405
J. phys. Chem. 1902, 86, 485-488
Our final conclusion concerns the identity forbidden (in & ,c) bl, modes. Intensity disparities involving vibronic origins of these modes in p-c6H2D4(also blJ indicate that the bl, modes in p-C&D4 are rotated on going to the 'Bh, state. DR in p-C6H2D4can be understood if the hydrogen displacements in the C8H6mode v12 are increased in the excited state, though this conclusion is more tentative than
that drawn for the e,, modes because less data are available.
Acknowledgment. We are grateful to the National Science Foundation for support and to Mr. G. Ali Ozkabeck and Dr. Lucille Chia for critically reading the manuscript.
Restricted and Unrestricted Hartree-Fock Calculatlons on the Geometry of the Methyl Radlcal J. Pacansky IBM Research labmatmy, Sen Jose, Calhnb 95193 (Received: September 1. 1981)
Extensive restricted Hartree-Fock (RHF) calculations are reported for the ground-state potential energy surface for the methyl radical. The surface, formed by computing total energy as a function of pyramidal bending and symmetric stretching of the C-H bonds, clearly reveals that a planar structure corresponds to the m i n i u m energy. Both unrestricted Hartree-Fock (UHF) and RHF calculations using Gaussian-type orbitals give a nonplanar structure; however, calculations utilizing larger basis sets always obtain a geometry which is planar. These results accentuate the problems associated with basis sets that are "inadequate".
Introduction Although the methyl radical is the simplest alkyl radical found in nature, it has been a formidable task to determine whether the system is planar or nonplanar.' The experimental evidence for the structure comes from ESR,' electronic,2 and infrared s p e c t r o ~ c o p y . ~ ~ ~ The results of theoretical calculations for the structure have been somewhat confusing; several ab initio calculations have reported that the radical has a nonplanar-pyramidal-like structure>6 while others report a planar geometry.' In this report, we demonstrate that a planar structure is found for the methyl radical for both UHFand RHF-type calculations using large Gaussian-type orbital (GTO) basis sets with and without polarization functions. A nonplanar geometry is found only when the basis set is too small to be dependable for structural analysis.
Computational Details The contracted Gaussian-type orbital (CGTO) basis sets used for the calculations are listed in Tables I-IV. Two different types of CGTO basis sets were used for carbon and hydrogen. The first, a (4s,3p) and (3s) basis for carbon and hydrogen, respectively, are listed in Tables I and 11. The second is a larger (6s,4p,2d) and (4s,2p) basis for carbon and hydrogen; these are listed in Tables I11 and IV. All of the original uncontracted basis sets in Tables I-IV were taken from the compilation of Van Duijnevelt;* (1)L. Kaplan in "Free Radicals",Vol. 11, J. Kochi, Ed., Wiley, New York. 1973. -. ~ -- _ - -(2)G.Herzberg, R o c . R. SOC.London, Ser. A , 262,291 (1961);Can. J. Phys. 39, 1511 (1961). (3)D. E. Milligan and M. E. Jacox, J. Chem. Phys., 47,5146(1967). (4)L. Y. Tan, A. M. Winer, and G. C. Pimentel, J.Chem. Phys.,57, I
4028 (1972). (5) J. Dyke, N. Jonathan, E. Lee, and A. Morris, J. Chem. Soc., Faraday Trans. 2,72,1385(1976). (6)W. A. Lathan, W. J. Hehre, and J. A. Pople, J.Am. Chem. SOC., 93,808 (1971). (7)Y. Ellinger, F. Pauzat, V. Barone, J. Douady, and R. Subra, J. Chem. Phys., 72,6390 (1980). 0022-3654/82/2086-0485$01.25/0
TABLE I: (4s,3p) CGTO Basis Set for Carbon 1 exponent contraction coeff S
P
3047.421 10 457.687 20 104.195 90 29.356 26 9.360 54 3.188 80 0.528 30 0.162 07 9.464 52 2.006 58 0.546 94 0.151 97
0.001 832 0.014 005 0.068 332 0.229 482 0.463 426 1 .o 1 .o 1 .o 0.037 978 0.208 938 1.0 1.0
TABLE 11: (3s) CGTO Basis Set for Hydrogen 1 exponent contraction coeff S
13.013 372 1.962 496 0.444 569 0.121 953
0.019 678 1 0.137 952 0 1.0 1.0
the exponents for the polarization functions were those given by Roos and S i e g b a h ~ ~Tables .~ I-IV also list the contraction coefficients in addition to the orbital exponents. In order to make a comparison with the larger basis sets, calculations were also performed using the much smaller STO-3G basis set.1° The RHF calculations were performed by using the computer codes MOLECULE and A L C H E M Y . ~ ~ The UHF calculations were made possible with the availability of the computer code HONDO.'~ (8) F. B. Van Duijnevelt, IBM RJ 945 (1971). (9)B. Roo8 and P. Siegbahn, Theor. Chim. Acta, 17,199 (1970). (10)R.Ditchfeld, W. J. Hehre, and J. A. Pople, J. Chem. Phys.,64, 724 (1971). (11)The program M O ~ U L Ewaa written by J. Alml6f to compute the
molecular integrals. The SCF calculations used the ALCHEMY program developed by P. S. Bagus, B. Liu, A. D. McLean, and M. Ywhimine. (12)M. Dupuis, J. Rys, and H. F. King, J. Chem. Phys.,65,111(1976); M. Dupuis and H. F. King, zbid., 68,3998 (1978). 0 1982 American Chemical Society
488
The Journal of Physical Chemistry, Vol. 86, No. 4, 7982
TABLE V: Surface for Total Energy ( E ) Computed as a Function of e , the Pyramidal Bending Angle, and R,the Symmetric Stretching of the C-H Bond Lengthsa
TABLE 111: t6s,4p,2d) CGTO Basis Set for Carbon 1
TABLE
exponent
contraction coeff
27736.592 4143.516 2 939.514 0 264.795 24 85.778 961 30.667 350 11.818 056 4.866 884 2.096 878 0.678 103 0.262 973 0.102 594 51.723 308 12.339 664 3.772 243 1.324 869 0.505 457 0.198 268 0.077 314 1.2 0.2
0.000 117 0.000 912 0.004 787 0.019 857 0.067 684 0.182 120 1.0 0.377 588 0.146 235 1.0 1.0 1.0 0.002 734 0.018 979 0.080 810 0.227 778 1.0 1.0 1.0 1.0 1.0
Pacansky
0,
R,bohr
deg
radius
E , hartree
0
1.90 1.95 1.975 2.0 2.025 2.05 2.10 1.90 1.95 1.975 2.0 2.025 2.05 2.10 1.90 1.95 1.975 2.0 2.025 2.05 2.10 1.90 1.950 1.975 2.0 2.025 2.05 2.10 1.90 1.95 1.975 2.0 2.025 2.05 2.10 1.90 1.95 1.975 2.0 2.025 2.05 2.10 1.90 1.95 2.0 2.05 2.10 1.90 1.95 2.0 2.05 2.10 1.90 1.95 2.0 2.05 2.10
-39.565 039 53 -39.571 749 48 -39.573 673 64 -39.574 730 94 -39.574 981 41 -39.574 481 27 -39.571 436 42 -39.565 026 39 -39.571 740 45 -39.573 666 79 -39.574 726 28 - 39.574 978 99 -39.574 481 12 - 39.571 440 97 -39.564 986 11 -39.571 712 59 -39.573 645 29 -39.574 711 31 -39.574 970 68 -39.574 479 62 -39.571 453 45 -39.564 916 20 -39.571 663 09 -39.573 606 33 -39.574 683 12 -39.574 984 0 3 -39.574 473 59 -39.571 470 40 -39.564 812 55 -39.571 587 59 -39.573 545 35 -39.574 636 9 5 - 39.574 922 49 -39.574 457 87 -39.571 486 20 -39.564 669 57 - 39.569 241 00 -39.573 456 41 -39.574 566 36 - 39.574 870 86 -39.574 425 51 - 39.571 493 31 -39.564 236 87 -39.571 138 46 -39.574 319 0 5 -39.574 27549 -39 571 443 28 - 39.563 549 67 -39.570 56545 -39.573 863 71 -39.573 940 82 -39.571 231 77 -39.562 526 80 - 39.569 675 73 -39.573 110 32 -39.573 326 35 -39.570 758 08
1
2
IV: t4s,2p) CGTO Basis Set for Hydrogen 1
exponent
contraction coeff
82.636 374 12.409 558 2.823 854 0.797 670 0.258 053 0.089 891 1.1 0.2
0.002006 0.015345 0.075577 1.0 1.0 1.0 1.0 1.0
-
3
4
5
7
Figure 1. The angle, 0, for pyramidal blending and R = r l the symmetric stretching of the C-H bond lengths.
+ r 2 + r3,
For the RHF calculations, the potential energy surface was constructed as a function of molecular geometry by computing the total energy for changes in the C-H bond lengths, R and 0, the angle for pyramidal bending. Both R and 0 are defined in Figure 1. A Dahsymmetry was maintained for calculations involving the planar geometry, while the nonplanar geometries were constrained to a C,, geometry. Consequently, since all three C-H bonds were varied simultaneously, then R is a symmetric stretching of the C-H bonds. The geometry corresponding to the lowest total energy, E-, was located by fitting each potential curve for total energy as a function of R for a fixed value of 0. The geometry corresponding to Emi,for the UHF calculations was located by using the gradient method.', ~
~
~~~
(13) J. W. McIver and A. Komornicki, J. Am. Chem. Soc., 94, 2625 (1972).
9
11
The surface was calculated by using RHF methods and a (6s,4p,2d),t4s,2p) CGTO basis set for carbon and hydrogen, respectively. E,in = -39.57499324; Re = 2.0206.
Results and Discussion The highest quality results involve the RHF calculations with the (6s,4p,2d) and (4s,2p) CGTO basis sets for carbon and hydrogen, respectively. As a consequence, only the energy surface for this series of calculations is listed in this report. Table V contains the total energy for values of 0 which range from Oo to 1l0,and R from 1.95 to 2.10
The Journal of Physical Chemistry, V O ~86, . NO. 4, 1982
Geometry of the Methyl Radical
TABLE VI: Results of RHF and UHF Calculations for the Total Enernv and Geometrv for the Methyl Radical symmetry
R(C-H), A
RHF D,h 1.073 C(4s,3p);Ht3s) D,h 1.070 Ct6s,4p);Ht4s) Ct6~,4p,2d); Ht4~,2p) D,h 1.069
- 0.5700
-%tal*
hartree
487
r
- 39.541 226
-39.555 843 -39.574 993
ZJHF ____
STO-3G
C,,
Dlh Ct4s,3p); Ht3s) C t 4 ~ , 3 p , l d )H; t 3 ~ , l p ) D l h
1.081 (tHCH = 118") 1.076 1.076
-39.077 002
- 39.544 561 -39.562 391
bohr radii. The lowest total energy, E ~= n -39.57499324 hartree, is found for a planar geometry with the C-H bond lengths at 2.021 bohr radii. Table VI lists the results of the RHF and UHF calculations for the total energy and geometry of the methyl radical using the various basis sets. For the RHF calculations, the total energy decreases significantly from that for the C (4s,3p), H (3s) basis set, -39.541 226 hartree, to -39.574993 hartree for the C(6s,4p,2d), H(4s,2p) CGTO. While the geometry is found to be planar for all of the RHF calculations reported here, the C-H bond length decreases slightly as the size of the basis set increases; this is a consistently observed for SCF calculation^.^^ The RHF calculations reported here should be compared with those reported by Dyke and co-workers6 where, using a much smaller STO-6G basis set, they computed a total energy of -39.447936 hartrees; they found a nonplanar geometry with an out-of-planebending angle of 8.7', a C-H bond length at 1.117 A. RHF calculations have also been reported at the STO-3Ge level where, again, a nonplanar geometry is found. Consequently, RHF calculations using small, inadequate CGTO basis sets give a nonplanar geometry for the methyl radical; this must be an artifact of the incomplete basis set at the SCF level because the calculations reported here using a number of different, more complete basis sets, with or without polarization functions incorporated, always give a planar geometry. Since a planar geometry is also obtained by using calculations at a more sophisticated CI level', then it seems clear that theory requires that the methyl radical be planar. The UHF calculations follow the same trend as the RHF calculations. As shown in Table VI, the total energy decreases from -39.077 002 hartree for the STO-3G calculation to -39.562 391 hartree for the C(4s,3p,ld), H ( 3s,lp) CGTO basis. The opimized geometry found for STO-3G basis is nonplanar, while planar geometries are computed by using the C(4s,3p), H(3s) and C(4s,3p,ld),H(3s,lp) CGTO basis seta, respectively. The C-H bond lengths are slightly longer than those computed at the RHF level but nevertheless are typical for ethylenic-type C-H bonds in an sp2 electronic configuration for carbon. Figure 2, an instructive curve is shown for total energy vs. 8, the pyramidal bending angle with the C-H bond length constrained at the equilibrium value, 1.069 A. The curve was obtained by using the RHF calculations and the C(6s,4p,2d), H(4s,2p) basis set. The total energies thus calculated are listed in Table VII. For changes in 8 from - 5 O to 5O, the potential curve changes by only lo4 hartree; changes in 8 greater than 5 O are characterized by much larger changes in total energy. In essence, the dynamic (14)U.Walhgren, J. Pacansky, and P. S. Bagus, J . Chem. Phys., 63, 2874 (1975);P. S. Bagus, U. Walhgren, and J. Pacansky, ibid., 67, 618 (1977).
-15
-10
0 0 (degree)
-5
5
10
15
Flgwe 2. The potential curve for pyramidal bendlng. Only the angle, 8,for pyramidal bending was varied; the C-H bond lengths were held fixed at 2.021 bohr radll. The total energies are listed in Table V I I .
TABLE VII: Total Energy Computed by Using RHF Calculations with the C(6s,4p,2d) and Ht4s,2p) CGTOa
e, deg energy, hartree 0 -39.574 993 24 1 2 3 4 5
6,
deg
7 9 11 13 15
- 39.574 990 58
-39.514 980 96 -39.57496191 - 39.574 928 14 -39.574 873 1 2
energy, hartree - 39.574 665 37
-39.574 259 34 -39.573 562 82 -39.57247763 - 39.570 904 89
The C-H bond lengths were constrained at their equilibrium value, 1.069 A . TABLE VIII: Gross Atomic Population Analysis for the 'A," State of CH, at R(C-H) = 2.025 bohr radii"
E , liartree
1
(la,')'
-11.222 496
s P d sum
(2a,')'
-0.904205
s
P d sum ( w ) 4
-0.577059
s
P d sum (2a'")
-0.374181
s
P d sum
carbon hydrogen
2.000 0.000 0.000 2.000 1.236 0.000 0.018 1.254 0.000 1.952 0.028 1.980 0.000 0.957 0.000 0.957
0.000 0.000 0.000 0.000 0.702 0.044 0.000 0.746 1.974 0.046 0.000 2.020 0.000 0.043 0.000 0.043
total
2.000 0.000 0.000 2.000 1.938 0.044 0.018 2.000 1.974 1.998 0.028 4.000 0.000
1.000 0.000 1.000
E b t d = - 39.57498141. RHF calculations using the Ct6s,4p,2d), Ht4s,2p) CGTO.
picture for the pyramidal bending of the methyl radical by the RHF calculations is characterized by a planar geometry located at a flat minimum on the potential curve that allows pyramidal distortion to readily occur. The results for the molecular orbital energies and gross Mulliken population analysis for the 2 A c state of the methyl radical are listed in Table VIII. These were a result of the RHF calculations using the C(6s,4p,2d) and H(4s,2p) CGTO basis sets. The salient features for the molecular orbital energies and population analysis are that the unpaired electron is located in a carbon 2p orbital with very little contribution from the hydrogens and that va-
4aa
J. Phys. Chem. 1982, 86,400-494
lence electronic transistors are most likely to occur from the le’ orbitals, i.e., the C-H bonds, to the half-filled 2a[ orbital.
Concluding Remarks Extensive RHF calculations using a large CGTO basis set indicate that the equilibrium geometry for the methyl radical is planar. This was clearly shown by computing an extensive part of the potential surface for changes in
the pyramidal bending angle and C-H bond lengths. The calculations also reveal that the theoretical predictions for the geometry of the methyl radical, at least using SCF methods, are not dependable when small basis sets are employed. Another possible source of confusion over the geometry of the methyl radical results from the analytical fitting of the very flat potential surface about the planar geometry. An extensive surface should be calculated and carefully fitted to obtain the correct equilibrium geometry.
Structures and Reactions of H,O+, H20, and OH on an Fe Electrode. Potential Dependence Alired
B. Anderson’ and N. K. Rayt
Chemisby Department, Case Western Reserve University, Cleveland, ohlo 44 106 (Received: September 1, 198 1)
An atom superposition and electron delocalization molecular orbital study has been made of the adsorption and reaction of single HsO+, H20, and OH molecules on an Fe5model of an iron electrode over a potential range of 4 V. Changes in electrode potential are simulated by shifting the Fe valence band by means of increases or decreases in Fe atom ionization potentials. Over a range of about 2 V, conditions are identified corresponding to H30+or H 2 0 reduction at the cathodic end of the range and OH oxidation at the anodic end, corresponding to first steps in H2 and O2formation. Throughout the intermediate range H20 is found to dehydrogenate, creating a surface OH layer which becomes increasingly more stable and positively charged as the potential goes anodic (eventually being oxidized to form FeO, or 02).This OH layer corresponds to initial stages of anodic passive film formation on iron.
Introduction The confluence of surface science and electrochemical techniques and molecular orbital theory is bringing understanding of molecular processes at electrode sufraces. The focus of this paper is a theoretical molecular orbital study of the chemistry, structures, and reactions of the hydronium ion (H30+),water, and hydroxyl species (OH, OH+, OH-) on the Fe(100) electrode surface. We relate our results to the experimental electrochemical and corrosion-passivation literature. Of particular note are our following results: (i) H30+ is easily reduced and dehydrogenated a t cathodic potentials to form adsorbed H + H20; (ii) H20 is easily dehydrogenated at all potentials to form adsorbed H + OH; (iii) OH is increasingly stable at anodic potentials, favoring formation of a stable [FeOHId+ species a t the surface. Several recent studies have been made already of water adsorbed to iron surfaces at the monolayer level in ultrahigh vacuum systems. Roberts and Wood,’ Dwyer, Simmons, and Wei? and Akimov3 have seen with XPS and Auger spectroscopies the formation of OH from water via dehydrogenation. Akimov further saw the reversible reaction 0 + H 2 0 * 20H on iron. With molecular orbital calculations, Anderson4 has produced probable reaction mechanisms and energetics for the above processes and for OH dissociation on iron and platinum surfaces. Electrochemical processes a t iron electrodes are well studied at the macroscopic level, but little is known of the electrode surface chemistry at the atomic level. The point of this paper is to address the latter topic and relate our theoretical results to what is suspected to happen at the ‘On leave from Department of Chemistry, University of Delhi, Delhi-7, India. 0022-3654/02/2086-0488$01.25/0
molecular level and is known to happen at the macroscopic level. A good review of many aspects of iron electrode chemistry in various aqueous solutions is in the work by S a b 5 Our discussion is restricted to average and typifying results; examples of effects of changing pH or iron concentrations on compositions may be found in ref 5. Generally, in neutral pH 7 water oxidation of an iron electrode is very slow over an anodic potential range of 0-1.2 V (relative to the normal hydrogen electrode). At around 1.2 V O2 evolution also commences at the electrode surface. At a cathodic potential of around -0.65 V H2 evolution commences. There is intense interest’-* in the nature of the “passive film” characterizing the iron electrode surface in the passive region, 0-1.2 V. It is generally believed5-*that an OH surface layer on iron plays some role in the formation of the passive film. In electrode surface electroreflectance studies Kolotyrkin and co-workers6show H 2 0 or OH oxygen-to-iron electron charge-transfer excitations decrease in energy as the electrode is made more anodic in the passive range. Stepina and 10fa7have, through tempera(1)M. W. Roberta and P. R. Wood, J . Electron Spectrosc. Relat. Phenom., 11, 431 (1972). ( 2 ) D. J. Dwyer, G . A. Simmons, and R. P. Wei, Surf. Sci., 64, 617 (1977). (3)A. G.Akimov, Elektrokhimiya, 15, 1510 (1979). (4) A. B. Anderson, Surf. Sci., 105, 159 (1981). (5)N.Sat0 in ‘Passivity of Metals”,R. P. Frankenthal and J. Kruger, Ed., Electrochemical Society, Princeton, 1978. (6) Ya. M. Kolotyrkin, R. M. Lazorenko-Manevich, L. A. Sokolova, and V. G.Plotnikov, Elektrokhimiya, 14,344 (1978). (7)T.G.Stepina and Z. A. Iofa, Elektrokimiya, 16,888 (1980). (8)N.H.Turner, R. 3. Colton, and J. S. Murday, “Oxidationof Iron by 02, H20and a 0 2 / H 2 0 Mixture”, Naval Research Laboratory Summary Abstract, unpublished.
0 1982 American Chemical Society
