Semiempirical and ab initio Calculations of Charged Species Used in the Physical Organic Chemistry Course Richard D. Gilliom Rhodes College, Memphis. TN 38112 In an earlier publication, Lipkowitz described a course where students learned the concepts of physical-organic chemistry and a t the same time became familiar with computational chemistry (I). We have applied much of this article to our undergraduate, senior-level class and describe several experiences that have been encountered by our use of the programs with the idea that they may be helpful to the instructor who is not completelv comfortable with the computational methods described by Lipkowitz but agree with the need to introduce them to students in their classes. Educational, organic, and medicinal chemists are making increasing use of molecular orbital calculations. Yet some appear tushy away from theuseofthese valuable techniques even though the new book by Clark gives valuahle aid in the use of the more widelv a\,ailable oroerams (21. We believe that much of the he2tancy to use k e methods available stems from the absence of tables com~arinethe accuracv of the various methods. The literature has many cornparisks of ah initio techniques making it relativelv easv to compare the usefulness of the various basis sets-(e.g.; ref 3). T h e situation with semiempirical methods is less satisfactory. Until recently no studyof the two procedures, ah initio and semiempirical, was available. Dewar and Storch have only now published the results of a comparative study, but it is mostly concerned with uncharged, paired electron species leavine the auestion for ions and radicals ooen (4). One study Fompaies some MO techniques with force field'calculations but is verv limited (5). The force field method and its applications have been comprehensively reviewed (6) recently and will not be dealt with in this work. This work is concerned with the semiempirical methods MIND013 (7),MNDO (81, and AM1 (9) available in the program AMPAC (10) from the Quantum Chemistry Program Exchange at IndianaUniversity. All ah initio work was carried out using the program Gaussian 82 (11). Both are inexpensive and available programs. Methods All computations were carried out using the Rhodes College DEC VAX785. Full geometrical optimization was performed on all structures with the exception of beta-aminoalanine. Studies were made of this compound in the gauche and trans conformations by freezing one dihedral angle, as well as with full optimization. In each case the optimization was beeun usine "standard" bond leneths and aneles. The electron densit& reported were obtaLed using tKe Mulliken ~ o ~ u l a t i analvsis on available as Dart of all the roer rams R88uIt8 Partial atomic charges and bond lengths for ammonium ions are aiven in Tables 1 and 2. Results are eiven for all three semiempirical methods and for the 3-21~"basisset as well as for the basis set containing polarization functions. These functions have been reported to be good for positive ions (I). The W I G * set is also given both a t the optimized geometry and for the 3-21G geometries. The same pcoperties
are given in Tables 3 and 4 for the carboxylic anions with the diffuse functions. 3-21+G (12) and the oroeram nrovided 631+G set along with the 3 - 2 1 set. ~ ~ a 6 l ggives e the dipole moments of three zwitterionic amino acids at the geometries optimized for each method. Table 6 gives the h e 2 of formation and the dipole moment for each of the three shorter neutral carboxylic acids. The experimental values are also given in the last two tables for comparative purposes. Dlscuslon In the positive ion calculations the charge distribution is more pronounced for the ah initio results than for those using semiempirical methods. This is not found in the anions;with thekxception of H atoms. I t is also interesting to note that charge shift occurs for those H atoms in a position to stabilize thk species by what has come to be called a hyperconjugative effect. I t will also be noted that the static bond dipoles ohtained by Mulliken analysis runs opposite to those reported by Wiberg and Wendoloski (13). The argument that these results are not contradictorv is eiven bv Reed and Weinhold (141 and is based upon theiact ;hat the; refer to different aspects of charce distribution. The zeroth moment obtained dy the ~ u l l i G e nmethod is probably of most interest to the bench chemist since it leads to the dioole moment of a molecule. If bond lengths are examined, it is found that ah initio methods give shorter X-H (where X is a heavy atom) bond lengths but that no such trend is found for bond lengths between two h e a w atoms. I t can be noted that when charee is transferred in &x-H bond, i t appears as achange in ho;d length. One of the most startling effects noted by the calculations is that the C-0 bond lengths, and charge densities, of a carhoxvlate ion differ and are not svmmetrical when ah initio results are examined with basis sets more complex than the 3-21G set. I t has been suggested that a symmetrical structure be used to shorten the-calculation and to obtain lower energies. This works to shorten the calculation hut the energy may not he lowered. Indeed when the 3-21+G basis set was used for formate ion, the symmetrical structure was hartrees less stable than the fullv found to be 2.5 X optimized structure. The same trend was found for ace& ion. In this case the methvl C was in the same olane as the other heavy atoms while {he out-of-plane H atoms are symmetrical about the heavv-atom olane. For semiemdrical calculations, the fully ~ ~ ~ i m i z e d ~ s t r u c tare u r esymmetrical s and no gain is noted by setting - the two C-0 bond lengths . to he unsymmetrical. I t may be noted from Tahles 5 and 6 that the computed dipole moments and heats of formation are somewhat closer to experimental values using semiempirical methods. Both MNDO and AM1 results are quite acceptable. For the practical bench chemist, the fact that MNDO has parameters for more atoms than AM1 will make this the favored method until the missing parameters become available for AM1. Other observations not eiven in the tables can be mentioned by the author. In t h i computations for the acids, the carhonyl0, the C atom, and the 0-H are all in the same plane with the 0-H syn to the C=O. This may result from Volume 66 Number 1 January 1989
47
Table 1. ParllaI Atomlc Charges In Charged Amlnes (X 10' eu). N
H(N)
C'
H(C9
fl
Table 2.
Bond Lencllhs In Charged Amlnes (Anastroms)'
HI@)
631G' (E1NH3)+ MINWl3 MNDO AM1 3-216 6-310'1 13-210 6310' ((CHdNd' MINDOW MNDO AM1 3-216 6-310'1 13-210 8-310' l(CHd3NH)' MINW13 MNDO AM1 3-210 6-310'1 13-210 6-310'
where values difter, the inplane value Is given firsf followed by MI"^.
MNDO AM1
me out-of-plane
the lone pair of the C-0-H being directed away from that of the C=O in the more stable conformation while they parallel each other in the less stable confiauration. There is a point to be aware of when using diffuseffunctions like the 321+G set in the Gaussian program. The program permits two methods of adding the diffise function-to the internal 321G set. The first is the surest and easiest, that of using the MESSAGE command. The second employs the GEN command so that the entire basis set is read into the program. If the latter method is used. the diffuse set must be added as a separate shell and not simply added to the last shell of the set being emoloved. . - If the latter is done an error results. For example, correct use gives an energy of -187.1918 hartrees for the 3-21+G set when i t is used in the calculation of formate ion while the energy obtained when using the polarization set in the wrong way is -186.7916. The acetate ion affords comparable values of -226.0193 and -225.5574, respectively. This error will not be made by the experienced computational chemist hut i t can be made easily by a chemist not familiar with the program. Conclusions
This study indicates that semiempirical methods are accurate enough for the general use of the bench chemist, 48
Journal o f Chemical Education
especially MNDO and AM1. Even MIND013 can be used for .those situations where i t has been shown to be of special usefulness (17).These methods seem to be especially valuable when time and computercostsareofconaiberati~n.The useof ah initio methods does not give the accuracy to justify their use unlessonly they providethe dataof interest such as the wave functions for inner shell electrons. The reader may find the basis set selection article by Davidson and Fuller (18)t o be useful. There a .m.e a r to be certain advantaees t o usine charged " ions in the teaching of computational chemistry over the use l charred of uncharted soecies.There is nothing s ~ e c i aahout species over thkir neutral counterpar&. The use of ions tends to demonstrate more clearly the location of charge than is seen in neutral species. These charges are given by a Mulliken population analysis and the deficiencies of this method can be discussed and the results used as an entrance to the literature where this complex problem is now under discussion. Acknowledgment
This work was funded in part by the Rhodes College Facultv Develo~mentCommittee. HDG thanks the Rhodea College ~ o m ~ u kCenter er for ample computational time.
Table 3.
Partlal Atomlc Charges In Carboxyllc Anlons (X
c'
H
-783 -626 -613 -790 -784 -720 -728
932 373 281 616 470 406 415
-366 -117 -56 -36 96 32 41
CH3C02MIND013 MNDO AM1 3-21G 3-21tG 6-31+G/ 13.216 6-314-0
-792 -613 -596 -8021-795 -7771-771 -7351-723 -7411-731
C2HsCOF1 MIND013 MNDO AM1 3-216 3-21+G 6-31+G/ 13-21G 6-31+G
-762 -608 -590 -798 -7741-740 -720 -720
0
los eu)*
c=
H(C9
845 332 321 615 600 563 546
-52 6 -268 -691 -767 -604 -588
-741-72 -371-38 47/48 1561158 7631762 1761169 1761169
868 348 326 851 344 500 473
-74 -57 -226 -549 -116 -275 -249
-63 -21 56 172 268 176 162
Ca
@ H l
nco,MINDOR MNDO AM1 3-216 3-21+G 6 - 3 1 t G I 13-210 6-31tG
-1091-67 -631-16 14/68 1191193 1971260 1251191 1291189
161 61 -180 -556 -945 -639 -641
. m r e values diwer, the ll~planevalve Is given flrrt, followed by me &-of-plane value, for O-C' me flm value Is on me Sam ride as the methyl group.
Table 4.
Bond Lengths In Carboxyllc Anlons (angstroms)'
Energyb
0-C'
KC'
MIND013 MNDO AM1 3-210 3-21tG 6-31+G
-98.7719 -101.6221 -109.4394 -183.1046 -167.1918 -188.1180
1.24-1.25 1.243 1.260 1.265 1.249 1.265 1.260
1.204 1.141 1.134 1.126 1.103 1.103
CH@EXPlL.' MIND013 MNDO AM1 3-21G 3-214-0 6-31+G
-113.2528 -110.0144 -115.4081 -225.9331 -226.0193 -227.1454
C2HrCO2MIND013 MNDO AM1 3-210 3-21CG 631+G
-122.4546 -115.5256 -121.9890 -264.7562 -264.8410 -266.1650
C'-C"
Cm-H
1.25-1.27 1.254 1.264 1.267 1.24611.251 1.267111269 1.26311.266
1.50-1.54 1.539 1.553 1.528 1.575 1.547 1.634
1.120 1.110 1.114 1.08211.087 1.08111.086 1.082110.86
1.262 1.263 1.265 1.250 1.27011.265 1.264
1.568 1.568 1.537 1.672 1.551 1.540
CCC~
HC02-
EXP~.=
1.493 1.526 1.502 1.530 1.533 1.526
Where valuea diwer, the Inplanevalve Is given first, followed by ihe outaf-pbne value: far O-C' ihe firot value is on the same side as the memyl group. bSee note b in Table 2.
'SBerBf3.
Table 5. Exptl:
MINW13
Dlpole Moments of zwlnerlonic Amino Aclds MNDO
AM1
3.216
Glyclne
11.6-16.7
10.38
12.08
11.34
10.71
Alanlne
12.6-17.0
9.72
11.39
11.00
6.11
BAlanine
14.6-19.4
5.79
7.91
17.35
16.65
5.66
7.41
gauche 6.54 5.39 bans 14.89 17.61 OptirnlzBd geometry 5.48 6.88
3-21tg 12.12
631+G'/
13-216
11.04
*See ref 5.
Volume 66
Number 1 January 1989
49
Table 6. Add
MIND0/3
Heat
of Formation and D i p o l e Moments ol A c l d s
MNDO
AM1
3-216
3-21+G
EXPTL.'
Formic
h= ' Dlpols
-88.79 1.86
-92.57 1.48
-97.38 1.48
4.55
5.16
-90.48-90.67 1.35-1.7
-107.05 1.94
-100.96 1.67
-103.02 1.87
1.85
5.65
-103.22-103.30 1.75
-1i3.27 1.89
-104.87 1.76
-108.53 1.97
Acetic
nD Dipole Propionic Dipole
-108.4 1.76
,Heat of formation, kcal/moi, see ref 15. Dipole momsnt, &byor, see 16
Literature Clted 1. LipkowiU, K. B.J. Chom.Educ. 1982.59.595. 2. Ciark. T. A Hondbwk o/Compulofionnl Chemiafry; Wil~y:Nea York. 1986: pp 93318. 3. Hehre, J. W.: &dm L.; Schleyer, P. R.; Pople, J. A. ~b Initio Moleeulor Olbitol Theory; Wiloy: New York. 1986; aod references therein. 4. Dewar, M. J. 5.; Storeh, D. M. J.Am. Chem. Sor. 1985,107,3898. 5. Abraham.R. J.;Hudson.B. J. J. Compuc. Chem. 1985.6.173. 6. Burkert. U.; Allinger, N. L. Moleeulor Mechonicq; ACS Mongraph 177; American Chemical Society: Washington, DC, 1982. 7. Bingham, R C.: Dewar, M. J. 5.;Lo, D. H. II Am. Chem. Soc. 1975,97.1285. 8. Dewar, M. J. 5.; Thiel, W. J. J. Am. Chem. Sac. 1977,999,4899. 9. De-ar, M. J. S.; Zaebisch,E.G.: Healy,E. F.; Sfewart,J. P. S. J Am. Chom.Soc. 1985, 107,3902.
".
50
Journal of Chemical Education
10. AMPAC. QCPE5ffi.Vol. 6. Number 1,1966. 11. Binkley. J. S.: Whiteaide, P. C.: Raghavachari.K.; Sesger.R.; DoFreea, D. J.; SeNegel. H. 9.; Friaeh, M. J.; Pople, J. A,; Kahn, L. R. GAUSSIAN82Releoao A: Came$& Mellon U n i ~ r r i t y :Pittsburgh, 1982. GAUSSIAN 86 h now available from J. A. Poplo. 12. C1ark.T.; C h a n d r s s e h , J.; Spitmagel, 0. W.; Schleyer.P. v. R. J. Comput. C h m . 1983.4.294. 13. Wiberg, K. B.: Wendolaeki, J. J . J. Phya. Cham. 1984.88.566. 14. Reed. A. E.; Weinhold, F. J. Chem.Phys. 1988.84.2429. 15. McCiellan, A. L. Tables of Expenmntai Dipole Moments, Freeman: London. 1963; Voi. 1. 16. Cox, J. D.: Pilcher, G. Themrochemistry oforgonicand Orgonom~tallkCompaundr: Academic, New Yock, 1970. 17. Lewis, D. F. V. Cham. Rsu. 1986,86,1111. Is. Dsvidaon, E. R.; Feller, D. Cham. Re". 1986,86,681.
