PotentialEnergy Function for Diatomic MoleculesM. R. Katti and D. P. Batra Citation: The Journal of Chemical Physics 38, 774 (1963); doi: 10.1063/1.1733738 View online: http://dx.doi.org/10.1063/1.1733738 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/38/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Extension of a general potentialenergy function for diatomic molecules J. Chem. Phys. 88, 2804 (1988); 10.1063/1.454014 Toward an Understanding of PotentialEnergy Functions for Diatomic Molecules J. Chem. Phys. 48, 1116 (1968); 10.1063/1.1668772 Accurate PotentialEnergy Function for Diatomic Molecules J. Chem. Phys. 45, 827 (1966); 10.1063/1.1727689 Erratum : PotentialEnergy Function for Diatomic Molecules J. Chem. Phys. 43, 1086 (1965); 10.1063/1.1696839 PotentialEnergy Function for Diatomic Molecules J. Chem. Phys. 38, 3036 (1963); 10.1063/1.1733648

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774 LETTERS TO THE EDITOR

electron spin densities are as given in the illustration of the radical. The spin densities calculated by Fischer for the cyclohexadienyl radical and by Hanna et al. for the pentadienyl radical are in approximate agree­ment with these observations.

A 35-G hyperfine interaction has been observed for (3 protons bonded at a 30° azimuthal angle to the axis of the p orbital in the planar cyclobutyl and cyclo­pentyl radicals. 9 From this observation, one would expect that the coupling constant for the methylene protons would be 2(0.349)(35) =24.4 G. The con­siderably larger value observed here is not understood at the present time.

In the previous ESR studies of irradiated solid ben­zene, the spectrum was resolved into three sets of what appear to be quartets.2 ,3 Further resolution was obtained by raising the temperature to -50°C. In the present work it has been found possible to examine solid benzene at O°C where still better resolution is obtained.9 This spectrum, although similar to that found previously,2,3 is very complex and is peculiarly asymmetric and not amenable to ready interpretation. It is apparent, however, that significant concentrations of at least two free radicals are present. In contrast the spectrum of irradiated solid 1, 4-cyclohexadiene at -60°C agrees with that which would be obtained by broadening the lines observed in the liquid phase to the width observed in the solid (about 2 G). The difference between the ortho (9.0 G) and para (13.0 G) hyperfine constants is readily apparent. The ap­pearance of the spectrum observed in solid benzene in the form of quartets of approximately equally spaced lines must be regarded as an artifact. In spite of the above, certain of the general features of the spectrum of solid benzene are similar to those observed in solid 1 ,4-cyclohexadiene so that there is little question that cyclohexadienyl radical is present along with some other as yet unidentified species. Attempts to observe radicals in liquid benzene have to date proven unsuc­cessful. For the most part this seems to be due to the simultaneous presence of a number of different radi­cals which makes the resolution of anyone spectrum particularly difficult.

* This work is supported, in part, by the U. S. Atomic Energy Commission.

1 S. Gordon, A. R. Van Dyken, and T. F. Doumani, J. Phys. Chern. 62, 20 (1958).

2 H. Fischer, Kolloid-Z. 180, 64 (1962). 3 V. A. Tolkachev, Yu. N. Molin,!.!. Tchkheldze, N. Ya.

Buben, and V. V. Voevodsky, Doklady Akad. Nauk S.S S.R. 141, 911 (1961); V. V. Voevodsky and Yu. N. Molin, Radiation Research 17,366 (1962).

4 R. W. Fessenden and R. H. Schuler, J. Chern. Phys. 33, 935 (1960); additional experimental details will be presented in a forthcoming pUblication.

6 R. W. Fessenden, J. Chern. Phys. 37, 747 (1962). 6 M. W. Hanna, A. D. McLachlan, H H Dearman, and H. M.

McConnell, J Chern. Phys. 37, 361 (1962). 7 H. Fischer, J. Chern. Phys. 37, 1094 (1962). 8 H. M. McConnell and D. B. Chesnut, J. Chern. Phys. 27,

984 (1957); A D. McLachlan, Mol. Phys. 2, 223 (1959). 9 R. W. Fessenden and R. H. Schuler (to be published).

Comments and Errata

Potential-Energy Function for Diatomic Molecules

M. R. KATTI AND D. P. BATRA

Defence Science Laboratory, Delhi, India

(Received 4 September 1962)

I N a recent note published in this Journal, Clintonl

has proposed a new potential-energy function for diatomic molecules. Clinton starts with

(1)

where R is the internuclear distance and the A, (i= 1, 2, 3) are independent empirical parameters. The A, (i= 1,2,3) are determined in terms of a dimensionless quantity 1J=[KeRl/De]! from the three conditions U(Re) = -De, UI(Re) =0, UII(Re) =Ke, and the func­tion (1) is expressed as

U(R) = - De(Re/ R)u[l- log(Re/ R)u] .. • , (2)

where De and Ke are the dissociation energy and the force constant.

The expression (2) is compact and has a simple analytical form and satisfies the criteria that a good potential must satisfy. However in order to establish the general validity of the proposed function it is neces­sary to carry out certain tests.

The following tests are applicable.

(1) By comparing theoretical curve with the experi­mental curve.

(2) By substituting the proposed function in the Schrodinger wave equation and solving it for the eigen­values and the vibrational wavefunctions.

(3) By evaluating the unused constants and com­paring them with the actual values.

(4) By evaluating a quantity Ro (the critical inter­nuclear distance Ro<Re for which U(R) =0 and com­paring it with the observed value.

In most of the cases, tests (1) and (2) are not feasible for reasons that accurate experimental curves are known for very few molecules and that the solution of Schrodinger equation involves severe mathematical procedures often requiring the use of perturbation techniques.

Clinton's expression gives Ro = Ree1/u which he has used to calculate Ro in the case of H 2+ with IJ= 1.88 and compared it with the observed value. The relation yields a considerably better value of Ro than the Morse curve. From this result in a single case of H2+ he has concluded that Eq. (2) is most useful in the calculation of Ro. This quantity Ro which is determined indirectly from mass spectrometry appearance potentials is known experimentally only in the case of H2+. Thus it

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LETTERS TO THE ED1TO:R 775

is optimistic to assume the validity of Ro relation in the case of other molecules also. We shall see later that Ro is mainly dependent on the magnitude of 0" or Re•

In the present note it is proposed to examine the performance of the function for evaluating the unused constants, a e rotation interaction constant, and the anharmonicity constant w.x. after the procedure of Varshni.2 The function gives

UIII(R.) /UII(R.) =X = - (20"+3) / R.,

and

hence

ae= _[XRe+1J6Be2 = 2V2 .116Be2,." (4)

3 We 3 w.

A comparison of Eqs. (4) and (5) with similar rela­tions due to the Morse, the Rydberg, and other func­tions considered by VarshnP shows that the present relations give results for ae and w.x. higher than those due to the Morse, which has been shown by Varshni2 to give highest percentage errors. It is interesting to note that Eqs. (4) and (5) are nearly identical with

obtained by Varshni2 for the function

proposed by himself. Thus Clinton's expression which is found efficient for the prediction of Ro fails to come up to the standard of Morse, Rydberg, etc., that are in common use. However for small values of (]' or Re there is improvement in the efficacy of Eqs. (4) and (5). It is concluded in the light of the results obtained here that as far as the prediction of ae and WeX. is concerned the workability of Clinton's expression is restricted to hydrides whose electronic states have small values of Re and hence 0".

This poor performance of Clinton's expression may be attributed to the evaluation of the three derivatives UIV(R), UIII(R), and UII(R) at R=R. which is in conformity with the earlier observation of Clinton that the expression is not as good as the Morse curve in the region of the equilibrium distance.

1 W. L. Clinton, J. Chern. Phys. 36, 555 (1962). 2 Y. P. Varshni, Revs. Modern Phys. 29, 664 (1957).

Notes

Measurement of th~ Spin-Lattice Relaxa­tion Time of the E(2E) State of CrH in A1 20 3 by Paramagnetic Resonance at X

Band Frequency

W. H. CULVER,* R. A. SATTEN,t AND C. R. VISWANATHAN

Physics Department, University of California, Los Angeles, California

(Received 26 June 1962)

THE spin-lattice relaxation time of the E(2E) state of Cr3+ in Ah03 (ruby) was measured in a double­

resonance experiment at 9100 Me/sec. It was found to be greater than 10-2 sec. This is to be compared with the probable value of 2X 10-4 sec at 103000 Mc/sec (in a magnetic field of 30000 Oe) determined from the relative strengths of the absorption of the Zeeman components of the Rl line l and a more precise measure­ment by Geschwind, Collins, and Schawlow2 with a paramagnetic resonance experiment similar to the one reported in this paper, which gave a relaxation time of 2.3X 10-3 sec at 23936 Mc/sec. Comparison of the relaxation times at X and K band at approximately the same temperature is in closer agreement with an B-2, Raman process, than an B-4, direct process. This type of magnetic field dependence is not what would be expected since hv<kT.

A ruby cylinder i in. in diameter and ! in. long, containing 0.05% Cr was emersed in liquid helium at 1.8°K. The crystal was optically thick as was evi­denced by the fact that trapping of the fluorescence radiation occurred. The decay of the fluorescence radi­ation was observed to deviate from exponential with a decay time of approximately 14 msec. This is to be compared with a decay time of 4.3 msec in a very dilute ruby.2

In the present experiment the ruby was pumped with green light and the fluorescence of the Rl line was observed. The crystal and magnetic field split levels involved in the fluorescence transition are shown in Fig. 1. At 1.8°K the relative population of the equilibrium ground-state sublevels is 100: 62: 54: 46. Consequently, as can be seen from Fig. 1, there is more trapping of light originating from the lower of the E(2E) Zeeman sublevels than originating from the upper Zeeman sublevel.

Measurements made by Martin3 indicate that all of the Cr3+ ions in the 2E state decay by radiative transi­tions. Approximately 0.7 of them decay to the ground state and 0.3 to two broad levels giving bands at 7080 and 7140 A. More of the fluorescence radiation from the 2E( - t) sublevel is reabsorbed and comes out eventually as 7080 and 7140 A radiation than that from the 2E( +t) sublevel.

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