Molecular Parameters of Diatomic Molecules A Programmable Calculator Program Jose Miguel Gallego ~ a r c i a Quimica Organica de Mexico. S. A,. Apartado Postal No. 1205. Mexicali, Baja California, Mexico P. 0. Box 1840. Calexico. California, 92231 U. S . A. The main objective of recent articles that have dealt with pocket programmable calculators (1-l2,17-19) has been to help the teacher and the students in performing repetitive calculations, doing laboratory report evaluations, and figuring "what i f ' calculations. Because of the importance of molecular spectroscopy in the undergraduate curricula 113, 141 a program written by M. Bader llfi)entitled "The Molecular Parameters of a Diatomic Molecule-A Computerized Physical Chemistry Experiment" was translated to the language of the TI-59 ~ o c k e~rozrammable calculator (PPC). This was done .t .. the lc~a rlat ( 1 1 1'1Y' uxnpnrrd uith a n m ~ p u ~and rr I,ec.m.;r or 1,) the llw v;tst with w h i + i t ran i,ccnrried tht~ar,nm laboratory. Description of the Program The original program was modified to make it more general and also to adjust it to the capacity of the PPC. One modification is that the user can do calculations for any type of diatomic molecule instead of just the combination of hydrogen or deuterium with the halogens. Another modification is that this program uses the built-in linear regression feature because it is part of the hardware of the PPC, thus saving memory space. This program can he used with or without the PC-100C Thermal Printer. The user first inputs the mass of each atom then all J, K ( I )and P (4values which are obtained from the IR spectra of the diatomic molecule under study. The program will output A , B, and C which are calculated as follows (for a more detailed explanation on the following equation see (15):
C = H I J - I ) t fYJI = 2P - 2(Hn - R d J '
(3)
The program then calculates i (the vibration frequency in the ground state) using a linear regression of all C and J2 values in eqn. (3). Z is obtained by dividing the y-intercept (2$ by 2. A and R are divided by 4, and the average of these values
610
Journal of Chemical Education
is used to obtain Bo and R , (the rotational constants in the ground and first excited state). The rotational constant in the zero-point state (Be)is calculated by:
H, = Ho +
(7)
14)
The anharmonicity constant, x,, is obtained by the following equation:
T h e vibration-rotation interaction constant is found (15) by: u = xPBe
16)
o,,the vibration frequency in the zero point state is determined by: -
We
= ---1 - 2xs
(7)
The force constant ( K ) is calculated by: K =(2~w,c)~p
(8)
Where c is the speed of light in cmlsec and p the reduced mass:
Where M , and M 2 are the masses of atom 1 and atom 2. The for the excited (I,) moments of inertia for the ground state (lo) and for the zero point state (I,) are given by: h l o= 8a2cHo h I,=-
8~'cB~
I,=-
h 8s2eR,
(10)
(11) (121
and the internuclear distances in centimeters for the ground
Table 1.
Input Obtained from the PPC Program Described In thls Artlcle Uslng the Thermal Printer PC-100C. (Data Obtained from (16)).
Table 2.
Output Obtained from the PPC Program in this Artlcle Uslng the Thermal Printer PC-100C. output Comment:
Input
1.007825 79.909
2674.72 0. 2541.64 2524.68 2507.09 2469.05 2470.58 2451.69 2432.39 2412.66 2392.56
Comment: M1
32.45333333
\
M2
P lines
6.327066097 3.3613353-40 1.426179-06 2.5577462 03
Ground State
First Excited State
state (ro), first excited state (rl), and for the zero point state (re) can be demonstrated by:
Zero Point State
Sample Output
Table 1shows the data run in this program which was obtained from Bader's sample program (16).Table 2 shows the data obtained. Conclusion
Colleges that cannot afford a complete computer system can use the P P C for their students. The student, who might be reluctant to use a computer with others looking a t him or h e r and who might feel pressure or embarrassment by his or her answer, can make his or her calculation with a PPC in his or her own privacy. From these results it can be seen that a small computer program can be translated to a PPC. The listing and samples output of this program can be obtained from the author. Acknowledgment
The author would like to thank especially Dr. Bader Morris of Moravian College for his permission to translate and use his original program and for his review of this article and also to thank Leticia Osuna Torrontegui for her help during the bibliographic research on the use of PPC in chemistry.
. .
46.PM ilY69l. 1171 Hsldrworth. D. K., "High Resnluthm Maaa Spectra Ansiysis with a Proyrammablo Calrulator,"~l.CHEM. EDUC.. 57.99 IIYWJI. I 181 Hhcdea. W. I;,and Taylor. D.W.."Simulati~~nufEnrymeActiunon the Pnwrammabb CalrulaUlr."J. CHYM.E~Uc..S7.620 1IYfflII. I191 Wizcr.l:.. "CsleulsUm in F1eahmanChemixlry.".I.C~~~.RDUC..S7.fi7O 119WJI.
Volume 58 Number 8 August 1981
611
