4664
J. Phys. Chem. 1993,97, 4664-4669
Theoretical Study of Chemical Reactions Using Density Functional Methods with Nonlocal Corrections Jan Andzelm,'v+ Carlos Sosa, and Robert A. Eades Cray Research, Inc.. 655 E Lone Oak Drive, Eagan, Minnesota 55121 Received: December 18. 1992
Density functional calculations have been performed for the C-H bond dissociation of methane, N2 dissociation, the C-H bond dissociation of acetylene, ethylene, and vinyl radical, the rotational barrier of acrolein, and the relative energies for isomers and transition structures of diazene. It is found that the nonlocal spin density (NLSD) approach brings significant improvements over the local spin density (LSD) energetics. In most of these systems, the accuracy of density functional methods is comparable to the best available correlated wave function based a b initio results.
Introduction
has been the subject of much discrepancy.21cExperimental bond dissociation energies range from 104.4 kcal/mol2lb to 110 kcal/ With recent developments of analytic gradient techniques,] mo1.2la progress in functionals for nonlocal corrections24 to the local Also of theoretical interest is the correct prediction of spin density appro~imation,5-~ and the availability of versatile conformational energies as well as the energetics of unimolecular software,lo,lldensity functional methods have become a popular reactions. Acrolein has been used to explain the preference for tool in chemistry.I0.l2Thus, it is important to study the accuracy planar conformation in these type of conjugated systems.23 On of this new approach. the other hand, NzH2has been used to study 1,2 hydrogen shifts.24 Initial results are encouraging. In the pioneering work by In unimolecular reactions, electron correlationand basis set effects B e ~ k e , ~it .was ' ~ established that thenonlocal spin density (NLSD) play an important role in the prediction of the energetics. method provides good bond energies for diatomic molecules. The computational effort of density functional methods scales Calculation of thermodynamic data for polyatomic m ~ l e c u l e s ~ ~ ~at~ Jmost ~ as N3, where N corresponds to the number of basis shows that the NLSD method provides energeticstypically better functions. Therefore, density functional methods may easily be than the H F method. The NLSD results are closer to correlated applied to large polyatomic systems. Consideringthe importance methods (e.g., MP2) or better.11-14 of quantitative predictions for large polyatomic systems, it is necessary to assess first the accuracy of density functionalmethods Density functional calculations of transition states for processes on small and theoretically demanding systems. In this study we involving organic and organometallic molecules have successfully report applicationsof local spin density methods with and without been carried out by Ziegler and co-workers.IIJ5 In the present nonlocal corrections for systems studied extensively using highpaper we employ the DGauss programIoaJ2to study reaction paths quality ab initio methods. and the energeticsof severalreactions. These systemswere chosen due to the availability of recent, accurate, correlated results. Ab Computational Method initio results can provide a stringent test for density functional methods. Unlike the heats of reaction, transition states and shapes The calculations in thisstudy werecarriedout using the DGauss of potential curves are difficult to investigate experimentally. programloaJ2on a Cray YMP. DGauss is a density functional Correlated wave function based ab initio results are the most program that uses Gaussian basis sets to expand LSD orbitals reliable source of informational6 and to fit the density and exchangecorrelation potentials. There The small size and the importance of CH4 CH3 + H in is extensive literature published in this field.10a,bJ2J5-27 The hydrocarbon chemistry have prompted a series of theoretical Gaussian approach to solve the density functional equations relies studies." It has been shown that well-correlated single reference on thevariational fitting of thedensity. Theexchange-wrrelation wave functions can properly describe the C-H bond breaking.I7e potential is a smooth function and can be effectively fit through Another small system that has attracted the attention of several numerical integration.28 The density functional method is based theoretical studies is N2.13J6918 The potential energy surface for on the Hohenberg and Kohn formalism5.6 N2 is difficult to describe due to its triple bond. Considerable = 7 l P l + U P 1 + E,c[Pl attention has been given to the C-H bond dissociation energy of acetylene. The dissociation energy for a C-H bond in acetylene where the energy is a functional of the charge density, p, Tis the has been the subject of controversy, kinetic energy of the noninteracting electrons, U is the classical Coulomb electrostatic energy, and E,, includes all the manyHCCH H CCH body exchange and correlation contributions to the energy.18a In the most recent, quadratic configuration interaction (QCI) the local approximation6 E,, can be expressed as follows calculations by Montgomery and PeterssonJ9report a binding energy of Do 131.5 kcal/mol. This result is in agreement with calculations using G1 methodsZoand the experimental data by Ervin et a1.Z1a However, recently, a dissociation energy of 127 where e,, is the exchange-correlation energy per particle in the kcal/mol has been reported for the H-CCH bond breaking.22 uniform electron gas. DGauss currently uses the form derived Similarly,the homolytic C-H bond dissociationenergy of ethylene by Vosko, Wilk, and Nusair.29 Nonlocal corrections (NLSD) were computed using the exchange and correlation functionals of Becke and Perdew (BP) r e s p e c t i ~ e l y . ~All ~ , ~the ~ nonlocal Present address: BIOSYM Technologies, Inc., 9685 Scranton Rd., San Diego, CA 92121. corrections were added perturbatively to the LSD energies
-
m1
-
+
0022-3654/93/2097-4664$04.00/0
0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4665
Chemical Reactions and Density Functional Methods
TABLE I: Relative Energies in kcal/mol for the CH3-H Bond Breaking along the Potential Energy Surface' HFb
MP4b
CCSDT-1f
R(A)
RHF
UHF
RHF
UHF
PMP4'
MR-CId
CI'
RHF
UHF
0.757 1.086 1.500 2.00 2.500 3.000
+4.3 -86.8 -50.6 -5.9 +47.9 +78.2
+4.3 -86.8 -50.6 -9.5 -1.9 -0.5
-17.0 -109.5 -76.4 -28.9 -3.5 -0.1
-17.0 -109.5 -76.4 -17.3 -3.3 -0.8
-13.8 -104.8 -71.3 -28.5 -9.3 -2.3
-13.9 -104.3 -76.5 -32.8 -10.8 -3.0
-18.6 -109.5 -76.9 -32.4 -10.6 -3.0
-16.6 -109.2 -76.9 -32.2 -11.1 -6.1
-16.6 -109.2 -76.9 -30.8 -7.6 -1.3
CCSDTJ
LSD'"g
-32.4 -10.3 -2.8
-30.5 -124.0 -94.2 -46.9 -15.7 -4.6
NLSD'OCg -20.8 -113.2 -83.8 -37.9 -10.4' -3.3'
A* -2.2 -3.7 -6.9 -5.5 0.2 0.3
exptb -112.4
Relative energies: AE = E(R) - E(R=,). See ref 17a. See ref 17e. See ref 17b. e See ref 17c. f S e e ref 17d. g The NLSD results (with delocalized spin densities) are -7.1, and +11.1 kcal/mol for R = 2.5 and 3.0 A, respectively. A is the difference between NLSD with localized spin densities (NLSD'OE)and CI results.
*
computed using the optimized LSD geometries. Recently, it was found that nonlocal corrections added perturbatively provide reliable bond energies, geometries, and vibrational frequencies.30 The calculations for the CH4and N2 systems were performed by elongating the C-H and N-N bonds. The C-H bond length and HCH angles were obtained from the literature.17a All the calculations for these two systems were carried out using double-{ plus polarization (DZVPP) basis sets. These basis sets consist of 9s5pld primitives with a 4s2pld contraction for C and N.12,27b The standard (medium) grid size and the auxiliary basis sets A12'b have been used in these calculations. The DZVPP basis set is a density functional optimized orbital basis set. It is similar to the one used in ref 17e. All the geometries for C2H2, C2H2+, C2H,and C2H4+were fully optimized at the LSD level using the DZVPP basis set. We have optimized geometries at the LSD/ DZVPP levels for acrolein as a function of the torsional angle. Single-point calculations were also performed for acrolein using a triple-f basis set augmented with polarization and diffuse functions (TZVP, TZVPP, and TZVPP++).27b These results have been compared with ab initio MP2/6-3 lG* geometries. Relative energies were compared with MP3/6-31 l++G** calc u l a t i o n ~ .Geometries ~~ and vibrational frequencies were computed using DZVP basis sets for N2H2. The vibrational frequencieswere computed with the local spin density approximation by numerically differentiating analytic first derivatives.lOa9l2
Results and Discussion The potential energy surfaces for the dissociation of N2 and CH4 have been previously studied using ab initio wave function based techniques.I6-Is The C-H bond dissociation energies of acetylene, ethylene, and vinyl radical are investigated and compared with results from G1 and QCISD method^.^^,^^ The rotational barriers for the cis-trans transition of acrolein are also investigated.23 Finally, the stability and transition states for diazene, N2H2,isomers are studied in this work. These results are compared with wave function based ab initio calculation^^^ and with previous density functional results as well.15 A. Dissociation of CH4 and N2. It is largely believed that a multireference scheme is required for a correct description of bond breaking. However, it is difficult and rather impossible for large molecules to include all configurations that might be important for the proper description of these potential energy surfaces. Often, potential energy surfacescomputed using Maller-Plesset (MP) methods based ona restricted HartreeFockreferencewave function tend to converge to the wrong energy limit.31 On the other hand, MP methods based on an unrestricted wave function (UHF) suffer from spin contamination.16,32-34 This is particularly true in the intermediate bond-breaking region. It has also been shown that thecoupledcluster (CC) methodcaneffectivelyreduce spin contamination for this system.17e More recently, it has been shown that MP methods based on restricted open shell reference functions properly describe potential energy surfaces within the MP models.35 Thus, methods based on a single reference wave function can be used to describe dissociation energies if they can
0.0
B 3 .-
-
-0.1
R 0
c)
8
z
c)
-0.2
-a
$ F M
-A
-0.3
0 -0.4
0 I
-0.5
I
1.8
2.0
2.2
2.4
2.6
2.0
R/Re
Figure 1. Comparison of the different theoretical potential energy curves for the dissociation of methane. Three points along the reaction path, R = 2.0, 2.5, and 3.0 A. 0 LSD, 0, NLSD, A MR-CI.
TABLE 11: Relative Energies in kcal/mol for the N2 Bond Breaking along the Potential Enerav Surface' R MRMR(A) UHFb MP4b CISDb LCCMb LSDIOCr NLSD"' exptb ~~
0.95 -68.7 -145.7 -144.4 1.00 -98.1 -182.6 -181.0 1.09 -107.6 -206.6 -203.7 1.17 -87.0 -183.3 1.32 -54.9 -123.4 -161.8 1.46 -26.7 -79.4 -120.1 1.59 -4.9 -46.9 -82.0 9.9 -7.4 -30.3 1.85 6.7 0.2 -4.3 2.12 1.2 0.0 -1.6 2.65
-142.2 -178.9 -201.9 -160.6 -1 19.3 -8 1.7 -30.7 -9.8 -1.8
-189.5 -228.9 -254.2 -247.0 -210.0 -163.2 -1 16.9 -56.2 -27.3 -7.0
-159.5 -199.9 -226.8 -221.3 -186.6 -141.9 -98.5 -46.5 -20.3 -3.7
~
-228.6
Relativeenergies: AE =E(R)-E(R.,). Seeref 18b. TheNLSD results (with spin delocalization) are -23.4, +3 1.4, +95.4 kcal/mol for R = 1.85, 2.12, 2.65 A, respectively.
recover from spin contamination and if higher-order excitations are properly treated. In Table I the results of ab initio and density functional calculations are compared for the dissociation of methane. To compare our density functional results with ab initio calculations the DZVPP basis sets27bhave been used throughout these calculations. The calculated dissociationenergy at the minimum of the potential energy curve corresponds to the D, value. The density functional calculations have been performed using a spin restricted, standard approach, which leads to delocalized spin densities. The localizationof spin densities has been achieved by performing spin-polarized (unrestricted) calculations on the CH3-H complex. In these calculations (NLSDI") there is the same number of spin up and down electrons so for the closedshell methane the total spin is formally singlet. The spin densities a and B have a tendency to localize on the CH3 and H fragments, respectively. This approach was found to be necessary to describe bonding in Cr2j6and the C2H412 molecules.
4666 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
6
A 0 0
A
1.4
1.6
1.8
2.0
2.2
2.4
2.6
R/Re Figure 2. Comparison of the different theoretical potential energy curves for the dissociation of nitrogen molecule. Four points along the reaction path, R = 1.46, 1.85, 2.12, and 2.65 A. 0 LSD, 0,NLSD, A CI.
TABLE III: C-H Bond Dissociation Energies of Acetylene in kcalhol ZPE 8.1 8.1 7.5 7.5
QCP Glb LSD NLSD expt (I
DO
131.5 133.5 143.2 132.8 131.3c
See ref 19. See ref 20. See ref 21
TABLE n7: Theoretical Equilibrium Geometries for CCH+, CCH. HCCH+. and HCCH MP2'
LSD
system
cc
CH
C
CH
CCH+ CCH HCCH+ HCCH
1.235 1.180 1.258 1.216
1.084 1.065 1.081 1.066
1.270 1.221 1.264 1.217
1.106 1.085 1.102 1.083
a
See ref 20; bond lengths in angstroms.
TABLE V kcal/mol
--
Ionization and CH Bond Dissociation Energies in
system
Gla
NLSD
C2H2 C2H2+ C2H2 C2H + H+ C2H2 C2H+ H C2H2 4 C2H H C2H4 C2H3 -t H C2Hs-C2H5 H
263.8 447.1 402.2 133.5 1 10.2 100.5
260.2 446.5 400.8 133.3 108.7 99.3
-+
4
a
+ + +
It is gratifying to see that the difference between MR-CI and NLSDI" results is very small in the bond-breaking region. The NLSD result overestimates the experimental bonding energy by 1 kcal/mol and the MR-CI values underestimate bond energies by 3 kcal/mol. Apparently, the NLSD/DZVPP results in the bonding region are closer to the experimental values. In Figure 1, comparisons are made between MR-CIi7Cand density functional results for the CH stretching energy surface. Similar to ref 17b,d, the points are displayed in terms of the reduced potential. -AE/De is plotted vs R/Re,where AE is the difference in the total energy between each point and the energy of CH3 H at infinite separation. De is the methane potential well,17aand Re is the CH distance at the equilibrium The MR-CI approach provides a well-balanced description of the shape of the potential. We compare our density functional results for three points along the potential surface, R = 2.0,2.5, and 3.0 A. The LSD results overestimate the potential curve in all three points (See Figure 1). However, NLSD results in the bond-breaking region are in very good agreement with the MRCI results. The dissociation of N2 has been previously studied using several theoretical methods18 (see Table 11). This is a particularly demanding case because it involves a triple bond dissociation. The RHF-based MP and CC approaches fail to provide a correct description of the dissociation process. The UHF-based correlation treatment or the multireference CI (MR-CISD) and the linearized coupled cluster methods (MR-LCCM) lead to a satisfactory shape of the potential energy curve in the dissociation limit. Similarly, as in the case of CH4 dissociation,both the LSD and NLSD localized approaches provide a smooth dissociation curve. The LSDI" curve is too low, and the binding energy is overestimated by 25 kcal/mol. The NLSDI" binding energy of -226.8 kcal/mol is in very good agreement with the experimental value of -228.6 kcal/mol. The NLSDl" potential energy curve is consistently lower than the curves of multireference correlated approaches (See Figure 2). In summary, the NLSD approach allowing for localization of the spin densities provides a smooth potential surface with a correct dissociationlimit for both CH and N N bond dissociationprocesses. B. Dissociation of the C-H Bond in Acetylene, Ethylene, and Vinyl Radical. Table I11 summarizescalculateddensity functional bond dissociation energies of acetylene. Theoretical data at 0 K has been corrected to 298 K. In this study, zero-point vibrational corrections were computed at the LSD level. Our LSD results overestimate the dissociation energy by almost 10 kcal/mol. NLSD calculations using Becke-Perdew (BP) potentials are within 1.5 kcal/mol when compared with wave function based ab initio and experimental values. Montgomeryand Peterssonl9calculated zero-point vibrational energies using scaled HF/6-31G* ZPE values. In general, the LSD frequenciesappear to be smaller than experimental harmonic values.lOaJ2 In a recent study on C-H dissociations for acetylenic species, Curtiss and PopleZO applied the G1 method. This is a composite procedure that combines optimization of geometries at the MP2/ 6-31G* level and single-point calculations on an MP4/6-31 lG* level. Additional corrections based on hydrogen molecules, hydrogen atoms and scaled H F ZPE are used as well.20 In the present paper we have also studied these acetylenic species. All the geometries were fully optimized at the LSD/ DZVP/Al level. Table IV shows all the optimized parameters. The LSD CH bond distances are consistently overestimated by 0.02 A.IOaJZ On the other hand, LSD CC bonds are close to MP2 results for acetylenic species and are longer for ethyne radical and cation. In particular, the shorteningof the CC bond in ethyne radical upon dissociation of H from HCCH, as found by MP2 optimizations, is not confirmed by the LSD method. The
+
i o 1.2
Andzelm et al.
See ref 20. b See ref 21
LSD 266.8 443.5 417.3 143.8 118.0 108.4
expt' 262.9 446.2 387.4-402.2 126.6-132.6 104.4-109.7
I
Although spin localization is not important in the bonding argon, it is necessary in the bond-breaking part of the potential curve. Otherwise both the LSD and NLSD approaches converge to the wrong energy limit. As usual, the LSD method overestimates the binding energy. The NLSD (Beckc-Perdew) approach predicts binding energies within 2 kcal/mol when compared with experiment. Table I summarizes relative energies for the C-H dissociation along the CH3-H reaction path. The Hartree-Fock approach provides an unrealistic potential energy curve at the dissociation limit. The MP approach does well in the bonding region but fails for distances larger than 2.0 A. Particularly, the UHF function causes irregularities in the potential curve and the spin-projected method (PMP) largely corrects for that effe~t.32-3~Coupled cluster (CCSDT) methods including single, double, and triple excitations using single reference restricted functions provide results close to the most accurate MR-CI ~ a l u e s . 1 ~ ~ ~ ~
-
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4667
Chemical Reactions and Density Functional Methods
TABLE VI: Geometries of Acrolein at Fixed Torsional Anglesa angle 180 MP2b LSD exptb 135 MP2b LSD transition MP2 (91.4)b LSD(91.5) 45 MP2b LSD 0 MP2b LSD exptb (I
C=C
CC
1.341 1.342 1.340
C
4
CHs
CH5
CH7
CHs
CCC
CCO
H&C
H5CC
H,C=C
H&C
1.471 1.462 1.468
1.226 1.222 1.214
1.087 1.102 1.090
1.084 1.099 1.080
1.086 1.101 1.084
1.111 1.129 1.113
120.5 120.1 120.4
124.0 124.2 124.0
121.0 120.4 119.7
122.3 122.3 122.2
122.5 122.9 122.4
115.0 114.5 114.7
1.340 1.340
1.479 1.470
1.225 1.221
1.087 1.102
1.084 1.098
1.087 1.102
1.110 1.127
119.9 119.7
123.0 122.7
121.1 120.9
122.1 122.0
121.8 121.7
115.8 116.0
1.336 1.335
1.494 1.488
1.224 1.217
1.086 1.100
1.084 1.099
1.089 1.103
1.108 1.127
122.2 123.0
123.3 123.5
121.7 121.5
121.5 121.3
121.0 121.0
116.3 115.9
1.339 1.340
1.481 1.473
1.226 1.221
1.086 1.101
1.089 1.099
1.088 1.103
1.108 1.127
120.7 120.5
124.0 124.5
120.4 119.8
122.0 121.9
121.3 121.2
115.5 114.8
1.340 1.341 1.340
1.481 1.474 1.478
1.227 1.223 1.215
1.085 1.102 1.098
1.084 1.099 1.081
1.087 1.101 1.088
1.107 1.125 1.106
120.8 120.3 121.5
123.9 123.8 124.2
119.9 118.7 118.5
122.1 122.3 121.5
121.7 122.0 121.1
115.9 115.7 115.8
Bond lengths in angstroms; angles in degrees. See ref 23.
TABLE Vn: Relative Energies for R o t a t i o ~of l Acrolein in kcal/mol at Various Torsional Angles in dee
SCHEME I
relative energy method
Oo
45'
ts
MP2/6-31G*" MP3/6-31 l++G**" MP3 + ZPE" expt" LSD/DZVP NLSD/DZVP LSD/TZVP++ NLSD/TZVP++ NLSD/TZVPP++ ZPE
1.5 2.2 2.2
3.3 3.7
8.2 7.1 6.6
2.3 2.1 2.2 2.2 1.9
5.2 4.6 4.4 4.3
+
135'
180°
3.3 2.9
0.0 0.0 0.0
4.3 3.8 3.8 3.6
0.0 0.0 0.0 0.0 0.0
I
J
11
I11
4-5
10.7 9.5 9.2 8.6 7.9
IV
V
TABLE VIII: Optimized Geometries for the NzH2 Isomers and Transition Structures'
See ref 23.
experimentalresults2' for the CC and CH bond lengths of ethyne radical of 1.215 and 1.07 1 A, respectively, are in good agreement with LSD results. Moreover, analysis of the electronic structure of ethyne radical indicates that the 5u bonding orbital has one electron less than corresponding orbital in acetylene. This should cause the weaker bond and the longer CC bond distance, as found in LSD calculations. Table V summarizes ionization and dissociation energies. As usual,lO",12 LSD energies overestimate binding energies (with exception of CzHz C2H + H+) and the NLSD method removes that discrepancy. The NLSD energiesof these reactions are, on average, within 2 kcal/mol of both G1 and experimental values. Therefore, the present study indicates that results obtained using Becke-Perdew nonlocal corrections are in good agreement with ab initio G1 values. C. Rotational Barrier of Acrolein. The geometries of acrolein, at fixed torsional angles, are presented in Table VI.
-
molecule I
I1
LSD
HFSb
MCSCF'
SCEP
1.216 1.067 124.5 RN-H 1.281 R N ~ - H , 1.080 R N , - H ? 1.122 R N : - H ? 1.365 OH,N,NI 121.1
1.197 1.083 124.7
1.233 1.028 123.2
1.268 1.094 1.136 1.364 120.9
1.219 e e 1.299 1.066 1.090 1.367 122.1
1.286 1.040 1.032 1.464 121.2
1.239 1.056 106.4 1.235 1.064 113.0 1.220 1.091 1.011 110.1 177.3
1.266 1.045 1.048 1.266 1.048 110.6 1.250 1.065 0.990 108.1 178.9
1.254 1.031 106.0 1.251 1.036 112.3 1.237 1.048 0.993 109.0 177.8
RN-N RN-H AH"
exptb
OH2N,N?
I11
IV
V
1.251 1.050 OH" 105.8 RN-N 1.245 RN-H 1.056 OH" 113.4 RN-N 1.233 R+H, 1.079 RN,-H? 1.006 6HIN,N? 109.5 eH2N2N, 177.4 RN-N RN-H
1.252 1.028 106.8
\
a Bond lengths in angstroms; angles in degrees. See ref 15. See ref 24b. See ref 24a. e The MCSCF structure is not of C2, symmetry, see ref 24b.
To compare results with MP2/6-31G* calculation, a basis set of DZVP quality has been used in our LSD calculations. An excellent agreement has been found between the MP2, LSD, and experimental results for bond distances and angles involving C and 0 atoms. C-H bond distances are overestimatedusing LSD methods, however, the relative differencesbetween various C-H bonds are reproduced well. The predicted torsional angle for the transition structure is 91.5O. This is in good agreement with 91.4O reported at the MP2 level. Table VI1 summarizes the energetics of rotations for acrolein. Larger basis sets and higher levels of correlation are important
for the cis-trans isomerization of acrolein. Wiberg and cow o r k e r ~have ~ ~ reported a barrier height of 6.6 kcal/mol. The LSD results lead to considerableoverestimation of the barrier by as much as 6 kcal/mol. Better basis sets, in particular, triple-f type, TZVP, improve the results. Further improvement can be achieved if the NLSD approach is used, although the change is not as substantial as that for the energetics of bond-breaking reactions.1°J2 Our best calculation has been obtained using the NLSD/TZVP++ approach with ZPE corrections. This type of basis set is comparable to the 6-3 1l++G** basis set used in MP3 calculations.23 The NLSD result of 7.9 kcal/mol is about 3.5
n/-
H,
Andzelm et al.
4668 The Journal of Physical Chemistry, Vol. 97,No. 18, 1993
predicted value of 1270 cm-I underestimates the experimental value by 110 cm-I. The predicted LSD frequenciesfor structures I1 and V (transition structures) are within 6% when compared with MCSCF results. The largest discrepancy may be observed for the asymmetric mode of isomer 11. The relative energies for the NzH2 structures with respect to the trans isomer aregiven inTableX. A~concludedpreviously,~~,~~ cis-diazene is slightly less stable by -5 kcal/mol than the trans structure. Transition state V for the trans-cis isomerization is about 50 kcal/mol higher than trans structure, in good agreement with results at the SCEP level of theory. The H2N=N (I) structure is higher in energy than the trans isomer (111) by 22 kcal/mol. The predicted relative energy for transition structure I1 is 70 kcal/mol. This is significantly lower than the results computed with MP4 or SCEPmethods. Although the NLSD approach improves agreement with correlated SCEP and MP4 results, the NLSD transition structures are still considerably lower than the current ab initio results. It remains to be seen if better treatment of correlation in ab initio calculations or the improvement in the nonlocal potentials can bridge that difference. Unlike energies of bond breaking,10x12'4 the LSD relative energies of various isomers are only slightly affected by the inclusion of the nonlocal corrections. There is only a small difference between HFS, LSD, and NLSD energetics for isomerization processes of diazene.
TABLE I X Vibrational Frequencies of N2Hz in cm-I molecule symmetry LSD HFS' MSCSFb expt" I
AI
2850 1704 1623 992 2743 1263
A2 BI
I1
A'
2882 2605 19533 1503 1319 652 3156 1635 1520 1276 3137 1291
A" 111
A, Au Bu
IV
AI
3078 1652 1270 1211 2967 1471 3812 2701 1691 1509i 1448 682
A2 BI
V
A'
A"
2704 1715 1621 998 2525 1258 2795 2465 19731' 1490 1329 733 3070 1636 1525 1256 3078 1298 3002 1639 1295 1230 2882 1479 3765 2538 1688 14833 1447 784
3253 1814 1611 1039 2868 1375 3082 2625 2 1863 1513 1330 574 3153 1663 1526 1351 3090 1374 3144 1535 1416 1267 3074 1616 3957 2876 1614 20751' 1536 684
3128 1583 1529 1286 3120 1322 2966 1558 1390 1259 2984 1439
Conclusion In the present paper we show that the density functional approach, as implemented in the DGauss program, can be used to study chemical reactivity. The nonlocal Hamiltonian of BeckePerdew has to be used and the localization of spin densities has to be allowed if a dissociation process is considered. Using this method, the potential curve of the CH4 dissociation has been reproduced by the density functional approach with accuracy close to MR-CI results. On the other hand, local and nonlocal energy functionals tend to overestimate the MR-CI N-N dissociation curve. The density functional energies of the C-H bond-breaking reactions for small hydrocarbon species compare well with those from the much more complicated G1 ab initio approach. The density functional geometries and vibrational frequenciesof isomers of diazene and isomers of acrolein compare well with those obtained using correlated ab initio methods. The, density functional energies of stable isomers and rotomers are close to correlated ab initio results, as well. However, the energetics of transition states are different and the NLSD approach does not change significantly in comparison with LSD results. The barriers for cis-trans reactions are underestimated for diazene and overestimated for acrolein as compard to both many-body or MCSCF ab initio results. A further investigation using a better nonlocal Hamiltonian and a better set of DGauss parameters is planned to assess the accuracy of density functional methods to study transition structures.
See ref 15. See ref 24b.
kcal/mol above the experimental data. Further systematicstudies are needed to verify whether this substantial overestimation of the rotational barrier is the result of the technique used (basis sets, grid selection) or the nonlocal density functional Hamiltonian (Becke-Perdew). D. N2H2Isomers and Transition Structures. Trans and cis isomerizationof diazene (NzH2) has been previously studied using both Hartree-Fock-Slater (HFS)IS and correlated methods.24 Structures I-V (see Scheme I) correspond to the isomers and transition structures reported in this study. In Table VIII, comparisons are made between different ab initio calculationsof the isomers and transition structures of NzH2. In the present work we use the LSD potential instead of the HFS (Xa)approach. Apparently, better density functional potential leads to improvement in the structural parameters when compared with experiment and ab initio correlated results. In particular, LSD N-N distances are within 0.015 A when compared to SCEP methods. In general, all theoretical methods overestimate the NH distance by0.014l.03 A. For trans-diimide, our LSD results overestimate the N-H bond distance by 0.022 A in comparison with experimental results. At all levels of theory, the predicted HNN angle is in good agreement with experiment. Table IX shows thevibrational frequenciesfor theN2H2 species. The calculated vibrational frequencies of isomers 111and IV are in good agreement with experimental frequencies, usually within 5%. The largest difference between theory and experiment corresponds to one of the A, frequencies (isomer IV). The LSD
TABLE X molecule
I I1 I11
IV V
Acknowledgment. The Corporate Computing and Networking at Cray Research is kindly acknolwedged for providing computational resources to carry out this work. We would like to thank Professor Ziegler for providing us with a copy of Dr Fan's thesis.
Calculated Relative Energies in kcal/mol for Isomen and Transition Structures of Mazene LSD NLSD HFS' HFb MP2b MP4b MCSCFC 21 66 0 5 46
22 70 0 5 49
20 67 0
20 89
28 78
26 78
0
0
0
4
7
6
6
46
See ref 15. See ref 11. See ref 24b. See ref 24a.
35 86 0 7 66
SCEPd 26 83 0 6 56
Chemical Reactions and Density Functional Methods
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