.
deviations, at h xd 41, and in the fifth row also, at Tl and Pb”**.
Fig. 1. The widths of the outer shells of the first- and second-row atoms plotted against their positions in the periodic table. The horizonta! axes give the Group numbers of the atoms; all are A Groups. Those for the second-row atoms are given at the top. ***
It was stated in ref. [Zj on the basis of a comparison with Tl and Pb that (r-~c) is anomalously large for Bi. Consideration of the trend in this quantity for all of the fifth-row atoms shows, however, that it is rather TI and Pb which are out of line (see fig. 2). This correction does not in any way alter the ideas or numerical results presented in ref. [Z].
P.POL,ITZ,PR
228
1.7 1.5 1.3 i.l 0.9
i
il
Iii IQ i/
Vr vi1 0
Fig. 2. The widths of the outer shells of the third-. and fifth-row atoms plotted against their pofourth-, sitions in the periodic table. The horizontal axes give the Group numbers of the atoms; all are A Groups. The vertical axis ior the fourth-row atoms is at the right.
It has recently been suggested that the gaseous diatcmic hydrides can be viewed as involving a penetration, to varying extents, of the outer shell of the atom A by the hydrogen atom [2]. In terms of this mode?, the large size of the aluminum outer shell would result in an anomalously large degree of penetration by the hydrogen. This has indeed been observed to occur [2]. A large degree of penetration means that a considerable portion of the outer shell electronic density will be in the region behind the hydrogen -
that is, on the side away from the other atom. This will give a signjficant negative contribution to the dipole moment. Thus, the large outer shell of the aluminum atom, and the consequent anomalous degree of penetration by hydrogen, would be exllected to result in a dipole moment for AlB which is iess positive than would be the case if the size of the outer shell were consistent with the general trend among the second-row atoms. By the same sort ti reasoning, the dipole moment of MgH is probably somewhat more positive than this trend would imply. The analysis of the dipole moment of AlH which has been presented here does not imply any disagreement with tne conclusion of Cade and Huo that in dividing the diatomic hydrides into two groups, BH and AlH should be included with the first group of hydrides (the alkali and alkaline earth metal hydrides) rather than the second. On the contrary, very recent results tend to support, at least partially, this conclusion [5] *.
REFERENCES
’
[1] P. E. Cade and W!F. Huo, J. Chem. Phys. 45 (1966) 1063. [2] P. Politzor, J. Phys. Chem. 70 (1966) 4041. [3] J.T. Waber and D.T. Cromer, J. Chem. Phys. 42 (1965) 4llG and personal communication from J. T. Waber. [+I] J. C. Slatcr, Phys. Rev. 81 (1951) 385. [5] P. Politzer. J. Phys. Chem. 71 (1967)
* An investigation of the relationship between the diatomic hydrides and their positive ions has once more brought out the tendency of the hydrides to fall into two groups. Although there is again some uncertainty regarding the exact boundary between the groups, in terms of the properties studied in this worlc AIH belongs with the hydrides of the elements of the left side of the periodic table.