Dipole Moment Calculations Using a Programable Desk Calculator

With the widespread availability of small and inexpensive programable desk calculstors, like the Hewlett-Psckard 9100A, it is now often easier to obtain immediate results from experimental data using such a calculator, rather than employing a. digital computer. A good example of this is the calculation of solute dipole moments from solution mea- surements of dielectric constsnts and densities over a. range of concentrations.

The Halverstadt-Kumler method' has been very popular and has spawned an excellent computer progrsmP which we have used for several years.' Nevertheless, the coding, punching and verification of data, plus the in- variable wait for results s t 8 computer center, can cause delay in planning further experiments. Far this reason we hsve programed the equations of the Halverstadt-Kumler method for use with the HP 9100A. This program e m readily be adapted to any small desk computer whose memory is limited. This limitation farced us to break the pro- gram into three parts, each of which is stored on one magnetic card: 1. A linear loast squares progrsm whose results are the slope and intercept of a straight line. 2. A program which calculates the statistical error in the slope of the line. 3. A program for eelculating the dipole moment plus its expected error from the Halverstadt-Knmler equa- tions.

I t is necessary to run parts 1 and 2 twice-once for the dielectric constant and concentration data. and once for the density and concentration data. to obtain the slopes, intercepts and errors necessary far part 3. The total calcu- lation time is onlv about 10 min. however. The dipole moments calculated are identical with the result8 of the For- tran computer prbgram of reference in footnote 2 and the dipole moment error of that program is closely reproduced by ours by seleoting a St,udent t factor for a 60Yo confidence level. This last feature is novel in our program in that i t per- mits use of any level of confidence desired by introducing as input the appropriate Student t factor. The program with instructions is available from us.

HALVERSTADT, I. F., AND KUMLER, W. D., J. Amer. Chem. Sac., 64, 2988 (1942). PA^^^^^^^, N. L., J. Amer. Chem. Soc., 79, 3443 (1957) and ALLINOER, N. L., AND ALLINCER, J., J. Org. C h m . ,

24, 1613 (1959). 'LEHMANN, P. A,, AND MCEACHERN, D. M., J . Md. S ~ ? U C ~ U T ~ , 7, 253 (1971).

CENTER FOR RESEARCH AND ADVANCED STUDIES NATIONAL POLYTECHNIC INSTITZTTE A. P. 14-740, MBx~co 14, D.F.

Volume 49, Number 9, September 1972 / 625