3168
J. Phys. Chem. 1987, 91, 3168-3171
Ab Initio Molecular Orbftal Calculation of the HONO Torslonal Potential J. A. Darseyt and Donald L. Thompson* Department of Chemistry, Oklahoma State University, Stillwater. Oklahoma 74078 (Received: July 28, 1986)
Ab initio SCF-MO calculations were performed to obtain a torsional potential function for the HONO molecule. Calculations were made for the cis and trans conformations with the STO-3G, 4-31G, 6-31G, 4-31G*, and 6-31G** basis sets. Complete geometry optimization was carried out within each basis set. It was found that the 4-31G basis set provided values for the geometry and energies closest to the experimental results. The trans-cis isomeric energy difference was calculated to be -0.642 kcal/mol and the energy barrier to rotation from trans to cis was found to 9.68 kcal/mol; the comparable experimental energies are -0.6 and 9.7 kcal/mol, respectively. Completely optimized geometries using the 4-3 1G basis set were used to calculate a detailed torsional potential. These points were fit with a cosine series.
Introduction We report here an a b initio study of the H O N O torsional potential. The purpose of the work was to obtain an accurate analytical potential function for the cis-trans conversion. The approach taken in this work was to perform a series of ab initio self-consistent field (SCF), Hartree-Fock (HF) level calculations of the torsional potential about the ON bond in the HONO molecule. Previous studies on this molecule have shown a large dependence of this potential on the choice of the level of approximation, with values ranging from +18.6 to -10.5 kJ/mol for the difference in energy between the trans and cis isomeric states.' Studies of other molecular systems have also found this effect .2 When performing a b initio calculations it is necessary to determine the best level of approximation to use to obtain the greatest degree of accuracy within a reasonable computational time frame. There are two general choices one can make. One can use a basis set with a high degree of flexibility or one can incorporate into the calculation a large number of configurations (CI). Increasing the basis set size and using C I are not equivalent, thus, a combination of the two is a third possibility. As the flexibility of basis sets increases or as the number of configurations become larger, an increasing amount of computer time is required. This increase in time, however, does not always result in a proportionate increase in a c c ~ r a c y . ] ~ Another ~-~ important question which must be addressed concerns the choice of geometry. A common choice is to use an experimentally determined geometry.6 Another possibility is to optimize the geometry of the molecule with a lower level approximation, then use this geometry in higher level calculations.'*2 The advantage of this procedure is that it saves computational time. A third possibility is to perform a full geometry Optimization at the same level of approximation as used in all calculations. This choice is usually impractical unless accuracy can be achieved with a reasonably low level approximation and the number of geometrical parameters being optimized is small. In the present work, these latter conditions predominate and therefore this was the course pursued. Computational Procedure Calculations were performed initially with basis sets of increasing flexibility, that is, STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G**. Within each basis set, the geometries were completely optimized at the trans and cis isomeric conformations. In addition, the difference in energy between the trans and cis conformation was determined. A summary of these calculations can be found in Table I. From Table I, it can be seen that the 4-31G basis set gives the only relative energy within experimental error for the trans-cis isomeric energy difference. Similar findings were reported by Murto et al.s but seem to differ somewhat from Turner.l In addition, both the magnitude and trends in the change in mag'Permanent address: Department of Physical Sciences, Tarleton State University, Stephenville, TX 76402.
0022-3654/87/2091-3 168$01.50/0
nitude of bond lengths and bond angles agree very well with the experiment. Finally, a calculation using the 4-31G basis set was used to determine the magnitude of the energy barrier between the trans and cis conformation. This number was calculated to be 9.68 kcal/mol in very close agreement to the value 9.7 f 0.7 kcal/mol experimentally determined by Hall and PimenteLg We therefore chose the 4-31G basis set to perform all subsequent calculations in our determination of a complete torsional potential of HONO. An advantage in this choice is that a complete geometrical optimization of all bond lengths and bond angles can be performed at each rotational angle, totally consistent within itself; that is, energies and geometries are all calculated with the 4-31G//4-31G basis set. In the next section, we will show why this is important. Calculations were made, using complete geometry optimization, at increments of 10'. In the vicinity of the barrier, the increment was decreased to 1'. Each of these runs required approximately 45 to 75 min of CPU time on a VAX11/780 computer. A plot of the results is shown in Figure 1. In addition, plots were made of the change in the various bond lengths and bond angles as a function of dihedral angle. This information is summarized in Table I1 and in Figures 2 and 3. Table I11 is a listing of the total energies in hartrees and relative energies in kcal/mol for the dihedral angles calculated.
Results and Discussion There have been several theoretical and experimental studies of the HONO p ~ t e n t i a l . ' ~ ~In~ 'this ~ ' ~study, we have carried out calculations to obtain an accurate analytical potential for the torsional motion. Previous ab initio calculations are not sufficient to accurately define the potential as a function of the dihedral angle. Therefore, we have undertaken this work to obtain an accurate analytical representation of the torsional potential. The accuracy of the results of ab initio SCF-MO calculations depends upon the level at which the calculations are p e r f ~ r m e d . ~ * ~ ~ ~ There are several recent papers which have used a variety of basis
(1) Turner, A. G. J . Phys. Chem. 1985, 89, 4480. (2) Rao, B. K.; Darsey, J. A.; Kestner, N . R. J. Chem. Phys. 1983, 79, 1377. (3) Hehre, W. J.; Radom, L.; Schleyer, P. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (4) Present work. ( 5 ) Murto, J.; Rasanen, M.; Asplala, A,; Lotta, T. J . Mol. Struct. 1985, 122, 213. ( 6 ) Darsey, J. A,; Rao, B. K. Macromolecules 1981, 14, 1575. (7) Finnigan, D. J.; Cox, A. P.; Brittain, A. H. J. Chem. SOC.,Faraday Trans. 1972, 68, 548. ( 8 ) Cox Peter, A.; Brittain, A. H.; Finnigan, D. J. J. Chem. SOC.,Faraday Trans. 1971, 67, 2179. (9) Hall, R. T.; Pimentel, G. C. J. Chem. Phys. 1963, 38, 1889. (10) Mcgraw, G. E.; Bernitt, D. L.; Hisatsune, I. C. J Chem. Phys. 1966, 45, 1392.
(11) Benioff, P.; Das, G.; Wahl, A. C. J. Chem. Phys. 1976, 64, 710. (12) Skaarup, S.; Boggs, J. E. J. Mol. Struct. 1976, 30, 389. (13) McDonald, P. A,; Shirk, J. S . J . Chem. Phys. 1982, 77, 2355.
0 1987 American Chemical Society
MO Calculations of HONO Torsion Potential
The Journal ofPhysica1 Chemistry, Vol. 91, No. 12, 1987 3169
TABLE I: Geometrical Parameters and Energies for Various Basis Sets STO-3G 0.9948 1.0009 1.4153 1.4020 1.2247 1.2270 10 1.4700 103.9011 108.2907 110.2589 -201.9156 -201.9155 -0.0935
H-O(trans)" H-O(cis) 0-N(trans) 0-N(cis) N=O(trans) N=O(cis) HON(trans)b HON(cis) ONO(trans) ONO(cis) energy(trans)' energy(cis) El,,", - EElsd
4-31G 0.9539 0.9646 1.3995 1.3776 1.1665 1.1773 107.9078 111.6141 11 1.3763 1 13.9447 -204.31 19 -204.3109 -0.6419
6-31G 0.9532 0.9640 1.3873 1.3676 1.1712 1.1818 108.4138 112.1547 111.5933 114.0230 -204.5219 -204.5206 -0.8321
4-31G* 0.9514 0.9604 1.3482 1.3280 1.1513 1.1591 105.2391 107.408 1 111.3293 113.7377 -204.4436 -204.4461 +1.5776
6-31G* 0.9508 0.9596 1.3468 1.3277 1.1532 1.1611 105.3721 107.5962 111.3648 113.7499 -204.6376 -204.6399 +1.4194
6-3 IG*
exptc
0.9469 0.9553 1.3456 1.3263 1.1533 1.1614 105.5637 107.7999 111.3973 113.7361 -204.6440 -204.6462 +1.3471
0.958 0.982 1.432 1.392 1.169 1.186 102.1 104.0 110.7 113.6 -0.51 i 0.2
'All bond lengths are in angstroms. bAll bond angles are in degrees. cTotal energies in hartrees. dRelative energies of E,,,,, - E,,, in kcal/mol. dReference 7 for geometries; ref 8 for relative energy.
TABLE 11: Trans, Cis, and Barrier-OptimizedGeometries for the 4-31G Basis Set @J= d= d= % % ISO(trans) O(cis) 85(barrier) Ale A2d H-0" 0.9539 0.9646 0.9602 +1.12 +0.66 1.3995 1.3776 1.4491 -1.56 +3.54 0-N 1.1773 1.1632 .+0.93 -0.28 N=O 1.1665 H O N b 107.9078 111.6141 110.6829 +3.43 +2.57 ON0 111.3763 113.9447 111.8808 +2.31 +0.45 "Bond lengths in angstroms. bBond angles in degrees. CThepercent difference between trans and cis conformation. dThe percent difference between trans and barrier conformation.
TABLE 111 Energy as a torsion angles, deg 00.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 85.00 90.00 100.00 1 1 1.oo 120.00 130.00 140.00 150.00 160.00 170.00 180.00
Function of Torsion Angle total energy, relative energies, kcal/mol hartrees 0.641 941 707 -204.310891 5 0.986 004 892 -204.3 I O 343 2 -204.308 802 1 1.953059012 3.372 672 622 -204.306 539 8 5.014 361 668 -204.303 923 6 6.639 860 982 -204.301 333 2 8.040 586 572 -204.299 101 0 9.059410 184 -204.297 477 4 9.599569931 -204.2966166 9.676 126 029 -204.296 494 6 9.622850515 -204.296 579 5 9.141 049 105 -204.297 347 3 8.209 135489 -204.298 832 4 6.918 851 483 -204.300888 6 5.396 765 653 -204.303 3 14 2 3.799 504 244 -204.305 859 6 2.302 330 521 -204.308 245 5 1.079 252729 -204.310 1946 0.278 802 249 -204.311 4702 -204.311 9145 0.000 000 000
1 1.40 *44*
I
1.361
1.170
r t
DIHEDRAL ANGLE (degrees) Figure 2. Plots of bond length in angstroms as a function of dihedral angle: (a) H - 0 bond length; (b) 0-N bond length; (c) N=O bond length.
1061 0
I
60
I
120
I
180
DIHEDRAL ANGLE (degrees) Figure 3. A plot of bond angle as a function of dihedral angle': curve a is the H-0-N bond angle; curve b is the 0-N=O bond angle. I
0
1
50
100
150
200
250
300
350
DIHEDRAL ANGLE (degrees)
Figure 1. A plot of the relative energy in kcal/mol as a function of dihedral angle. Circles are the calculated values and the solid curve is the analytical function which best fits the points.
sets a n d incorporated various levels of CI t o calculate t h e HONO torsional p o t e n t i a 1 . l ~ T ~ h e r e is, however, disagreement a s t o t h e best level t o use in performing these calculations. As a first step in this work we have considered six different basis sets, which a r e summarized along with experimental values in T a b l e I. C o m p l e t e optimization of all geometrical parameters
3170 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987
was performed within each basis set calculation. A comparison was made to experiment for each optimized calculation. It can be seen hat the results calculated by using a 4-31G//4-31G basis set gave much closer overall agreement with experiment than any of the other basis sets used. For example, the 4-31G basis set calculated the bond lengths of the H-O(trans), H-O(cis), O-N(trans), 0-N(cis), and N=O(trans) closer to the experimental values than any of the other five basis sets. The average deviation from experiment for all bond lengths for the 4-31G basis set is only 0.55%. For the same respective bond lengths of the other five basis sets, the deviation is 2.41%, 0.61%, 1.11%, 1.10%, and 1.30% for the STO-3G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets, respectively. Although the minimal basis set STO-3G gave the largest average percent error, among the split valence basis sets the 6-3 lG** gave the highest average percent error. In fact, the 6-31G** basis set gave the highest overall percent error among all the split valence basis sets for all bond length calculations. The only bond length calculated closer to the experimental value than that calculated by the 4-31G basis set was the N=O(cis) calculated by using the 6-31G basis functions. This bond length was calculated within 0.35% of experiment compared to 0.73% calculated by using the 4-31G basis set. The average percent error for the bond angles for the 4-31G basis set was 3.47% fc the angles HON(trans), HON(cis), ONO(trans), and ONO(cis), compared to 1.46%, 3.79%, 1.77%, 1.85%, and 1.95% for the STO-3G, 6-31G, 4-31G*, 6-31G*, and 6-31G**, respectively. It is possible that the experimentally determined geometry is in error since we obtain closer agreement using the smaller basis sets. The 4-3 1G basis set gives closer agreement with the experimental bond lengths, but is about 1.9% "less accurate" on average when used to calculate bond angles. However, an error of 1.O% in the calculation of the N=O bond length, for example, leads to an error of about 160 cal/mol in the calculation of the energy, but an error of 1.O% in the calculation of the O N 0 bond angle leads only to an error of about 30 cal/mol. The 4-31G basis set allows the least amount of error in the energy calculation due to variation of geometry. In this study, the most important criteria for accuracy is the calculation of the (trans-cis) conformational energy difference and the energy barrier to rotation from trans to cis. The experimental value to the trans-cis energy range from -372 cal/mol13 to -600 cal/mol,I where the trans conformation is the minimum-energy structure. As can be seen from Table I, the basis set which calculates a value closest to the experimental one is the 4-31G. In fact, even when a very large basis set is used along with fourth-order corrections to the energy (MP4), the value calculated for the energy difference (trans-cis) is not as close as that obtained with 4-31G.' The energy barrier to rotation was also calculated. A complete geometry optimization was performed for this barrier geometry with the 4-31G basis set. This barrier was found to be located at C$ = 85' with an energy value of 9.68 kcal/mol above the trans conformation. This barrier has been found experimentally to have a height ranging from 8.7 to 13.9 k ~ a l / m o l .The ~ position of the barrier has been estimated to be at 88'.14 These results, along with the minimized geometry at the trans, cis, and barrier conformations are summarized in Table 11. Again, it can be seen that using a 4-31G basis set produces values in very good agreement with experiment. Figure 1 shows the results of calculations of the torsional potential using a 4-31G//4-31G basis set. The circles represent the calculated values. The calculation was performed at IO' intervals except in the vicinity of the barrier where the interval was 1'. The absolute energies in hartrees along with the relative energies in kcal/mol are presented in Table 111. The curve through the points is the best fit by a cosine series I
5
E($) =
C I
=o
ai cos (i&)
(14) Jones, L. H.; Badger, R. M.; Moore, G. E. J . Chem. Phys. 1951.19, 1599.
Darsey and Thompson TABLE IV: Fourier Exaansion Coefficients i ai,kcal/mol 5.096 2200 0.602 824 0 -4.648 248 0 -0.266 900 6 -0.124351 1 -0.0135105
Computed values for the expansion coefficients a, are given in Table IV. Figures 2 and 3 are plots of the variation of the geometrical parameters as a function of dihedral angle. Figure 2a is the H-O bond length. It decreases continuously from a maximum of 0.9646 A to a minimum of 0.9539 8, as the dihedral angle changes from 0 to 180'. Figure 2b is the variation in the 0 - N bond length. It changes from a minimum value of 1.3776 A at 4 = 0' to a maximum of 1.4497 8, at C$ = 90'. The value at the trans conformation is 1.3995 A, about halfway between these values. Figure 2c is the change in the N=O bond length as a function of the dihedral angle. It possesses a minimum of 1.1621 A at C$ = 110. The value at C$ = 180 is 1.1665 8,. Note that the bond length for 0-N is shorter than would be expected in the minimum energy conformation (1.453 8, in NH,OH), indicating some probable double bond character. In addition, the large variation in this bond length indicates the influence of delocalization in the planar conformations which is probably responsible for the energy barrier being higher than would be expected for rotation about a single nitrogen-oxygen bond. Notice also that the N=O is shortened in proportion to the N - O bond lengthening. This tends to support the hypothesis of delocalization of the 7~ electrons. Similar results were also reported by Skaarup and Boggs.I2 Figure 3 depicts the change in the two bond angles H O N and ONO. Two features are noteworthy. First, both angles increase as the geometry changes from the trans to the cis conformation. The increase is greatest in the area of the barrier maximum, as would be expected. However, note that the 0-N=O bond angle has a maximum at about 40', whereas the H-0-N bond angle continues to increase. It has been suggested that this may be due to an attractive interaction between the hydrogen and the N=O oxygen as the molecule is rotated into the cis conformation.' This is also supported by calculations currently in progress by the authors. It should be noted that Table I1 contains a summary of some of this information along with a calculation of the percentage change in all bond lengths and bond angles for the trans, ciis, and barrier conformations of the HON=O molecule. A great deal of emphasis was placed on optimizing the geometry within every level of calculation. It is known that if the geometry is optimized in one basis set and then calculations are performed in another, first derivatives of the potential energy may not be minimized. This problem is particularly acute when very large or very small energy differences are being calculated. For example, when we calculated the isomeric energy difference between trans and cis for HONO, the value obtained, using a STO-3G basis set in which the geometry was optimized with a 6-31G* basis set, was +4.45 kcal/mol. This predicts that the cis conformation is much more stable than the trans conformation. However, when the same calculation was performed using a STO-3G optimized geometry, the value obtained was about -0.10 kcal/mol. The calculation using the STO-3G optimized geometry correctly predicts that the trans is more stable than the cis, although less than is found experimentally. Similar results were found with other combinations of basis sets. The purpose of this study was to obtain an analytical potential function describing the cis-trans isomerization. We have used low-level Hartree-Fock calculations to calculate the torsional potential. Hartree-Fock level calculations have been widely used to calculate barriers to internal r o t a t i ~ n . ' ~While more accurate results than those presented here could be obtained with high( 1 5 ) Payne, P. W.; Allen, L. C . In Applications of Electronic Structure Theory, Schaefer 111, H . F., Ed.; Plenum: New York, 1977; p 29.
J. Phys. Chem. 1987, 91, 3171-3178 er-level HF calculations, we have carried out calculations at the 4-31G level with full geometry optimization. The results obtained are in good accord with the experimental data. The approach used is a reasonable compromise to obtain a reasonably accurate analytical torsional potential function for this molecule. We have obtained good agreement with experimental geometry parameters as well as with the measured values for the barrier. As pointed out above, it is possible that the computed geometry may not be
3171
accurate since we did not include polarization-type functions in the calculations. If so, then the experimental geometry is in error.
Acknowledgment. The authors thank Mr. B. G. Sumpter and Ms. Gillian Lynch for helpful discussions. This work was supported by the US.Army Research Office. Registry No. HONO, 7782-77-6.
Electronic States and Nature of Bonding of the RuC Molecule by Ait-Electron ab Initio HF-CI Calculations and Equilibrium Mass Spectrometric Experiments Irene Shim,* Department of Chemical Physics, Chemistry Department B, The Technical University of Denmark, DTH 301, DK-2800 Lyngby, Denmark
Heidi C. Finkbeiner, and Karl A. Gingerich* Department of Chemistry, Texas A& M University, College Station, Texas 77843 (Received: September 1 1 , 1986; In Final Form: February 5, 1987)
In the present work we present all-electron ab initio Hartree-Fock (HF) and configuration interaction (CI) calculations of 28 electronic states of the RuC molecule. The ground state of the RuC molecule has been determined as a 3A state. The molecule has two low-lying excited states, '2+and 'A. The electronic structure of the RuC molecule has been rationalized in a simple molecular orbital picture. The electronic spectra observed by Scullman and Thelin have been assigned as transitions between the 3A ground state and two close-lying excited states of 311and 3+ symmetry. The chemical bond in the RuC molecule is a triple bond composed of two x bonds and one u bond. The 5s electron of Ru hardly participates in the bond formation. It is located in a singly occupied nonbonding orbital. The chemical bond is polar with a charge transfer of 0.27e from Ru to C in the 3A ground state at the internuclear distance 3.09 au. Mass spectrometric equilibrium measurements over the temperature range 2086-2770 K have resulted in the selected dissociation energy Doo = 146.3 rl: 2.5 or 612.1 i= 10.5 kJ mol-' for RuC(g).
Introduction Platinum metals and platinum metal alloys are essential components of catalytic converters and also of catalysts for the important industrial processes of petrol refining as well as of coal gasification and liquefaction. In the action of such catalysts with carbon-containing gases the bond formation between the platinum metal and the carbon must play an important role. The knowledge of the nature of the bond between carbon and the metal in the smallest possible unit, namely the diatomic platinum metal carbide molecule, should therefore be of considerable basic scientific and also applied technological interest. In continuation of our theoretical and experimental investigations of diatomic carbides,'" we present here our detailed results for the RuC molecule. Reviously, the RuC molecule has been studied experimentally in optical s p e c t r o ~ c o p yand ~ ~ ~the dissociation energy of the molecule has been derived from high-temperature, mass spectrometric equilibrium measurements.@ Both the optical spectra (1) Shim, I.; Gingerich, K. A. J . Chem. Phys. 1982, 76, 3833. (2) Shim, I.; Gingerich, K. A. J . Chem. Phys. 1984, 81, 5937. (3) Shim, I.; Gingerich, K.A. Sur!. Sci. 1985, 156, 623. (4) Scullman, R.; Thelin, B. Phys. Scr. 1971, 3, 19. (5) Scullman, R.; Thelin, B. Phys. Scr. 1972, 5, 201. (6) McIntyre, N. S . ; Auwera-Mahieu, A. Vander; Drowart, J. Trans. Faraday SOC.1968, 64, 3006. (7) Auwera-Mahieu, A. Vander: Peeters R.; McIntyre, N. S . ; Drowart, J. Trans. Faraday SOC.1970, 66, 809.
0022-3654/87/2091-317 1$01.50/0
TABLE I: Relative Energies (ir au) of the Lowest Lying Terms Originating from Different Orbital Configurations of the Ru Atom and Also of the Lowest Lying Terms of the C Atom'
state Ru 5F(4d)7(5s)' Ru 5D(4d)6(5s)2 Ru 3F(4d)8 c 3P(2s)2(2p)2 C lD(2~)~(2p)~ c IS(2s)2(2p)2
calcd
exptP
0.0000
0.0000
0.0458 0.0831
0.0319 0.0401
0.0000
0.0000
0.0573 0.1393
0.0463 0.0985
'The calculated energies are results of HF calculations. bCenter of gravity of each multiplet has been calculated from the data of Moore, C. E. Nutl. Bur. Srand. Circ. No. 467, 1952 and 1958, Vol. 1 and 3. and the dissociation energy of RuC have been reviewed by Huber and Herzberg.Io However, the available experimental data have given rise to only very limited information about the RuC molecule. Thus, the optical spectra4v5were too complex to be assigned, and the dissociation energy derived from the mass spectrometric data were in all cases based on third law evaluations of limited measurements utilizing estimated molecular constant^.^-^ In the present investigation we have performed all-electron Hartree-Fock (HF) and configuration interaction (CI) calcula(8) Gingerich, K. A. Chem. Phys. Letr. 1974, 25, 523. (9) Gingerich, K. A.; Cocke, D. L. Inorg. Chim. Acta 1978, 28, L171. (10) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979.
0 1987 American Chemical Societv
