Animation of Imaginary Frequencies at the Transition State
and of displaying the primary molecular vibrations calculated by semi-empirical quantum method^.^ Unfortunately, it does not possess all of the "hells and whistles" of the computationally more robust MOPAC program that is capable of Robert H. ~ i ~ ~ i n s ' performing potential energy surface scans (PES) and of locab Depanmenl of hardra Sc ences ing transition states. Fayettevd e Slale Jn vers ly I decided to test whether HyperChem would animate the Fayetteville, NC 28301 imazinaw vibration alone the reaction coordinate bv submi& tin8;hezImatrix that ha% been calculated (by M ~ P A C for ) Computational chemistry is one of the most dynamic arthe optimized transition state for the chloride disolacim eas in the study in the undergraduate curriculum (1,2).A chloride from chloromethane in a n S N reaction. ~ initial6 few vears aeo I beean introducing some conceots of comnuwhen thez-matrix was submitted to HyperChem, a n error tational chimist& during the k r s t semester of organic message was received. The symbol "X" that had been used chemistry to help students grasp the concepts of the conby the student to represent a dummy atom (3. 4 ) was not formational nature of alkanes and cycloalkanes. We use r&ognized by ~ y p e r d h e mHowever, . when the dummy atom PCMode12 for geometrv optimization by molecular me- . it was recognized readily by Hywas given the symbol 'XXXX", chanic~.~ perChem. Indeed, a single negative force constant was calcuFor their last experiment, students in my second-semeslated and vibration along the reaction coordinate was aniter organic chemistry class are required to design and conmated. duct (both with supervision) a n experiment that is not preMost of the students from the organic chemistry class were sent in their laboratory manual a s a n introduction to not present during the summer when the HyperChem vihraresearch. This year several students chose to perform caltions were animated; however, the imaginary vibrations were culations that were best done by semi-empirical quantum shown to two of the students who had earlier indicated thev mechanical calculations using MOPAC,4 with one student did not understand what I had meant. Their reaction was th;! ~ choosing to perform AM1 calculations on the S Ndisplacesame. "Gee. I wish I had been able to see this when we were ment in a series of alkyl halides (Fig. 1) to investigate talking alx,ut SN:!reactions. Kow, I undcrstiind." whether his calculations would parallel the experimental h s t experwnce has indicated that the conccot ofdurnrn~ order of reactivity. I t was explained that the test of a true atoms is difficult for many students to underst'and. ~ a v i n ~ transition state is the nresence of one. and onlv one.. imaziperformed a number of transition state7 calculations hv nary frequency that is characterized by a negative force MOPAC a s part of my research on the chemistry of l-azabrconstant along the reaction coordinate. Several members cyclohutonium ions (5, 6)that do not require the use of of the class were unable to understand the basis for this. dummy atoms, I decided to submit the MOPAC z-matrix for the N-C2 cleavage tranH H\ sition state to HyperChem ci H H , ; c - c ~ I CI-C;,,H lH + CC (Fig. 2). This, too, gave one negative force constant with H H the animation of the vibraL I I tion clearly indicating that it ~ of chlorlde by chloride in methyl chloride. Figure 1. The S Ndisplacement corresponded to the transi-
-
-
This summer I began using HyperChem: which has a good-to-excellent graphical interface. I t is capable of reaction dynamic calculations, geometry optimization by both molecular mechanics and a number of semi-empirical methods (including all of those supported by MOPAC), somewhat crude representations of the molecular orbitals (these have been somewhat improved with ChemPlus (a HyperChem add-on) 'Member of the Molecular Computation and Visualization in Undergraduate Education (MoleCVLJE)consortium headquartered at Eiizabethtown Colleoe. " Elizabethtown. PA. An exoansion on this work 6 ScncdJ eo as a program on translllon slale lheory lo oe re eased laler oy that orgamzal on 'PCMooe s a prodJc1 of Serena Sollware. Box 3076. Bloomnglon N 47402 We Jsed tne verslon wrlnen to take advantage 013 86 architecture. kopies of the experiment can be obtained by writing the author. 4 ~ O 6.0 ~ tor ~ MS-DOS C is available from Serena Software. Bloominaton. IN. Anew oublic domain version recentlv became available on-ine i~-mailivarbchem.ut.eel. . The two versihns oive essent a y oenl ca re% IS n comparable lmes Tne p ~ o c doma n vers on apparenl y w I nano e arger systems b ~ me t I mes rcponed are meaningless. '~yper~hem is a product of Hypercube,Toronto, Canada. "aussian 92 for Windows provides a tool for scripting to HyperChem forvisualization of molecular vibrationscalculatedby Gaussian 92. 'The N-C3cleavaae is ComDlicated bvvirtue of methvl ~. rino , , rotation. Inversoon, an0 n~~rogen nverQron Factors necessary for so v ng tnls lransd on slale prooao y are beyono lnose norma y expecteo ol Jndergraduate students ~
~
~~~
~~~
~
-
~
I
I
F gde 2 Rmg open ng oy 1-melhy.I-azabcyco[l 1 Olbdlon~~m on
oy N-C2 c eavage Table 1. lnput Data for Optimization of Chloromethane and Chloride Ion
AM1 GNORM = 0.1 CHARGE = -1 SYMMETRY BONDS Methyl Chloride plus Chloride Ion Input CI
~~~~
~~
Volume 72 Number 8 August 1995
703
now require students to animate the imaginary frequency in transition-state calculations.
Table 2. Input Data for the Displacement of Chloride from Chloromethane by Chloride Ion
Experimental
AM1 GNORM=O.l CHARGE=-1 SYMMETRY STEP=0.03 POINTS=41
The Reaction of Methyl Chloride with Chloride ion
Methyl Chloride plus Chloride ton Input
.ooooooo
CI C
0 .000000
0
-1 .OOOOOO
1.7
.oooooo
XX
1.0000000
0 90.000000
0 .OOOOOO
0
CI
2.8717868
1 90.000000
0 180.000000
0
H
1.1092710
1 107.625561 107,589473
1 180.000000 -59,993221
0
1.1092966
0 107.589473
0 59.993221
0
H H 6 6 6
1 2 14
7 7 7
-s6.00
-5700
-58.00
-59.00
-6O.W
$ -p
The z-matrix shown in Table 1 was employed to o~timizethe c o m ~ l e xbetween methvl chloride and 2 1 0 chloride ion. Following optimization, the z-matrix for the opti2 3 1 -.9795 mized structure was modified to provide for the 2 1 3 ,1169 carbon-chlorine bond a s the reaction coordinate ,1168 with the input fileR(obtained by modification of the archive file, ie., FOR012, of the minimization) em2 1 3 ,1168 nlnvrd i ~ -. ~-, 2).h. l ~ -.* .- , One could manually examine the MOPAC output to find the point with the highest heat of formation and manually enter that z-matrix into MOPAC for a transition state calculation, but i t was found much more convenient to use PES Scanner for MOPACg for these purposes. The results of the PES Scan are shown in Figure 3. The z-matrix associated with the 2.21 Angstrom C-C1 bond distance was then modified to remove the reaction coordinate, t h e keywords " T S ' a n d "BONDS" were added, and then submitted to MOPAC for geometly optimization providing both C-C1 lengths of 2.215 Angstroms. Thez-matrix from the optimized transition state
O O 0 1 0 0
0 .OOOOOO
-2690 -.lo19
Table 3. Input Data for the Minimization of 1-Methyl-1-Azabicyclo[l.l.O]Butonium Ion
-8,oo
o
-62.00
x
AM1 CHARGE=I GNORM=0.05 BONDS
uC
-68.00 1.60
1.80
2.00
2.20
c-a ois,mcc
2.40
2.80
2.60
3.00
(*nps,ramsl
Figure 3. Energy profile for the displacement of chloride by chloride. tion state between the azabicyclobutonium and the aziridinvlmethvl cations. Conclusion I was suff~cientlyimpressed by student reactions that I will now begin teaching infrared spectroscopy during my organic class before discussing transition state theory to provide students with a basic understanding of molecular vibrations. Then transition state theory will be approached on the basis of molecular vibra- N tions. I expect to use this a s a demonstration for the oreanic chemistrv C ~~-" class. We have a senior-level special topics class, C and I have taught computational chemistry in C
-
H
1.1
1
H H H u,
1.1
1
1.1 1.1
1' 1
.
'
.
i i,
i,
110.0 110.0 110.0 110.0 110.0 110.0
1 1 1 1 1 1
180.0 -150.0 60.0 180.0 150.0 40.0
1 1 1 1 1 1
1 2 2 3 4 4
1100 110.0
1 1
180.0 -60.0 fin --.- n
1 1
5 1 2 5 1 2
4
-6 ,3 - 9
i.i,-.nn
i ,
.
2 3 3 2 3 3
3 4 4 1 2 2
Table 4. Input Data for the N-C2 Cleavage Reaction of 1-Methyl-1-azabicylco[1.l.O]butonium Ion
14889155 1.4939807 1.4333615
1 60.543734 160.544020 1 129.703164
1 .OOOOOO 0 1-124.0007411 1 -129.081365 1
-.0699 -.0332 -.I337
H H H
1.1160841 1.1149750 1.0978888 1.1161252 1.1150054 1.1243854
118839463 122.073612 1 129.825419 1118.832682 1 122.081888 1110.055333 108,208167
-150521530 58.394216 1 124.137850 1150.515104 1 -58.409532 1147.955136 -92,512173
H
1.1243937
1 110.049048
1 27.006331
~~~
-
8The calculation time may be reduced somewhat by usina fewer ~ointsalona the reaction coordinate. 'PESscannerfor M&AC isa productof cumberland H Chemical Computations. PO. Box 48662, Cumberland.
Journal of Chemical Education
1 1 1 1
-.1454 -.0331
that class. -. Recause method annears .--. ~. ... .this ..... . .......- . .rr-----t-n- he -eeneral for all transition states that one cancalenlate by use of MOPAC and GAUSSIAN, I will H
704
H H
1.5 1.1 1.1 1.1
AM1 CHARGE=I GNORM=0.05 STEP=O.O2 POINTS=55 BICYCLIC-AZIRIDINYLPATH .0000000 0 ,000000 0 .OOOOOO 0 0 0 0 -1 .OOOOOO 0 .OOOOOO 0 1 0 0
~
- mnnm e .,
H
1 1 1
2 3 2
0 2 3
.1888 1 1 1 1
3 4 4 5
2 3 3 1
1 2 2 2
,2343 ,1888 ,1831 .I410 .1553
1
5
1
2
,1410
was extracted from the archive file (FOROlZ), modified by replacing the keywords "TS" and "BONDS" with the keyword "FORCE", and the frequencies calculated by MOPAC. The frequency calculation and vibrational animation by HyperChem were performed by inputting the optimized z-matrix for the transition state, setting HyperChem to do a n AM1 calculation with the charge = -1 and the multiplicity = 1, then clicking on 'Vibrations" in the "Compute" drop-down box. The imaginary vibration had a force constant of -464.91 by MOPAC and 4 6 4 . 8 8 by HyperChem.
272,00
270.00
268.00 266.00 26,,00
.6
i;
E
262.00
., 260.00
k 0
Ring Opening of I-Methyl-l-Azabicyclo[l. I.O]Butonium Ion by N-C2 Cleavage
"B 258.00 This is the easier of the two described demonstrations to perform and understand because it requires no dummy atoms. The z-matrix shown 256.00 in Table 3 was used to perform geometry optimization (AM1 shown here). 254.00 After minimization of the energy, the z-matrix was extracted from the resulting archive 252.00 file (FOROlZ), modified to that shown in Table 4, and submitted to MOPAC. Again, it was con250.00 4 I venient, b u t not necessary, to employ P E S 1.40 1.60 1.80 2.00 2.20 2.40 2.6 Scanner for MOPAC for locating a point near N-C2 Distonce in hgrtromr the transition state (Fig. 4). This point was used as the starting point for the transition Figure 4. Energy profile for the ring opening of l-methyl-l-azabicyclo[l.l.O]butonium state o~timization.The archive file from this 'On by N-C2 'leavage. calculakon was modified to perform the force calculation and suhmitted directly to HyperLiterature Cited Chem for calculation and animation of frequencies. The 1. See. for example, Retro, W.J. J Chem. Educ 1334. 71.416420. imaginary vibration (force constants of -500.48 from 2. For some ofthe capabilities of computational chemistry the reader is referred t o the fallowing: (aiC1ark.T.A HondboohofCompnrotioriolChemistry:~~~actiml~uide MOPAC and -492.97 from HyperChem) involves movelo Chemrcoi Slruclure a n d Energy Coleulalions: Wiley-Inferscience: New York, ment of the CH2 away from the nitrogen atom and a n um1985.lhl Foiesman, J. B.;Frisch,A. Exploring Chamistv with Eleclronie Sirirelure Meihods:A Guide to Usinp Goussion: Gaussian Inc.. Pitfshurgh. 1993. brella inversion a t the carbon. u
Acknowledgment
The author wishes to thank Hypercube and Autodesk, Inc. for supplying members of the MoleCVUE consortium with HyperChem.
3. Schlegel, H. B. in Modern Elertmnic Structure Theory, Yarkony. D. R., Ed.: World Scientific Publishing: River Edge, NJ, 1998: pp 1-24. 4. Schlegel, H. B. in New Thmreiicol Concepts for U n d e m t o n d i ~O~gonirReoeliom: Beltran. J.; Csizmadia. I. G.,Eds.; Kluwer Academic Publishers: Norwell, MA, 1989: .no. 33-63. 5 . H i ~ @ n sR., H.: Behlen. F. M.; Egg1i.D. F:KreymhorpJ. H.:Cmmwell. N. H.J Org
C C m . 1972.87.52P526. 6. Himins, R.H.; Cromwel1.N.H.
J.Am Chem. Soc 1913.95.120-124.
Volume 72 Number 8 August 1995
705
