extending Luo and Benson new electronegativity scale to in- clude Group VIII elements. The Vx-values obtained corre- lated well with the ionization potentials of ...
467 Iraqi J. Sci., Vol. 37, No. 2, 1996 An Approach to Calculate The Unshielded Core Potentials, Covalent Radii and Electronegativities of The Noble Gases. Bahjat R. J. Muhyedeen Department of Chemistry, College of Science University of Baghdad, Jadriyah, Baghdad, Iraq. Vx Benson
Luo Vx
An approach was made for the calculation of the unshielded core potentials (Vx) of the noble gases and thus extending Luo and Benson new electronegativity scale to include Group VIII elements. The Vx-values obtained correlated well with the ionization potentials of these elements. Thus, the covalent radii and the electronegativities on the Pauling scale of the noble gases were calculated, and the values obtained were found to be in good agreement with those of others.
468 Iraqi J. Sci., Vol. 37, No. 2, 1996
INTRODUCTION Interest in noble-gas chemistry has progressively grown ever since well-defined and characterized noble-gas compounds were prepared in the early sixties [1]. Thus, attempts at obtaining accurate atomic parameters for the elements of the Group VIII have assumed special importance. In this paper an approach is made to calculate for these elements their unshielded core potentials (Vx) which were shown by Luo and Benson (2) to form a good basis for a new electronegativity scale that correlates quantitatively with such properties as the ionization potentials, the heat of formation, and bond dissociation energies [2]. Based on the values of Vx, the covalent radii of the noble gases could easily be obtained, and thus give an alternative approach to that usually used in estimating this important property.
METHOD Linear equations were developed from values of unshielded core potentials (Vx) of groups VI and VII and their corresponding first ionization energies (IP). The elements of the same Period, pre-group VIII, were used in the determination of the Vx-values of the noble gases; e.g., Vx-values of oxygen and sulfur were used to calculate Vx of Zeon. Analysis parameters of such equations are given in Table 1. Data of ionization poten-
469 Iraqi J. Sci., Vol. 37, No. 2, 1996 tials were obtained from standard sources values of unshielded core potentials of and VII were obtained from Luo and Benson [2].
[3,4], while Group VI
Table 1 Slopes And Intercepts For The Linear Correlation of IP with Vx For Main Groups VI And VII. The General Form IP=a+ bVx. Elements O, F S, Cl
a - 5.922 - 1.484
b 2.409 2.053
Se, Br
- 8.826
2.092
Te, I
+ 1.749
1.657
Po, At
+ 2.123
1.563
RESULTS AND DISCUSSION 1. Unshielded Core Potentials The values of unshielded core potentials, of the noble gases, except He, were calculated from linear equations which are listed in Table 1. For the calculation of Vx of He, another linear equation was developed from the Vx-values which we ob-tained for the other elements of Group VIII (i.e. Ne, Ar, Kr, Xe, Rn) and their corresponding IP's. The equation so obtained was of the form given below and illustrated in Figure 1: IP(eV) = 0.705 + 1.822 Vx(Ao-1) ............. (1)
470 Iraqi J. Sci., Vol. 37, No. 2, 1996
Fig. 1 Relation Between Vx And IP For Group VIII Elements The parameters of regression equation are*: PCC=0.9992; The values of Vx thus obtained are listed in Table 2.
analysis for this SDS=0.04; SDI=.05. for the whole group
471 Iraqi J. Sci., Vol. 37, No. 2, 1996 Table 2 The Calculated Unshielded Core Potentials Of Group VIII** Elements He
Vx 13.105+0.005
Ne
11.408
Ar
8.400
Kr
7.190
Xe
6.263
Rn
5.520
** The value for He is from Eqn. (1) those for the other elements from the eqns given in Table 1. Alternative value for He may values of Vx for Ar and Xe Vx(He)=13.598 which compares with in Table 2 of 13.105+.005. This rationale based on recent work, lished
*PCC=Pearson Correlation Coefficient SDS=Standard Deviation of Slope SDI=Standard Deviation of Intercept
be obtained from only which gave the listed value procedure has its yet to be pub-
472 Iraqi J. Sci., Vol. 37, No. 2, 1996 in which better correlations were found between ionization potentials and atomic parameters of the noble gases when they were sub-divided into two sets one includes He, Ar, Xe and the other contains Ne, Kr, Rn [5]. The high value of correlation coefficient between IP and Vx is highly expected because both properties are based on size parameter of the atom. 2. Covalent Radii Several empirical or semiempirical relationships have been established to correlate covalent radii (Rcov) with different parameters and properties such as electronegativity [6], atomic chemical potential [7], ionization potential [5], unshielded core potential [2], etc. Examination of all these properties in relation to Rcov reveals that there is a good correlation between the size factor (i.e., Rcov) of the atom and its physical properties. The great attention paid to this fact, proliferates a deep interest in investigation of atomic properties from this view point, and thus leading to better understanding about atomic nature. The covalent radii of the noble gases, with the exception of helium, were calculated from their unshielded core potentials. The Vx parameter is defined as the ratio of Nx/Rx. The value of Nx for Group VIII, except He, is taken to equal 8, the total number of electrons less the core electrons. The Rcov value could then be calculated from the simple relation:
473 Iraqi J. Sci., Vol. 37, No. 2, 1996 Rcov = 8/Vx
……………. (2)
The calculated values of Rcov and their comparison with other values found in the literature [8] are shown in Table 3. It is evident from this Table that the proposed approach in which is based on a rather simple direct calculation, gave in general values in very good agreement with those obtained by extrapolation procedure. Table 3 The Calculated Covlent Radii of Group VIII Elements From Vx- Values. Elements He
Rcov 0.61*
Rcov 0.50
Ne
0.70
0.65
Ar
0.95
0.95
Kr
1.11
1.10
Xe Rn
1.28 1.45
1.30 1.45
* The value for He is the other elements from eqn. 2.
obtained
from eqn. 3, for
474 Iraqi J. Sci., Vol. 37, No. 2, 1996 However, for helium an alternative procedure has to be followed based on the rather good correlation between the ionization potentials of the nobel gases and their covalent radii which has the form: IP(eV) = 2.0716 + 13.1498 (1/Rc)1.1 …… (3) and illustrated in Figure 2 with regression parameters: PCC=0.9993; SDS=0.284; SDI=0.016. The results from this equation are shown in Table 3. In this case also good agreement is obtained between the He covalent radius and that given by others.
Fig. 2 Behaviour of Covalent Radii Against IP’S Group VIII Elements.
475 Iraqi J. Sci., Vol. 37, No. 2, 1996 3. Electronegativities In 1964 Yuan suggested Vx-value as basis for a new electronegativity scale. Twenty four years later, Luo and Benson attempted to correlate Vx-values for the main groups of the Periodic Table, with the exception of the noble gases, with some physical and thermodynamic properties [9-11]. In the present work, the author extended Luo and Benson approach to include group VIII. The calculated Vx-values from Luo and Benson [2] were converted to Pauling scale (Xp), for thirty seven elements of groups I-VII, except Tl, to get a simple formula of a power type as follow: Xp = 1.086 Vx 0.521
….. (4)
The parameters of regression analysis for this equation are: PCC=0.9770 ; SDS=0.035 ; SDI=0.126. This conversion allows comparison to be made with values obtained by Pauling and Mulliken [12]. Our Vx-values of group VIII were converted to Pauling scale using equation 4. The results are outlined in Table 4. It is evident from the Table that there is good agreement with the reported values, with the exception of He where a rather high value is obtained. CONCLUSION It has been demonstrated that the simple concept of unshielded core potential could be used effectively to arrive at some valuable atomic parameters for the group VIII elements, such as
476 Iraqi J. Sci., Vol. 37, No. 2, 1996 covalent radii and electronegativities. The rather simple relations obtained relating Vx to ionization potentials, covalent radii and electronegativities, gave values in good agreement with those obtained by others.
Table 4 The Estimated electronegativity Values of Group VIII Elements Using The Conversion Scale-Equation Xp=1.086 Vx 0.52 Electronegativity Values Elements
Present work Values
He
4.15
Pauling Values ref (12) -----
Mulliken Values ref (12) 3.5
Ne
3.86
-----
4.3
Ar
3.29
-----
3.6
Kr
3.04
2.9
3.2
Xe
2.82
2.6
2.8
Rn
2.64
-----
-----
ACKNOWLEDGEMENT Special thanks are due to Derwish for valuable discussions.
Professor
G.
A.
W.
477 Iraqi J. Sci., Vol. 37, No. 2, 1996
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5- B. R. Muhyedeen, A. T. M. Al-Thib and G. A. W Derwish, Accepted in Iraq. J. chem. (1993). 6- E J. Little and M M Jones, J. Chem. Educ., 1960,37,231. 7-
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