POTENTIAL CURVES AND BONDSTRENGTH OF PO
3461
Potential Curves and Bond Strength of PO
by Ran B. Singh and D. K. Rai” Department of Spectroscopy, Banaras H i n d u University, Varanasi-5, I n d i a
(Received A p r i l 23, 1966)
Potential energy curves for P-0 interactions corresponding to the X 211, A 22+,and B 2+ states of PO have been calculated by the Rydberg-Klein-Rees method as modified by Vanderslice, et al. The ground-state dissociation energy has been estimated.
Introduction The spectra of the PO molecule have been studied to a small extent as compared to the closely analogous molecule NO. Since the work of Dressler,Ib however, a number of workers have directed their attention toward PO. These studies include the rotational analysis of the A-X system by Rao2 and the B-X system by Singh,3 the discovery of the visible bands by Durga and R ~ oand , ~ the recent discovery of a number of new band systems in the far ultraviolet by Santaram and R ~ o .This ~ paper deals with the experimental potential energy curves of the electronic states for which sufficient spectroscopic data are available. Santaram and Rao,6 from a qualitative analysis of the various spectroscopic data, have suggested a value 6.8 e.v. for the dissociation energy of PO. This value was in disagreement with the values suggested by Dresslerlb (5.4 e.v.), Ghosh and Ball7 (7.4 e.v.), and Herzberg8 (6.2 e.v.). An attempt has been made to clarify this situation. Method, Results, and Discussion The Rydberg-Klein-Rees as modified by Vanderslice, et a1.,12for constructing the potential energy curves of diatomic molecules is a semiclassical method and utilizes spectroscopic data to determine the values of the bond length corresponding to the classical turning points in the vibrational motion of the molecule. Spectroscopic data for P O were taken from Ghosh and Ball,’ Dressler,lb Rao,2 and Singh.3 The results of the calculations are given in Table I. Recently,13 experimental potential energy curves have been used to estimate the dissociation energies by a comparison with the results obtained from an empirical function. This method is quite if the are known Over large range of energy. The three-parameter Lippincott function,
which fits14to a good extent the RKRV curves for a large number of diatomic molecules, has been used for the estimation of ground-state dissociation energy. I t is found that a value of Doabout 5.4 e.v. gives the best fit to the RKRV curve in the known range. The results are given in Table 11. The vibrational levels of B 2 2 +state, as shown by Dressler,lb converge very rapidly to a limit 55,000 cm.-l above the ground state. The E state shows a predissociation at about the same height and this may be caused by the B state. Kanak Durga and R ~ o , ~ in their study of the visible band systems of PO, reported that vibrational levels in D and D’ states above v = 0 level (at about 49,000 cni.-l) are predissociated. If the absence of the levels with v > 0 in D state is correctly ascribed t o predissociation, the values 6.8 and 7.4 e.v. for the Do (PO) are ruled out. The above argument, however, does not rule out unambiguously Do (PO) 6.2 e.v. as given by Herzberg.8
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(1) (a) Quantum Chemistry Group, Uppsala University, Uppsala, Sweden; (b) K. Dressler, Helv. P h y s . Acta., 28, 563 (1955). (2) K. S. Rao, Can. J . Phys., 36, 1526 (1958). (3) N. L. Singh, ibid., 37, 136 (1959). (4) K. K. Durga and P. T. Rao, I n d i a n J . Phys., 32, 223 (1958). (5) C. V. V. S. N. K. Santaram and P. T. Rao, 2. Physik, 168, 553 (1962). (6) C. V. V. S. N. K. Santarlzm and P. T. Rao, I n d i a n J . Phys., 37, 14 (1963). (7) P. N. Ghosh and G. N. Ball, 2. Physik, 71, 362 (1931). (8) G. Herzberg, “Spectra of Diatomic Molecules,” D. Van Nostrand Co. Inc., New York, N. Y., 1950. (9) R. Rydberg, 2.P h y s i k , 73, 376 (1931); 80, 514 (1933). (10) 0. Klein, ibid., 76, 226 (1932). (11) A. L. G. Rees, Proc. Phys. SOC.(London), 59, 998 (1947). (12) J. T. Vanderslice, E. A. Mason, W. G. Maisch, and E. R. Lippincott, J . Mol. SPectrZl.9 3, 17 (1959); 5 , 83 (1960). (13) D. Steele, Spectrochim. Acta., 19, 411 (1963). (14) D. Steele, J. T. Vanderslice, and E. R. Lippincott, Rep. Mod. Phys., 3 4 , 2 3 9 (1962).
Volume 6 9 , Number 10
October 1966
RANB. SINGHAND D. K. RAI
3462
Table I: FtKRV Curves for the PO Molecule State
T,, cm.-l
x 2II
0"
U,cm.-1
rmin, A.
r-,
A.
+u
Te om.-'
615.1 1834.9 3041.4 4234.6 5415.1 6582.6 7737.1 8878.6 10007.1
1.427 1.394 1.373 1.357 1.344 1.332 1.322 1.313 1.305
1.529 1.572 1.604 1.631 1.656 1.679 1.700 1.721 1,742
615.1 1834.9 3041.4 4232.6 5415.1 6582.6 7737.1 8878.6 10007.1
B2Z+b
30731.8
579.6 1716.8 2826.6 3909.0 4961.3 5988.3 6985.5 7953.8 8893.3
1.414 1.382 1.362 1.346 1.333 1.322 1.312 1.303 1.295
1.519 1.566 1.602 1.633 1.662 1.690 1.717 1.744 1.769
31311.4 32448.6 33558.4 34640.8 35693.1 36720.1 37717.3 38685.6 39625.1
AQ+b
40406.8
693.8 2071.7 3436.8 4783.3 6116.3 7432.1
1.386 1.355 1.335 1.320 1.307 1.296
1.482 1.522 1.552 1.577 1.600 1.622
41100.6 42478.5 43843.6 45190.1 46523.1 47838.9
The mean of Q I / ~ and 2IIs/, has been taken as the zero of the According to Rao,2 both the states have the same energy scale. symmetry, and are presumably Zf.
The upper state of the y system which is a 2+state is perturbed2 in its v = 0 level at two values of J. These perturbations are homogeneous in character; i.e., they are caused by a Z state. The B 22+state cannot be the perturbing state because the near equality of rotational constants for A and B states make it unlikely that the rotational energies of these can come into coincidence at two values of J. Now, the groundstate atoms can lead to the following six states TI, 22,42,411, Q, and 611 of which 211 is the ground state. If the B state is identified with the state arising from
The J o u d of Physical ChmiSttY
Table I[: Calculations for the Ground State of the PO Molecule Using the Lippincott Function (Three-Parameter Form)" De = r,
A. 1.742 1.721 1.700 1.679 1.656 1.631 1.604 1.572 1.529 1.427 1.394 1.373 1.357 1.344 1.332 1.322 1.313 1.305
44375.7
De = 44861.7
De = 50023.5
R.K.R.V.
(om. -1)
(cm. -1)
(cm.-1)
(om.-1)
9936.3 8808.9 7668.1 6517.6 5357.0 4190.8 2964.3 1809.4 608.6 608.2 1820.3 3019.2 4188.5 5351.6 6500.8 7625.5 8750.5 9860.3
10045.1 8905.4 7752.1 6589.0 5415.7 4236.7 2996.8 1829.2 615.2 614.9 1840.2 3052.3 4234.4 5410.2 6572.0 7709.0 8846.4 9968.3
11200.9 9930.1 8644.0 7347.2 6038.8 4724.4 3341.6 2039.7 686.0 685.6 2052.0 3403.5 4721.6 6032.7 7328.2 8596. n 9864.3 11115.2
10007.1 8878.6 7737.1 6582.6 5415.1 4234.6 3041.4 1834.9 615.1 615.1 1834.9 3041.4 4234.6 5415.1 6582.2 7737.1 8878.6 10007. I
a The De N 6.8 and 7.4 e.v. were also used for calculations, but the results are not reported here as they deviate greatly from the RKRV values.
these products, a simple quantum mechanical argum e n P may be used to calculate the curves for 42 and 41T. It is found that these curves do not cut the A state at the appropriate height, Thus it seems more likely that the B state dissociates into 2D (F') 3P (0)which leads to DO 5.4 e.v. and there is some lower state of the type 22 or 42 arising from normal atoms which is causing the observed perturbations.
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Acknowledgment. The authors are grateful to Professor N. L. Singh for his interest in this work, R. B. S. wishes to thank C.S.I.R. (India) for financial assistance. (15) J. T. Vanderslice, E. A. Mason, and W. G. Maisch, J. Chem. Phys., 31, 738 (1959).
