3664
J. Phys. Chem. 1994,98, 3664-3668
Comparison of Several Semiempirical and ab Initio Methods for Transition State Structure Characterization. Addition of COz to CHJNHCONH~ J. Andrb,' V. Moliner, J. Krecbl,? and E. Sills* Department of Experimental Sciences, Universitat Jaume I , Apartat 242, 12080 Castellb, Spain Received: March 31, 1993; In Final Form: January 14, 1994"
The potential energy surfaces for the addition of C 0 2 to CH3NHCONH2 have been the subject of intensive research. Stationary points representing reactants, transition state, and products have been located and characterized using MNDO, MIND0/3, AM1, and PM3 semiempirical methods and ab initio 3-21G, 6-31G, and 6-31G* basis sets within Hartree-Fock (HF) procedures. The electron correlation has been estimated at MP2/3-21G, MP2/6-31G*//HF-6-31G*, and MP2/6-31G**//MP2/3-21G levels. The pathway connecting stationary points was traced by the IRC procedure. An analysis of the results shows that the addition is an asynchronous process, and the transition state structure can be described as a four-membered ring.
1. Introduction The complete characterization of a chemical reaction system requires the full determination of the potential energy surface (PES) for the reaction system as a function of the nuclear coordinates. In the conventional transition state theory, this requirement is reduced to a determination of the surface around the stationary structures: reactants (R) and products(P), possible intermediates, the quadratic surface around the transition state (TS) structures, and thelowest energy pathway connecting them.' A major problem in theoretical studies of chemical reactions has been the lack of information concerning the TS structure; however, the development of sophisticated spectroscopy techniques may resolve this problem in the future.2 For this reason, it is a longstanding goal of physical organic chemistry to establish the method of predicting a variation in the structures and properties of the TS structures of chemical reactions. There are a number of theories presented for this purpose: the pioneering works of Bell, Evans, and P01anyi;~the principle of least nuclear m ~ t i o n ; ~ or the Marcus equations (for a review, see ref 6 ) . Lately, these ideas have been incorporated by Shaik et al. in a series of papers.' Other theories or concepts introduced by many chemists, e.g., Hammond postulate: Thornton rules: More O'Ferrall diagram,"J and concepts of Harris and Kurz," Jencks,12 Gajewski,13 and MurdochI4 may be of some use. The structure and energy of TS are of prime importance in theoretical studies of chemical reactions. On a PES, the theoretical determinationof geometries and energies for reactants, intermediates, and products can be calculated accurately by ab initio MO methods.'$ Improvementsin optimization algorithms during recent years have made the location of TS structures also relatively routine. From a chemical point of view, a number of methods or algorithms for finding TS structures have been proposed; details of some of these algorithms can be found in reviews.l"l* Semiemperical methods can be used for somewhat larger systems, but in this case only comparison with experiments or ab initio calculations can be used to judge the quality of the results. In recent studies,19-23 we noticed several similarities in related TS structures. These similarities suggest that it may be possible to compile a set of standard TS structures, as Reynolds and Thompson have proposed.24 Having determined these standard
features, it would then be useful to investigatethe TS of addition reactions in order to determine the extent of, and the reasons for, the resemblancewith the standard structures. Such an analysis, coupled with improved saddle point optimization algorithms, wouldgreatly facilitate TS location. If the similarities are widely observed in TS geometries using different semiempiricalmethods and ab initio procedures with different basis set levels, then it would appear wise to determine these standard features from saddle points for addition reactions. These common features are reviewed by Houk et alezsfor hydrocarbon pericyclic reactions. Since semiempirical and ab initio MO methods provide information concerningthe TS structure, it would be convenient to test them in the search for this crucial geometry. In the present investigation, semiempiricaland ab initio MO calculations were carried out for the addition reaction of C02 to CH3NHCONH2. This reaction system was chosen because the reaction can be considered a model of the molecular reaction that takes place in the active site of biotin.26 Biotin (vitamin H) is an important cofactor whose presence is crucial for many carboxylation and decarboxylation reactions in living cells. In our earlier ~ t u d i e son ~ ~this . ~ system ~ using a simple model (addition of carbon dioxide, C02, to methylamine, CH3NH2) and other work^,'^^^^ we have obtained several TS structures of different reactions and we have analyzed their dependenceon the choice of the basis set. The results show that the TS structure is not sensitive to the basis set used in the HF-SCF schemes. In this sense, this work can be considered as a prolongation of these studies. In section 2, we briefly outline the method of calculation used for the quantum mechanical calculations. In section 3, we have described and discussed the results, analyzing the structure and energy along the reaction path. The profiles are described using the intrinsic reaction coordinate (IRC) method. The analysis of the transition vectors allows us to decide which variables control the transformation. The evolution of electron distribution helps us discuss the results. Changes of bond orders interpreted from a modified version of the More OFerrall diagrams explain the nature of the process. A short conclusions section closes this paper. 2. Method of Calculation
t Permanent address: Department of Organic Chemistry, Institute of
Chemical Technology, 166 28 Prague 6, Czech Republic. t Permanent address: Departament de Qulmica Flsica, Universitat de Valencia, 46100 Burjassot, Valencia, Spain. Abstract published in Aduance ACS Abstracts, March 1 , 1994.
0022-3654/94/2098-3664$04.50/0
The calculations were carried out using the MONSTERGAUSS2' and the GAUSSIAN 922*programs, using MINDO/ 3, MNDO, AM1, PM3 semiempirical methods and ab initio at 0 1994 American Chemical Society
PESs of COl
+ CH3NHCONHl
3-21G,6-31G,and6-31G*basissetlevels. Thecorrelationenergy has been considered at Mdler-Plesset 2'9 perturbation theory employing MP2/3-21G, MP2/6-31Ga//HF-6-31G8, and MP2/ 6-31G"//MP2/3-21G basis sets. The exact characterization of the TS was achieved by using a simple algorithm" in which the set of coordinates describing the system is separated into (4,) and (4,). where (qJ is the control space set which is responsible for the unique negativeeigenvalue in the respective force constant matrix connected with variables that form the transition The remaining coordinates,set ( q j ) , is calledcomplementaryspace. First, tbeTSs werelocalized with the VA05 subroutine," and the transition vector was determined by diagonalizing the force constant matrix. As a second step we optimizedthe complementaryspace using the OC method?' In the third step, acomplete optimization with the use of the VAO5 method was achieved for the complete space of all variables. Finally the stationary points, reactants (R, where the partners have been calculated as separate molecules), TS, and P are characterizedby calculatingharmonicvibrationalfrequencies employingtheGAUSSIAN 92program. Theoptimizationswere terminated after the overall average gradient length had been reduced to
