I S THE CONFIGLWTION R OR S 7 CH( ONE >2 OH +cH
CBR5 CH2BR CH3
>
.
1
THEN MAKE THE ASSIGNMENT OF
>
CONFIGURATION USING THE STANOARO RULES ZLOCKWISE SEQUENCE 1->2->3
=
R
:OUNTERCLOCKWISE = S
BR?OH?CH? => MOLECULE = R THE LOWEST GROUP ( CH3 ) 1:s ON THE VERTICAL: STANDARD RULE I S APPLIED FPOI1 1 < OH > TO 2 < C6R3 ) TO 3 ( CHL'BR ) COLiNTERCLOCKblISE I S . . . S
OH
1
,-ER M
tCH3 E P I U H X H 3 => NOLECULE = S
H
Figure 2. Assignment of R/S conflguratlon.program RIS.
Acknowledgment Rene Barone is grateful to Ministere de 1'Education Nationale (Bureau des techniques nouvelles d'enseignement) for financial support.
'HE LOWEST GROUF
NE PULE I S INVEPTEU
CNDOR-INDO Calculations on a Mini-Computer Elson Longo, Albedo Nicodemo Senapeschi, Ricardo Longo, and Dorlval Mllanl' Universidade Federal de Sao Carlos Via Washington Luiz, Km 235 13.560. S o Carlos Sio Paulo, Brasil Rapid development of computer science has made possihle the use of the computer, especially the mini-computer, by undergraduate students. This fact along with the parallel development of quantum mechanics (QM) has made possible computational calculations of molecular properties by students. The semi-empirical CNDOW and INDO methods as elaborated by Pople et al. ( 9 4 1 )can only be used in large- and medium-size computers. -
-~
BR>W>CH3 => MOLECULE = S CH3 LOWEST GROUP ON HORIZONTAL RULE I S INIJERTEO
.
=>
BR>OH>CH3 => MOLECULE = R
lH%
CH3
-
' Department of Mathematics.
Figure 4. Review of Cahn-hgold-Prelogrules, program R/S Volume 61 Number 6 June 1984
525
T o overcome this limitation, the original CND012 and INDO programs were adapted to he run on a mini-computer without any modification of the basic theoretical structure proposed by Pople et al. The modifications in the algorithms resulted in shorter computational times. The adapted program was written in FORTRAN IV to be run on an HP-2100 minicomputer; its structure consists of 14 suhroutines occupying a real memory of 52 kbytes. This modular structure makes the program flexible and easily adaptable to any other minicomputer, because of the characteristics of its COMMON suhroutine and of the subroutines that calculate the integrals. The subroutines of the orieinal nroeram . - were keot and optimized. However, only the main program is always kept in the workine memorv. This orocedure ~ e r m i t t e dthe occuoation of a mhimum of available memory, since only the s i b routine needed for the calculation of a particular step was used. The other subroutines were maintained in the virtual memory. The common area was structured to have two distinct regions: (1) a constant one in which were allocated the elements and matrices that are invariable during the operation; and, (2) a variable one that accommodates the elements and matrices that are used in a specific subroutine. These modifications were made in such a way that the executing subroutine always has a t its disposal only the essential information for a given step. This arrangement resulted in a more flexible program and saved memory as well. The matrices in the oroeram are for molecules containing up to 25 itoms or 50 hasis functions. One atomic orbital basis function is allowed for hvdroeen 119)... four for each oneof the elements Li through F i2s, Tp,, 2py, 2p2) and nine for each one of the elements Na through C1(3s, 3p,, 3py, 3p,, 3dZy, 3d,,, 3dyz, 3dz2, 3 d , 4 The main oroeram (MAIN) controls the subroutines in the . following sequence (see Fig. 5). ( 1 ) DAD1 reads the data entry, i.e.: (a) Name of molecule. (b)ootion for thr CNDO/2 or INDO methods restricted to cl&d shell molecules, (c) number of
-
atoms, charge and multiplicity of molecule, (d) a series of cards, one for each atom, containing its atomic number and r a roeftir~enr te.; used in its coordmntes. (2) ~ 0 ~ ~ ~ ~ e n e the the subroutine INTGK. 'l'h~ssuhroutineuses only 1 kbvte of memory, while in thr original subroutine the coefficienr was listed as using 59.7 kbytes. (31 INTGR cnlculatri the intemals of overlap ( S i p )and the Coulomb integrals (YAB); these ihtegrals are calculated for each pair of atoms. (4) HUCKL first carries out a ZDO extended Huckel-type approximation to the Fock matrix with diagonal elements formed from -'I2 (I A) and off-diagonal elements formed from (BAO @#)Spu/2 This matrix is diagonalized by (5) DIAGO and an initial density matrix is constructed. At this point, the matrices that contain the overlap and Coulomb integrals, as well as the matrices of the hamiltonian core. are constructed bv the suhroutine (6) INTCS. (7)~ ~ F ~ ~ c o n s r rthe u cFock t s matrix by adding the CNDO intearals and. deoendine uoon the uotion used. the INDO correkions tothese integrais. Next, the Fock matrix is diagonalized hy DIAGO and the hamiltonian core in the closed-shell segments is stored. The SCFCL uses as input the density matrix and the CNDO or INDO hamiltonian. This SCFCL subroutine is repeated until the electronic energy converges. At this point, the Fock matrix is printed by (8) SCFW1, and the resulting eigenvectors and eigenvalues are printed by (9)SCFW2. (10) CPRIN then computes and prints the dipole moments, atom densities, and nuclear repulsion energy. The results obtained with the program executed on the mini-computer are identical to the ones reported by Pople et al. in their original program.
+
+
Internal Rotation Barriers Students have used the adapted program to study the internal rotation harrier (IRB) for several oreanic molecules of the general structure H~C-X, where X CH3, NH2, OH, CHzF, and C H y C H 3 . The experimental geometries were chosen in order to define the distance and the hond angles of these molecules (12-14). The IRB were dekrminkd in two stages. In the first one the barrier points were calculated using the CNDOA method. Then, the interpolation between these points was carried out; for this a cubic spline (15) program was developed. This
=
141 HUCKL
Figure 5. Flowchart, CNDOl2-INDO program. 526
Journal of Chemical Education
Figure 6. internal rotation banierr for: (a) ethane; (b) methylamine;(c) methanol; propane. (Dots. CNDO12 caicdations: open circles. cubic-spline Interpolation.) (dl fluoroemane; (e)
Table 1. Calculated and Experlrnental Values of the Internal Rotation Barrier for the Studied Molecules (kcallmole)a Molecule HG-OH HsC--CH3 H3C-NH2 HsCCH2CHs
KC-CH9F
CNDO12
ab-inilio
phis paper)
(20)
0.95 2.18 1.27 2.37 2.00
1.12 3.26 2.13 3.70 3.63
experimental values 1.07 (14) 2.93 (16) 1.98 (77) 3.33 (18) 3.30 118
techniaue makes the internolation in each interval usine a third-order polynomial, wkch reduces the errors occurrrng in other internolation rules. The nromam is reasonahlv simnle. The results show that there is ago02 correlation betkeenthe data obtained by the interpolation with those from the QM calculations (CNDOA method) (Fig. 6). The results of Table 1 show that the experimental and theoretical data of the IRB are qualitatively comparable. On one hand, this series of molecules exhibits the tendency of having their barrier decreased by the electron-withdrawing groups bonded to the methyl moup. The obtained results also show that the experimental;alu& of IRB are higher than those calculated by the CND012 and INDO methods from the experimental geometries. They are also lower than those calculated by the ab-initio method, whose values are dependent on the choice of the hasis functions. When the exnerimental bond distances are optimized the calculated reiults are closer t o the experimental values (16). The direct use of the experimental geometry results in lower harriers. In summary the CND012-INDO program described here provides easy access t o a semi-empirical method. With this Droeram a t the the. - one is able to studvmolecular ~ronerties . . oretical level even in cases where only a mini-computer is available. A program listing is available from Project SERAPHIM. Send a check for $2.00 made out to Project SERAPHIM, acct. 20350, to John W. Moore, Department of Chemistry, Eastern Michigan University, Ypsilanti, MI 48197.
Enzyme Kinetics Calculations-The Direct Linear Plot Procedure K. A. H. Adarns Mount Allison University Sackville. N.B. Canada EOA 3C0
A. C. Storer National Research Council of Canada Ottawa. Ontario Canada KIA OR6
ALel Cornlah-Bowden University of Birmingham Birmingham, England B15 2TT The availability of low-cost computing facilities makes it pwible to ask students to exnlore a neater numher and wider ;angeof prnt,lems in ensy& kinetiis without making excessive demands on their limited time resources. Students should he required to perform some manual data manipulation and analysis, in order for them to develop a better understanding of the principles and procedures involved. From this experience they will also discover something about the advantages of the application of computers to biochemical problems. The Michaelis-Menten equation can be rearranged to three forms that give linear plots, from which K, and V, can be evaluated. Cornish-Bowden has discussed the relative merits of thew commonly usrd straight-line plots in terms of the way they reflect errors in initial velocity (22). A different approach to dottine the Michaelis-Menten eauation. the direct linear pldt, has geen descrihed by ~ i s e n t c aand l ~ornish- ow den
(23,24) (see also (22) pp. 2&30). This procedure for obtaining estimates of K, and V., is based on distribution-free (or nonparametricistatistichand is much less dependent un sssumptions than the least-squares uppruach to data fitting 122). ,--,~
We have written a computer promam to calculate estimates of (K,IV,,)ij and (l/~,,)ij ;sing pairs of initialvelocities (ui and ui) measured a t different substrate concentrations (s; and sj). ~ l t h o u g hthese will, in general, be poor estimates subject to large random errors, there are a large number of them, and, if they are arranged in rank order, the median (middle) values are statistically satisfactory estimates from .,,V,,IK,, and lIK, which the other parameters K,, V, may be readily calculated. The most striking advantage of this approach (one that is of special importance in analyzing student experiments!) is that occasional very bad experimental points have little effect on the determination of a median, though they can have a devastating effect on a least-squares calculation. The vast majority of textbooks (even the most recent ones) continue the "romance" with the douhle-reciprocal plot, in spite of the severe way it is affected by experimental errors. Two exceptions are Rawn, who briefly mentions the direct linear plot procedure (25) and Wood, Wilson, Benbow and point out that Hood, who, in the second edition of their book.. . i t is strongly preferred (26). The program MM-DLPLOT, written for the Commodore P E T microcomputer with 16K RAM, fits experimental data to the Michaelis-Menten equation according to the method of Cornish-Bowden and Eisenthal (23, 24). The user is prompted to input the number of data points and suhstrate concentration-initial velocity pairs. For completeness, and especially for students, the data are given a title and the units of concentration and velocitv are also entered. The nroeram calculates the 95%confidencelimits for the paramete& b;the method of Porter and Traeer (27). modified as described bv Cornish-Bowden, Porter, &d ~ r & e r(28).The lower, median Vma.lKm, IIK,, l/V,.,, and and upper values of K,, V, KJV,, are printed. Errors can be printed on request and a table of substrate concentration. observed velocitv. .. calcul a d velocity, and error is presented. Finidly n summary table of the median vnlues of K,, and .,'\ (with associated units) is printed, and the prov&s the option for the use; to plot u against s on the screen. The program MM-DLPLOT is available from K. A. H. Adams, Department of Chemistry, Mount Allison University, Sackville, New Brunswick, Canada EOA 3C0 on cassette tape for $15, PET 4040 diskette for $25, or print-out for $4. It is also available on P E T 8050 diskette from Project SERAPHIM. Send a check for $4 (U.S.) made out to Project SERAPHIM, Acct. 20350, t o John W. Moore, Department of Chemistry, Eastern Michigan University, Ypsilanti, MI 48197. Although the program has been written and tested for a Commodore PET, i t requires only minor alterations to allow it to be run on other microcomputers that use extended Dartmouth BASIC. The original FORTRAN version (28), intended for batch orocessine on mainframe comnuters. is still available ~ e p a r t m e n tdf Biochemistry, from A. ~orniihh-~owden, Universitv of Birmineham. . P.O. Box 363. Birmineham. England ~ 1 2TT. 5
Constructing Nonlinear Scatchard Plots George W. Dombl ~niversitybfCincinnati Cincinnati. OH 45221 The interactions of macromolecules and smaller ligands are often treated in advanced undergraduate biochemistry courses or in qualifying graduate courses. The well-studied Scatchard binding isotherm (29) is usually included, with cases of both linear and nonlinear plots. Often examples are given to illusVolume 61 Number 6 June 1984
527
