JOURNAL O F T H E A M E R I C A N CHEMICAL SOCIETY Regislned i n U.S. Patent Ofice.
@ Cogyrighl, 1971, b y the Amnican Chemical Society
VOLUME93, NUMBER 2
JANUARY27, 1971
Physical and Inorganic Chemistry Molecular Orbital Theory of the Electronic Structure of Organic Compounds. VII. A Systematic Study of Energies, Conformations, and Bond Interactions L. Radom, W. J. Hehre, and J. A. Pople* Contribution from the Department of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213. Received July 16, 1970 Abstract: A moderately simple level of ab initio molecular orbital theory is uniformly applied to a study of the energies and conformations of the complete set of acyclic molecules containing one, two, or three first-row atoms (C to F) and which can be written as classical valence structures without charges or unpaired electrons. Using the concept of bond separation, the interaction of bonds in these molecules is described, and their heats of formation are estimated (mean absolute error = 3.1 kcal mol-'). Energies of complete hydrogenation for the molecules with two first-row atoms are calculated with a mean absolute error of 7.4 kcal mol-'. Calculated isomerization energies are in good agreement with known experimental values,
lthough there have been many ab initio molecular orbital calculations of the energies of individual organic molecules, there have been few attempts to study a wide range of compounds at a uniform level of approximation. In this paper, we shall present the results of a systematic study of simple molecules which (1) are acyclic; (2) contain only the atoms H, C , N, 0, and F; (3) contain up to three heavy atoms ( C , N, 0, or F); and (4) may be represented by a classical valence structure (single, double, and triple bonds) with no formal charges or unpaired electrons associated with any atom. Within these limitations, we have attempted a complete study of all distinguishable isomers, including those related by rotation about individual bonds. The first objective of the work is to make a series of predictions of the relative energies of rotational isomers and, consequently, predictions of the conformations of the lowest energy forms of the various species considered. The second objective is to make a comprehensive study of the relative energies of this complete set of molecules. Although it is widely recognized that single-determinant molecular orbital theory is incapable
A
* Address correspondence
to this author.
of describing energies of complete atomization satisfactorily, recent work has suggested that the energies of certain types of reaction may be satisfactorily described at this theoretical In a previous paper in this ~ e r i e swe , ~ suggested that the energy of large molecules should be studied in terms of two consecutive types of formal reactions. In the first (the bond separation reaction), the large molecule is broken down into species with not more than two heavy (nonhydrogenic) atoms, formal bond characters being retained. In the second step, the resulting two-heavy-atom molecules are completely hydrogenated to molecules with one heavy atom (methane, ammonia, water, . , .) by addition of an appropriate number of hydrogen molecules. lt2 Preliminary studies*f4showed that the energies of both sets of reactions were quite well described by relatively simple molecular orbital methods. In this paper we shall examine the energies of the complete set of mole(1) L. C. Snyder and H . Basch, J . Amer. Chem. Soc., 91,2189 (1969). (2) L. C. Snyder, J . Chem. Phys., 46, 3602 (1967). (3) R. Ditchfield, W. J. Hehre, J. A. Pople, and L. Radom, Chem. Phys. Lerr., 5, 13 (1970).
(4) W. J. Hehre, R. Ditchfield, L. Radom, and J. A . Pople, J . Amer. Chem. Soc., 92,4796 (1970).
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cules specified above from this point of view, comparing with experimental data when possible. In order to carry out a comprehensive investigation of this kind, it is necessary t o use a simple quantum mechanical method together with a systematic scheme for selecting the nuclear geometry for the various molecules. For the quantum mechanical method we have used selfconsistent molecular orbital theory with a fairly small extended basis set of contracted Gaussian functions.5 The geometries are chosen according to a standard model used previously,6 with some further specifications for rotational isomers. Thus, only a single, relatively simple calculation is performed on each isomer, permitting a broad survey of the energies of this wide range of compounds. Quantum Mechanical Method The quantum mechanical method used is single-determinant self-consistent-field molecular orbital theory. Each molecular orbital # t is constructed as a linear combination of atomic orbitals (LCAO) *I
= ccIri4, Ir
Solution of the Roothaan7 or Pople-Nesbets equations for closed- and open-shell species, respectively, gives the LCAO coefficients cPi and then the total energy, given the coordinates and atomic numbers of each of the nuclei. For the functions &, we have used the (extended) 431G basis set5consisting of a set of contracted Gaussian type functions. The 1s atomic orbital for heavy atoms (C, N, 0, and F) is a sum of four Gaussian s functions. The valence atomic orbitals (1s for hydrogen; 2s, 2p for heavy atoms) are split into inner and outer parts which are respectively sums of three and one Gaussian functions. Common Gaussian exponents are shared between 2s and 2p functions. The exponents were obtainedj by minimizing the calculated energy of the atomic ground states and rescaling for molecular use. Full details together with the set of standard molecular scale factors are given in ref 5. Overlap populations and orbital charges reported in this paper were obtained by performing a Mulliken population analysisg over the extended basis set and then summing the inner and outer parts. Geometric Model In order that a uniform treatment be applied to both known and unknown molecules, a standard geometrical model is used. This has been partly specified in an earlier paper.6 In this model, the symbol X m is used for an atom X bonded to m neighboring atoms. Standard bond lengths are then specified (single, double, and triple bonds as appropriate) for all bonded pairs of atoms Xm-Yn. The complete list of standard lengths is given in Table I of ref 6 . The orientation of bonds from a single atom was also specified previously and is very simple for the molecules considered in this paper. C4 is always tetrahedral (bond angles 109.47'), C3 is ( 5 ) R. Ditchfield, W. J. Hehre, and J. A. Pople, J . Chem. Phys., 54, 724 (1971). (6) J. A. Pople and M. Gordon, J . Amer. Chem. Soc., 89,4253 (1967). (7) C. J. Roothaan, Rea. Mod. Phys., 23, 69 (1951). (8) 3. A. Pople and R. K. Nesbet, J . Chem. Phys., 22,571 (1954). (9) R. S. Mulliken, ibid., 23, 1833 (1955).
Journal of the American Chemical Society
always planar trigonal (bond angles 120'), and C2 is always linear. N3 is taken to be pyramidal (CaVlocal symmetry and 109.47' bond angles) if it is attached only to saturated atoms. If it is attached to one or more unsaturated atoms, it is taken to be planar trigonal (bond angles 120O). Both N2 and 0 2 are chosen to be bent (bond angle 109.47"). These local geometries do, in fact, only reflect actual experimental geometries rather crudely. For example, N3 attached to an unsaturated atom is often not completely planar. Nevertheless, in the absence of complete experimental data, the use of some such set of simple rules is necessary. To complete the standard geometrical model, we have to describe dihedral angles, giving rotations about individual bonds. Here we proceed in a similar manner, specifying standard dihedral orientations for each appropriate Xm-Yn bond. We attempt to choose these orientations so that they correspond approximately to local minima in the potential surfaces for the simplest molecules with this particular kind of bond. Each such orientation then corresponds to a rotational isomer. The set of proposed standard dihedral orientations is given in Table I. This covers all molecules dealt with in this study. In most cases, the choice of standard dihedral geometries is directed by complete experimental structural information on simple species containing the appropriate bond, but it has been supported and supplemented by a theoretical study of potential energy curves not reported in detail here. Table I. Standard Dihedral Geometries Bond
Geometry
c4-c4 c4-c3 c3=c3 C4-N3 C4-N2 C3-N3 C3=N2 C4-02 C3-02 N3-N3 N3-N2 NkN2 N3-02 N2-02 02-42
Staggered Double bond eclipsed Planar Staggered Double bond eclipsed Planar Planar Staggered Planar Orthogonal Planar Planar :NOH planar Planar Orthogonal
0 : N refers to the fourth tetrahedral direction for pyramidal nitrogen.
We shall only comment on a few of the entries in Table I. Microwave studies have shown that a methyl C-H bond eclipses the double bond in propene, l 4 acetaldehyde, l5 N-methylformaldimine, and nitrosomethane. l7 These results lead to the rules for C4-C3 and C4-N2. Both experimentl8 and calculations 19,20 (10) C. C. Costain and J. M. Dowling, ibid., 32, 158 (1960). (11) D. R. Lide, Jr., J . Mol. Spectrosc., 8,142 (1962). (12) D. J. Millen, G. Topping, and D. R. Lide, Jr., ibid., 8 , 153 ( 1962). (13) D. G. Lister and J. K. Tyler, Chem. Commun., 152 (1966). (14) D. R. Herschbach and L. C. Krisher, J . Chem. Phys., 28, 728 (19 58). (15) R. W. Kilb, C . C. Lin, and E. B. Wilson, Jr., ibid., 26, 1695 (1957). (16) J. T. Yardley, J. Hinze, and R. F. Curl, Jr., ibid., 41,2562(1964). (17) D. Coffey, Jr., C . 0. Britt, and J. E. Boggs, ibid., 49, 591 (1968). (18) P. A. Giguere and I. D. Liu, Can. J . Chem., 30,948 (1952). (19) L. Pedersen and K. Morokuma, J . Chem. Phys., 46,3941 (1967).
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suggest that hydroxylamine has potential minima with :NOH cis and trans,21 hence the :NOH planar assignment for N3-02. For some molecules, the potential minima are not determined exactly by symmetry and we have rounded the experimental results in these cases. Thus, for N3-N3 and 02-02 we have taken the standard conformations, defined by the :NN: and X O O Y dihedral angles, respectively, to be orthogonal (dihedral angle 90’) in each case, this being close to the experimental conformations for hydrazineZZand hydrogen peroxide. * 3 Table I does not define “long-range” (i.e., extending over more than one bond) conformational preferences, as for example in the cumulated systems CH2=C=CH2, CH2=C=NH, and NH=C=NH. By analogy with allene, we might expect the other two molecules to have mutually orthogonal terminal groups, This is indeed supported by calculations (not reported here) on planar and orthogonal forms of these molecules, and so we have taken the standard conformations to be orthogonal. Conformational Isomerism The standard dihedral geometries so defined lead to a limited number of standard conformations for each molecule corresponding, approximately, to local potential minima. We have performed 4-3 1G calculations on all such standard conformations and the results are shown in Table 11. In this table, the molecular conformations are specified only to the extent they are not uniquely determined by the standard rules. For example, ethanol is listed as trans and gauche forms, the fact that all bonds are staggered being omitted because it is already implied by the standard dihedral geometries for C4-C4 and C4-02 bonds. It is convenient to discuss in turn the conformational isomers arising from rotation about the various bonds. Let us first consider rotation about the C-N bond in substituted methylamines, XCH2NH2. Here, there is the possibility of trans (I) and gauche (11) conformers (as defined by the XCN: dihedral angle). When X =
X I
has lower energy, while the gauche form is favored when X = OH or F. The microwave spectrum of the trans form of ethanol (X = CH,)has been assigned23,26and the spectral results suggest that the gauche conformer is also present. 2 6 * 2 7 Recent theoretical workz8on fluoromethanol (X = F) has shown the most stable form t o be gauche, in agreement with our result and, in addition, has shown that the trans form is a local maximum. A detailed discussion of the potential function for this and related molecules will be presented In substituted hydrazines NHaNHX, rotation about the N-N bond leads to two possible orthogonal forms which we have distinguished by the labels HNNX external (V) and HNNX internal (VI). When X = H I
I
I1
(20) W. H. Fink, D. C. Pan, and L. C. Allen, J . Chem. Phys., 47,895 (1967). (21) It is convenient to describe conformations involving pyramidal
nitrogen in terms of the fourth tetrahedral direction, which we denote ;N.
(22) T. Kasuya and T. Kojima, J . Phys. SOC.Jup., 18,364 (1963). (23) R. H . Hunt, R. A. Leacock, C. W. Peters, and K. T. Hecht, J . Chem. Phys., 43, 1931 (1965). (24) T. Masamichi, A. Y. Hirakawa, and K. Tamagake, Nippon Kuguku Zusshi, 89, 821 (1968).
Radom, Hehre, Pople
H I
A
/h
x‘
‘H
V
\
H’
H
VI
CHI, the external form has the lower energy and this agrees with the infrared result 30 that approximately 90% of the molecules exist in the external form. For X = O H and F, the internal form has the lower energy while in the intermediate case, NH2NHNHz,the orientations about the two N-N bonds are, respectively, internal and external. Rotation about the N-0 bond in 0-substituted hydroxylamines, NH20X, leads to cis (VII) and trans (VIIT) conformers (as defined by the :NOX dihedral
n VI1
CHI, the gauche form is calculated to have lower energy while the trans form is favored when X = OH or F. In the intermediate case, NHzCHZNH~, there are two C-N bonds, and the favored orientations about them are respectively gauche and trans. Spectroscopic dataz4 suggest the presence of both gauche and trans forms for ethylamine (X = CH,). Rotation about the C-0 bond in substituted methanols, XCH20H, also gives rise to trans (111) and gauche (IV) conformers (as defined by the XCOH dihedral angle). When X = CH, or NHz we find the trans form
IV
I11
VI11
angle). We predict that the cis form is more stable when X = H or CH,, as suggested by infrared spectral s t ~ d i e s . l ~The ? ~ ~trans form is favored for X = OH and F, while the intermediate case NH20NH2 has cis and trans orientations about the two N - 0 bonds. For N-substituted hydroxylamines, analogous cis (IX) and trans (X) conformers are possible. Here we
IX
X
(25) Ch. 0. Kadzhar, I. D. Isaev, and L. M. Imanov, Zh. Strukr. Khim., 9,445 (1968). (26) M. Takano, Y.Sasada, and T. Satch, J . Mol. Spectrosc., 26, 157 (1968). (27) J. Michielsen-Effinger, Bull. Cl. Sci. Acad. Roy. Belg., 53, 226 (1967). (28) S. Wolfe, A. Rauk, L. M. Tel, and I. G. Csizmadia, in prepara-
tion.
(29) L. Radom, W. J. Hehre, and J. A. Pople, in preparation. (30) J. R. Durig, W. C. Harris, and D. W. Wertz, J . Chem. Phys., 50, 1449 (1969). (31) M. Davies and N. A. Spiers, J . Chem. SOC.,3971 (1959).
MO Theory of the Electronic Structure of Organic Compounds
292 Table 11. Calculated Total Energies
Stoichiometric formula
Skeleton
C-F N-N N-N
Hydrogen Methane Ammonia Water Hydrogen fluoride Ethane Ethylene Acetylene Methylamine Formaldimine Hydrogen cyanide Methanol Formaldehyde Fluoromethane Hydrazine Diimide
NsN N-0
Nitrogen Hydroxylamine
N=O N-F
C--C-N
Nitroxyl Fluoramine Hydrogen peroxide Oxygen Hypofluorous acid Fluorine Propane Propene Propyne Allene Ethylamine
C-N--C C=C-N C+N
Dimethylamine Vinylamine Acetaldimine
C=N-C C--C=N CEC-N C==C=N N--C-N
N-Methylformaldimine Acetonitrile Ethynylamine Ketenimine Methylenediamine
C-N-N
Methylhydrazine
N G N
For mamidine
C-N=N
Methyldiimide
C=N-N NXEN N=C=N
Formaldehyde hydrazone Cyanamide Car bodiimide Ethanol
C-C c-C
c=c C-N C=N CkN
C-0 c-0
0-0 O=O 0-F
F-F C--C--C C+C C 4 Z C
c=c=c
c
