Ab Initio Study of the Photochemical Dissociation of Methylamine - The

J. Phys. Chem. 1996, 100, 123-129

123

Ab Initio Study of the Photochemical Dissociation of Methylamine Kevin M. Dunn*,†,‡ and Keiji Morokuma† Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, and Department of Chemistry, Hampden-Sydney College, Hampden-Sydney, Virginia 23943 ReceiVed: August 25, 1995X

The threshold photochemistry of methylamine along three dissociation channels is examined using CASSCF and MRSDCI wave functions. Excitation of a nitrogen lone pair electron into a Rydberg s orbital produces an excited state that can decompose via NH rupture, CN rupture, or CH rupture. In the case of NH and CN rupture the excited state and ground state surfaces cross as the molecule dissociates, forming a conical intersection. The NH rupture excited state products lie above the excitation energy, and so dissociating molecules are funneled through the conical intersection and emerge as ground state products. The CN rupture excited state products lie below the excitation energy, and dissociation would proceed mostly on the excited state surface. In the case of CH rupture, the excited state products lie above the excitation energy, but since there is no conical intersection in this channel, CH rupture has to occur only after internal conversion to the ground state. These three mechanisms are all consistent with recent experimental evidence.

1. Introduction It has long been known that the threshold photochemistry of methylamine involves the excitation of a nitrogen lone pair electron into a 3s Rydberg orbital, resulting in the rupture of an N-H bond.1 Recently Butler and co-workers have reported that excitation at 222 nm can result in N-H rupture, C-N rupture, C-H rupture, or H2 elimination.2 By measuring the photofragment kinetic energies under collisionless conditions, they were able to determine that while C-N rupture proceeds on the excited state surface, N-H rupture occurs via a conical intersection, resulting in ground state products. The C-H rupture process is less well understood. They have also determined that hydrogen elimination proceeds via a four-center transition state. The current work will seek to determine the general features of the ground and first excited singlet state surfaces using CASSCF (complete active space self-consistent field) and MRSDCI (multireference single and double excitation configuration interaction) ab initio wave functions. We will then compare these features with the available experimental observations. The experimental enthalpies of reaction in the ground state for the three bond rupture processes are3

∆H° ) 102.6 kcal/mol

(1)

f H + CH2NH2


(2)

f CH3 + NH2


(3)

CH3NH2 f H + CH3NH

The ultraviolet absorption spectrum of methylamine shows two progressions assigned to the amino wagging and methyl rocking vibrations.4 This band peaks at 220 nm, corresponding to a vertical excitation energy of 130.0 kcal/mol.5 The first excited doublet state of NH2 is known to lie 31.8 kcal/mol above its ground state.6 Excitation at 222 nm under collisionless conditions produces photofragments with maximum kinetic energy of 27, 18, and 12 kcal/mol for the N-H, C-N, and C-H rupture †

Emory University. Hampden-Sydney College. X Abstract published in AdVance ACS Abstracts, December 1, 1995. ‡

0022-3654/96/20100-0123$12.00/0

processes, respectively.2 These kinetic energies place lower limits on the energies of the product states. Furthermore, the shapes of the kinetic energy distributions indicate that the potential energy drops from the transition states to the products for N-H and C-N fission, but not for C-H fission. The C-H photofragment kinetic energy distribution peaks near 0 kcal/ mol, indicating little or no barrier to the reverse reaction. The preceding eight experimental energies will be used to evaluate the accuracy of the CASSCF/MRSDCI potential energy surfaces. 2. Theoretical Method The first ultraviolet absorption of methylamine involves the excitation of an electron from the HOMO, a lone pair on the nitrogen, to the LUMO, a Rydberg s orbital surrounding the entire molecule. To adequately describe the latter orbital, diffuse functions must be included. We have used the 6-31++G** basis set for all calculations in the present work.7 CASSCF wave functions were used to locate all of the optimized points on the potential energy surfaces. In the Franck-Condon region, the active space included the nitrogen lone pair and Rydberg s, px, py, and pz orbitals, henceforth referred to as CASSCF(2e, 5MO) or CASSCF(2, 5). For points along the bond rupture coordinates, the electrons in the relevant bonding orbital must also be included in the active space, resulting in CASSCF(4, 6) wave functions. It would have been most appropriate to include the electrons for all three bonds under consideration. This CASSCF(8, 8) wave function would have been too large for the present study. Instead, MRSDCI wave functions built on top of the three CASSCF(4, 6) wave functions were used to evaluate the relative energetics along each of the bond rupture coordinates. This left the problem of comparing energies along the bond rupture coordinates (based on CASSCF(2, 5)) to those in the Franck-Condon region (based on CASSCF(4, 6)). We found that in the Franck-Condon region, CASSCF(2, 5) + MRSDCI + Davidson correction (DC) produced energies very close to CASSCF(4, 6) + MRSDCI + DC. Evidently in the Franck-Condon region, MRSDCI + DC is able to compensate for the use of a smaller CASSCF active space and thus to allow comparison to energies along the bond rupture coordinates using lager CASSCF active spaces. © 1996 American Chemical Society

124 J. Phys. Chem., Vol. 100, No. 1, 1996

Dunn and Morokuma TABLE 1: CASSCF(2,5)/6-31++G** Stationary Points in the Franck-Condon Regiona Cs(2) ground a

excited c

Cs(1) ground b

excited d

E(CASSCF (2, 5)) -95.246 168 -95.062 584 -95.237 837 -95.062 303 E(+MRSDCI) -95.562 224 -95.371 995 -95.554 022 -95.371 685 E(+DC) -95.592 587 -95.403 559 -95.584 680 -95.403 104

Figure 1. CASSCF(2, 5) structures in the Franck-Condon region. See Table 1 for geometry parameters.

Except for some of the points in the NH bond rupture channel, all calculations were performed in Cs symmetry. Figure 1 shows two different conformations belonging to Cs symmetry. Structure b, with symmetry denoted as Cs(1), has both amino hydrogens coplanar with the nitrogen, carbon, and one methyl hydrogen, Ha. Structure a, with symmetry denoted as Cs(2), has the amino hydrogens straddling the plane containing the nitrogen, carbon, and one methyl hydrogen, Ha. The two conformations can interconvert by simultaneous rotation and inversion of the amino group. Three kinds of points on the potential energy surfaces have been optimized in the present work. Minima on the ground and first excited singlet state surfaces are dominated by a single RHF or ROHF configuration. In the Franck-Condon region, the ground state is dominated by a closed shell RHF configuration, while the excited state is dominated by an ROHF configuration in which the nitrogen lone pair orbital and the Rydberg s orbital are each singly occupied. Minima in the Franck-Condon region were optimized using Hondo 8.4.8 Minima in the product regions are dominated by ROHF configurations in which one orbital on each of two product fragments are singly occupied. These ROHF configurations correlate to separate doublet states of the product fragments. We were unable to optimize the product minima using Hondo because of problems with MCSCF convergence in this region. Molpro 92 performed more reliably in this region and was used to optimize all product minima.9 However, three of the product minima could not be optimized even using Molpro. For these points, the ground and excited states have the same symmetry, and Molpro was unable to evaluate the gradient for the excited state under these circumstances. In these three cases, the product excited state geometries were estimated, either from the appropriate transition state or from other optimized product states. Transition states for the bond rupture processes constitute the second type of optimized point on the potential energy surfaces. In the case of methylamine, transition states appear only on the excited state surface and result from the interaction between the ROHF configuration which dominates the wave function in the Franck-Condon region and the repulsive ROHF configuration which dominates the products. All transition states were optimized using Hondo. The third type of point appears when the ground and excited states cross along some of the bond rupture coordinates. The minimum in this seam of crossing (MSX) constitutes a diabatic transition state between the ground and excited state surfaces.10 The methodology for locating the minimum in the seam of

rCHa rCHb rNHc rNHd rCN RHaCN RHcNC RHdNC RHbCN RHbCHa δHcNCHa γCNHcHd

1.091 1.084 1.000 1.000 1.452 114.58 112.00 112.00 109.28 108.04 60.80 50.37

1.086 1.079 1.020 1.020 1.450 107.03 121.74 121.74 108.83 110.00 86.37 5.84

1.084 1.088 0.989 0.990 1.436 109.21 121.37 120.93 112.38 107.32 0.00 0.00

1.078 1.083 1.019 1.019 1.449 109.24 122.57 121.26 107.81 111.33 0.00 0.00

a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′′ a′′ a′′ a′′ a′′ a′′

894.13 1144.53 1270.09 1587.35 1623.02 1805.55 3136.56 3221.27 3754.38

603.51 1051.20 1174.20 1548.03 1597.05 1636.04 3201.68 3306.56 3406.89

335.96 1044.15 1452.32 1640.65 3257.47 3842.23

214.24 934.24 1352.67 1585.49 3344.74 3465.16

983.49 1187.19 1395.20 1596.39 1654.20 1774.36 3153.66 3250.56 3905.03 4022.50 2125.82i 86.22i 1378.20 1610.14 3194.27

932.28 1062.12 1349.84 1548.31 1593.64 1637.65 3205.15 3341.08 3404.60 3416.31 51.04i 483.70 1152.65 1587.58 3295.19

a

Energy in Hartrees distances in angstroms angles in degrees, and frequency in cm-1. δabcd is defined as the dihedral angle between atoms a, b, c, and d. γabcd is the angle between the a-b bond and the c-b-d plane. In Cs(2) symmetry, a positive value of γCNHcHd places Hc and Hd straddling Ha.

crossing was described in 1985 by Koga and Morokuma and applied to the crossing between two low-lying triplet states of chlorobenzene.11 The theory was generalized by Farazdel and Dupuis and incorporated into the Hondo program.10,12 Hondo 8.4 contained some errors in the seam minimization code, the corrections to which we have described previously.13 Even with these corrections, however, Hondo 8.4 optimizes only the seam of crossing between two states with the same occupation pattern, e.g. two CASSCF states with the same number of doubly occupied orbitals. In the present work, we were required to optimize the seam of crossing between two states with different occupations: for the ground state all doubly occupied orbitals and for the excited state two open shell orbitals. To accomplish this, we wrote a Unix shell script, Seam 1.0, which calls Hondo for the generation of the next point on the seam of crossing but which can call any of several ab initio codes for the evaluation of the energy and gradient. In the present work, this script called Hondo for the gradient evaluation, but this choice was simply a matter of convenience. In general, Seam 1.0 can optimize the seam of crossing between states described by any type of wave function available from any of the supported ab initio codes. In fact, different programs might be used for each of the two states. While these points were all optimized using slightly different CASSCF wave functions, the relative energetics were all evaluated using Molpro at the CASSCF + MRSDCI + DC level of theory. This will be shown to compensate for minor differences in the active spaces. Some small residual error remains, however, both due to the differences in the active spaces and because the (unknown) MRSDCI stationary points

Photochemical Dissociation of Methylamine

J. Phys. Chem., Vol. 100, No. 1, 1996 125

Figure 2. CASSCF(4, 6) + MRSDCI + DC potential energy surfaces for the N-H dissociation channel. The dashed line has Cs(1) symmetry, while the solid line has C1 symmetry. All lettered points (except k) were optimized at the CASSCF level. The geometry at point k was taken from point j except that the NH2 group was rotated perpendicular to the Cs plane.

may have slightly different geometries from the optimized CASSCF stationary points. The accuracy of the MRSDCI energies will be addressed in the next section. 3. Results Franck-Condon Region. Figure 1 shows the optimized structures of methylamine in the ground and first excited singlet states in the Franck-Condon region, details of which are given in Table 1. The ground state minimum is structure a, which has Cs(2) symmetry and an ammine out-of-plane angle of 50°. At the CASSCF + MRSDCI + DC level of theory, the calculated vertical excitation energy is 129.8 kcal/mol or 5.64 eV. Structure b is a second-order saddle point on the ground state surface with Cs(1) symmetry in which the ammine group is coplanar with one of the methyl hydrogens. This structure lies 5 kcal/mol above the ground state minimum. The first excited singlet state results when one of the nitrogen lone pair electrons is excited to a Rydberg s orbital. Structure c is the minimum on the first excited singlet surface. The ammine group is nearly coplanar with the C-N bond with the ammine hydrogens straddling one of the methyl hydrogens. If the ammine plane is brought coplanar with one of the methyl hydrogens, structure d results with a barrier to internal rotation of only 0.3 kcal/mol. Thus, in the Franck-Condon region, the first excited singlet should be considered as having the ammine group essentially coplanar with and freely rotating about the C-N bond. N-H Dissociation Channel. In Cs(1) symmetry the ground state is 1A′ with all orbitals doubly occupied. As the N-H bond eclipsing the methyl hydrogen (Hc in Figure 1) is lengthened, the N-H σ bond becomes HOMO and separates into a singly occupied s orbital on the hydrogen atom and a singly occupied sp hybrid on the nitrogen atom. Both these orbitals belong to a′, and the dissociation products are in the ground 2S and first excited 2A′ states for hydrogen and CH3NH, respectively. Thus in Cs(1) symmetry, ground state methylamine dissociates to

hydrogen in the ground state and CH3NH in the first excited state. In Cs(1) symmetry the first excited singlet state is 1A′′, with a singly occupied nitrogen p orbital belonging to a′′ and a singly occupied Rydberg s orbital belonging to a′. As the N-H bond eclipsing the methyl hydrogen is lengthened, the Rydberg s orbital mixes with the N-H σ* orbital, and a transition state results from the avoided crossing between these two orbitals. Beyond the transition state, the singly occupied orbitals consists of the a′′ nitrogen p orbital and the a′ 1s orbital on the departing hydrogen atom. This correlates to ground state products, 2S for hydrogen and 2A′′ for CH3NH. Thus as the N-H bond is lengthened, the ground state energy rises toward excited state products while the excited state passes through a transition state, after which the energy falls toward ground state products. Somewhere along the way the ground and excited states cross in a multidimentional seam of crossing within Cs(1) symmetry. In Cs(2) symmetry both the ground and first excited singlet states are 1A′. The occupied orbitals are nominally the same as in Cs(1) symmetry except that in the excited state the singly occupied nitrogen p orbital is now in the Cs plane and belongs to a′. As an N-H bond is lengthened, Cs symmetry is broken. The ground and excited states do not cross in either Cs(2) or C1 symmetry, and a conical intersection is formed about the seam of crossing in Cs(1) symmetry. This situation is shown graphically in Figure 2. The dashed lines represent the ground and excited states in Cs(1) symmetry, and the solid lines represent the ground and excited states in C1 symmetry. Points a, b, c, and d have been discussed above in the Franck-Condon section. All subsequent points were optimized using CASSCF(4, 6) wave functions. Energies were evaluated at the CASSCF(4, 6) + MRSDCI + DC level. Points e and f are the optimized transition states and are actually identical except for the H-C-N-H dihedral angle. In structure e, atom Hd is coplanar with atom Hb (C1 symmetry), while in structure f it is coplanar with atom Ha (Cs(1) symmetry).

126 J. Phys. Chem., Vol. 100, No. 1, 1996

Dunn and Morokuma TABLE 2: CASSCF(4,6)/6-31++G* Transition States for Lowest Excited Singleta Cs(1)

Figure 3. CASSCF(4, 6) transition state structures. Arrows point along the normal coordinate with imaginary frequency. See Table 2 for geometry parameters.

Structure f is shown in Figure 3, with details given in Table 2. Note that the CASSCF(2, 5) + MRSDCI + DC energy is within 0.0016 hartrees of the CASSCF(4, 6) + MRSDCI + DC energy, allowing us to smoothly connect points along the N-H fission channel to points in the Franck-Condon region. Point g is the optimized minimum in the seam of crossing (MSX). Its structure is shown in Figure 4, with details given in Table 3. Points h, i, and j are the products in which one N-H bond was fixed at 10 Å and all other geometry parameters were optimized. Point k could not be optimized and was taken as being identical to j but with the remaining N-H bond rotated perpendicular to the Cs plane. The lines connecting the labeled points in Figure 3 have been drawn from one-dimensional CASSCF(4, 6) scans of the potential energy surface scaled to connect the labeled points. Also shown on Figure 2 is the vertical excitation energy, Ev. The physics of the dissociation of methylamine in the first excited state can be understood from the energetics the points e, f, j, and k relative to the vertical excitation energy. Both e and f lie below Ev, and as these points are the lowest transition states on the excited state surface, N-H rupture is the dominant dissociation process, in agreement with the experimental observations.2 The excited state products, j and k, are above Ev and are energetically inaccessible. Consequently, molecules which cross the N-H transition states at e and f will be funneled through the conical intersection and emerge as ground state products. If this is so, the maximum kinetic energy available to the products will be hν - E(h or i). For excitation at 222 nm, this is 27.5 kcal/mol, in very good agreement with Butler’s experimental value of 27 kcal/mol.2 C-N Dissociation Channel. As the C-N bond is lengthened in Cs(1) symmetry, the ground state (1A′) energy increases. The C-N σ bond becomes HOMO and separates into an sp3 hybrid orbital on the methyl group and an sp2 hybrid orbital on the NH2 fragment. At the product limit the methyl group has flattened out with a singly occupied p orbital perpendicular to the plane of the molecule. This product has D3h symmetry and is the ground state for the methyl radical, 2A′′2. The NH2 product has C2V symmetry and is in the first excited doublet state, 2A1.

CNb 1c

NHb fc

Cs(2) CHb qc

E(CASSCF(2, 5) E(+MRSDCI) E(+DC) E(CASSCF(4, 6) E(+MRSDCI) E(+DC)

-95.029 160 -95.345 401 -95.380 131 -95.062 058 -95.352 190 -95.381 316

-95.044 148 -95.356 149 -95.389 063 -95.073 349 -95.362 475 -95.390 726

-94.856 201 -95.261 421 -95.367 734 -95.029 237 -95.324 754 -95.352 965


1.073 1.074 1.031 1.029 1.861 101.30 124.89 123.60 101.11 116.39 0.00 0.00

1.084 1.084 1.339 1.012 1.442 107.74 119.41 117.88 110.25 109.94 0.00 0.00

1.726 1.072 1.013 1.013 1.307 99.13 120.96 120.96 118.33 93.14 83.62 10.49

a′ a′ a′ a′ a′ a′ a′ a′ a′ a′ a′′ a′′ a′′ a′′ a′′ a′′

1964.74i 519.31 845.64 1122.11 1528.54 1549.99 3250.69 3288.97 3359.97 3443.27 24.46 767.62 976.17 1550.19 3434.83

2085.34i 633.46 1049.91 1170.40 1389.74 1559.74 1604.11 3186.47 3272.47 3641.09 279.79 789.21 1244.81 1606.06 3270.29

1427.03i 530.78 813.24 1163.80 1435.24 1627.40 1733.78 3332.00 3469.19 560.98 965.94 1084.32 1424.68 3460.90 3539.61

a Energy in Hartrees, distances in angstroms, angles in degrees, and frequency in cm-1. δabcd is defined as the dihedral angle between atoms a, b, c, and d. γabcd is the angle between the a-b bond and the c-b-d plane. In Cs(2) symmetry, a positive value of γCNHcHd places Hc and Hd straddling Ha. b Fission. c Channel.

Figure 4. CASSCF(4, 6) minima in the seam of crossing. See Table 3 for geometry parameters.

In the Cs(1) excited state, one of the nitrogen lone pairs has been excited to a Rydberg s orbital. As the C-N bond is lengthened, the Rydberg s orbital mixes with the C-N σ* orbital, and a transition state results from the avoided crossing between these two orbitals. Beyond the transition state, the singly occupied orbitals consist of the a′′ nitrogen p orbital and a p orbital on the CH3 fragment. This correlates to ground state products, 2A′′2 for CH3 and 2B2 for NH2. As in the N-H dissociation channel, the ground and excited state surfaces cross in Cs(1) symmetry, forming a seam of conical intersection. Figure 5 shows the ground and excited state potential surfaces along the C-N dissociation coordinate. The dashed lines represent the ground and excited states in Cs(1) symmetry, and


J. Phys. Chem., Vol. 100, No. 1, 1996 127

TABLE 3: CASSCF(4, 6)/6-31++G** Local Minima in the Seam between the 1A′ and 1A′′ Potential Energy Surfacesa fission CN n

NH g

EA(CASSCF(4, 6)) EB(CASSCF(4, 6)) EA - EB

-95.132 131 -95.132 231 0.000 100

-95.106 518 -95.106 325 -0.000 193


1.071 1.071 1.004 1.004 2.498 93.01 125.88 121.03 94.31 119.45 0.00 0.00

1.083 1.088 1.938 1.005 1.439 109.30 120.60 115.51 111.13 108.49 0.00 0.00

a Energy in Hartrees, distances in angstroms, angles in degrees, and frequency in cm-1. δabcd is defined as the dihedral angle between atoms a, b, c, and d. γabcd is the angle between the a-b bond and the c-b-d plane. In Cs(2) symmetry, a positive value of γCNHcHd places Hc and Hd straddling Ha.

the solid lines represent the ground and excited states in Cs(2) symmetry. Points a, b, c, and d have been discussed above in the Franck-Condon section. All subsequent points were optimized using CASSCF(4, 6) wave functions. Energies were evaluated at the CASSCF(4, 6) + MRSDCI + DC level. Point 1 is the optimized transition state on the CASSCF(4, 6) surface, and its structure is shown in Figure 3 and Table 2. Note that the CASSCF(2, 5) + MRSDCI + DC energy is within 0.0012 hartrees of the CASSCF(4, 6) + MRSDCI + DC energy, allowing us to smoothly connect points along the C-N fission channel to points in the Franck-Condon region. Point m is a second-order saddle point on the CASSCF(4, 6) surface, lying 3 kcal/mol above point 1. However, the CASSCF + MRSDCI + DC energy of point m lies 3 kcal/mol below point 1. While it is possible that m lies below 1 on the CASSCF + MRSDCI + DC surface, the geometries have not been optimized at this level of theory. Consequently, we cannot say for certain which of these two points is the true transition state on the CASSCF + MRSDCI + DC surface. What can be said is that the essentially free rotation of the NH2 group observed in the Franck-Condon region continues along the CN bond rupture coordinate. The transition state, l, lies 3.8 kcal aboVe Butler’s excitation energy of 128.8 kcal/mol (222 nm), but when the difference between the zero-point vibrational energies of structures a and l are included, the transition state lies 2.4 kcal/mol below the excitation energy. Similarly, the zero-point correction places point m 4.6 kcal/mol below the excitation energy. Thus, excitation at 222 nm produces excited state molecules with enough energy to cross the C-N bond fission barrier in either Cs(1) or Cs(2) symmetry. Point n is the optimized minimum in the seam of crossing (MSX), shown in Figure 4 and Table 3. Points o and p are optimized products, in which the C-N bond was fixed at 10 Å and all other geometry parameters were optimized. In this channel Cs(1) and Cs(2) products are identical and were only optimized in Cs(1) symmetry. As in Figure 2, the lines connecting the labeled points have been drawn from onedimensional CASSCF(4, 6) scans of the potential energy surface scaled to connect the labeled points. While the potential energy surfaces in the C-N dissociation channel have the same general features as in the N-H channel,

there is an important difference. Unlike the N-H excited state products, the C-N excited state products lie below Ev and are energetically accessible. Thus, while excited state molecules which cross the N-H transition state are funneled through the conical intersection, those crossing the C-N transition state are not obliged to do so. Relatively few trajectories would pass through the MSX at point n, and the majority of the dissociations will emerge as excited state products at point p. If this is so, the maximum kinetic energy available to the products will be hν - E(p). For excitation at 222 nm this is 11.1 kcal/mol, somewhat less than Butler’s experimental value of 15 kcal/mol.2 Furthermore, the MRSDCI energy difference between the ground and first excited states of NH2 (points o and p) is 0.5 kcal/mol higher than the experimental value.6 All of this points to a residual error in the excited state MRSDCI energies of between 1 and 4 kcal/mol. Within these limits, our MRSDCI surface is consistent with Butler’s cinclusion that C-N rupture proceeds mostly on the excited state surface. C-H Dissociation Channel. The potential energy surfaces along the C-H dissociation coordinate are qualitatively different from those in the other two bond rupture channels. In the Cs(1) ground state, the C-H σ orbital becomes HOMO as the bond is lengthened and at large separation becomes a singly occupied s orbital on the departing hydrogen atom and a singly occupied p orbital on the carbon atom. The CH2 group becomes nearly coplanar with the C-N bond, with the CH2 and NH2 planes perpendicular to one another. In the ground state product, the nitrogen p orbital is doubly occupied and the carbon p orbital is singly occupied. Thus, unlike the other two channels, ground state methylamine dissociates to ground state products in the C-H dissociation channel. Upon internal rotation into Cs(2) symmetry, both CH2 and NH2 cease to be coplanar with the C-N bond, the geometry around both carbon and nitrogen becoming distorted tetrahedral. The ground state energy is stabilized by some 12.5 kcal/mol compared to the Cs(1) structure. In the Cs(1) excited state product, the carbon is sp3 hybridized, with the in-plane orbital being a doubly occupied lone pair. The pz orbital on nitrogen and the departing hydrogen s orbital are singly occupied. In Cs(2) symmetry the excited state product could not be optimized, as it has the same symmetry as the ground state. To estimate the energy, the geometry was frozen at the Cs(2) excited state transition state geometry except that the departing hydrogen was removed to a distance of 10 Å. At this geometry, there is significant overlap between the carbon and nitrogen p orbitals to form π and π* orbitals. The π orbital is doubly occupied, and the π* orbital is empty. The singly occupied orbitals are the hydrogen 1s orbital and a Rydberg s orbital on the CH2NH2 fragment. With the formation of this double bond in the excited state comes a significant stabilization of 21.9 kcal/mol compared with the Cs(1) structure. This stabilization would increase somewhat if the excited state geometry could be optimized. The potential energy surfaces along the C-H dissociation coordinate are shown in Figure 6. In the C-H dissociation channel there is no conical intersection and no diabatic path to ground state products. Consequently, it would seem that C-H dissociation must take place on the excited state surface. However, the C-H transition state, q, as well as the excited state products, u, are higher in energy than either the MRSDCI vertical excitation energy or the photon energy at 222 nm. In fact, the transition state energy is some 21.3 kcal/mol above the 222 nm excitation energy. It is possible that residual errors might cause the MRSDCI energies to be somewhat overestimated. In the C-N dissociation channel this was seen to be the case, with the residual error being on the order of 4 kcal/

128 J. Phys. Chem., Vol. 100, No. 1, 1996

Dunn and Morokuma

Figure 5. CASSCF(4, 6) + MRSDCI + DC potential energy surfaces for the C-N dissociation channel. The dashed line has Cs(1) symmetry, while the solid line has Cs(2) symmetry. All lettered points were optimized at the CASSCF level.

Figure 6. CASSCF(4, 6) + MRSDCI + DC potential energy surfaces for the C-H dissociation channel. The dashed line has Cs(1) symmetry, while the solid line has Cs(2) symmetry. All lettered points (except u) were optimized at the CASSCF level. The geometry at point u was taken from point q except that the departing hydrogen was removed to a distance of 10 Å.

mol. It is unlikely that the error would be significantly higher in the C-H channel. If the excited state MRSDCI energies were in error by more than about 5 kcal/mol and if this error were similar in all three dissociation channels, it would bring the N-H excited state rupture products as well as the C-H excited state rupture products below the excitation energy. Consequently, N-H dissociation would take place on the excited state surface, the products emerging with very little kinetic energy and no

significant barrier to the reverse reaction. This is exactly the opposite of Butler’s experimental observations.2 We therefore feel confident that the MRSDCI energies are in error by no more than a few kcal/mol and that the C-H dissociation excited state products are not energetically accessible at 222 nm. 4. Conclusions Table 4 compares nine MRSDCI energy differences to the experimentally available data. Note that the experimental result


J. Phys. Chem., Vol. 100, No. 1, 1996 129

TABLE 4: MRSDCI Energy Differences Compared to Experimental Values

E(i) - E(a) E(o) - E(a) E(s) - E(a) Ev E(p) - E(o) hν(222 nm) - E(i)b hν(222 nm) - E(p) hν(222 nm) - E(s) hν(222 nm) - E(t)

MRSDCI (kcal/mol)

experimental (kcal/mol)

101.6 85.4 97.2 129.8 32.3 27.2 11.1 31.6 19.6

102.611 79.511 94.611 130.05 31.86 (27.0)a (15.0)a (12.0)a (12.0)a

a a Values in parentheses are maximum obserVed translational kinetic energies.2 The corresponding theoretical values are maximum aVailable energies. b hν(222 nm) ) 128.8 kcal/mol.

quoted from ref 2 is the maximum product translational energy in the 222 nm (128.8 kcal/mol) photodissociation experiment. The vertical excitation energy, Ev, has a theoretical value of 129.8 kcal/mol, very close to the most intense peak in the threshold ultraviolet spectrum at 220 nm (130 kcal/mol).5 The energy difference between points o and p has a theoretical value of 32 kcal/mol, in excellent agreement with the experimental excitation energy of NH2 of 31.8 kcal/mol.6 The bond dissociation energies in the first three rows and the vertical excitation energy of methylamine agree well with experiments within 6 kcal/mol. Worth noticing is that the differences between the photon energy and product potentials energies in the N-H and C-N fission channels are in excellent agreement with the experimentally determined maximum product translational energies. For the C-H fission channel, however, the photon-products energy difference is substantially larger than the observed maximum product translational energy. Even if the products emerge in Cs(1) symmetry (point t), this is not sufficient to result in products with as little translational kinetic energy as observed experimentally. That the translational kinetic energy is so small is consistent with the production of hot ground state products in which a significant fraction of the excitation energy has gone into vibrational motions of the products. Our calculations point to two different mechanisms for N-H and C-N bond fission. In the N-H fission channel, the excited state products are higher in energy than the excitation energy and dissociation in the excited state is energetically inaccessible. Molecules that cross the N-H transition state are funneled through the conical intersection with the ground state surface and emerge directly as ground state products with large translational kinetic energy. In the C-N fission channel, the excited state products are lower than the excitation energy. Since trajectories that pass through the conical intersection would represent only a small fraction of the energetically accessible trajectories, molecules that cross the C-N transition state overwhelmingly emerge as excited state products with less translational energy than in the case of N-H fission. Our conclusions regarding both the N-H and C-N fission mechanisms confirm those proposed by Butler.2 In the C-H fission channel, however, Butler was unable to determine whether bond fission resulted in excited state products or ground state products. What could be determined was that products emerge with relatively little translational kinetic energy and that there is a small or zero barrier to the reverse reaction. These observations are consistent with either dissociation from the ground state following internal conversion or dissociation from an excited state which is relatively flat beyond the transition state. While our calculations show that the excited

state surface is quite flat beyond the transition state, that transition state is some 22 kcal/mol higher than the excitation energy. In light of the accuracy of the other theoretical energies, we believe that C-H fission takes place via internal conversion to a hot ground state, with a large fraction of the available energy partitioned to internal motions of the products. Such internal conversion would be facilitated by the presence of conical intersections. A search of the potential energy surfaces at both long and short bond lengths revealed only two such intersections, one in the N-H channel and one in the C-N channel. The N-H conical intersection, shown in Figure 2, is known to be heavily traveled. Many of the excited state trajectories will travel through the conical intersection in the direction of N-H stretching and will result in direct N-H fission. Some of them will travel through it in the direction of shortening the N-H bond and will stay in the reactant region in the ground state. During this time, the excess energy will be distributed among various vibrational modes, and molecules will dissociate into ground state products in all three bond fission channels. N-H and C-N bond fission will be dominated by direct processes, however, and products from the indirect process will not likely be observed. Only in the C-H bond fission channel, in which there is no direct processes, will products from the indirect process be observed in the form of fission products with relatively little translational kinetic energy. Acknowledgment. K.M.D. acknowledges the Visiting Fellowship at the Emerson Center. We also thank L. J. Butler for a preprint of her paper. The present research is in part supported by Grant F49620-95-1-0182 from the Air Force Office of Scientific Research. References and Notes (1) Kassab, E.; Gleghorn, J. T.; Evleth, E. M. J. Am. Chem. Soc. 1983, 105, 1746. (2) Waschewsky, G. C. G.; Kitchen, D. C.; Browning, P. W.; Butler, L. J. J. Phys. Chem. 1995, 99, 2635. (3) Gardner, E. P.; McNesby, J. R. J. Phys. Chem. 1982, 86, 2646. (4) Tsuboi, M.; Hirakawa, A. Y.; Kawashima, H. J. Mol. Spectrosc. 1969, 29, 216. (5) Tannenbaum, E. M.; Coffin, E. M.; Harrison, A. J. J. Chem. Phys. 1953, 40, 1099. (6) Biesner, J.; Schneider, L.; Ahlers, G.; Xie, X.; Welge, K. H.; Ashford, M. N. R.; Dixon, R. N. J. Chem. Phys. 1989, 91, 2901. (7) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163. Hariharan, P. C.; Pople, J. A. Mol. Phys. 1974, 27, 209. Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. (8) Dupuis, M.; Marquez, A.; Davidson, E. R. HONDO 95.6; IBM Corp.: Kingston, NY, 1995. (9) MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles, with contributions of J. Almlof, R. Amos, S. Elbert, K. Hampel, W. Meyer, K. Peterson, R. Pitzer, and A. Stone. Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. Knowles, P. J.; Werner, H.-J. Theor. Chim. Acta 1992, 84, 95. (10) Farazdel, A.; Dupuis, M. J. Comput. Chem. 1991, 12, 276. (11) Koga, N.; Morokuma, K. Chem. Phys. Lett. 1985, 119, 371. (12) Dupuis, M.; Chin, S.; Marquez, A. CHEM-Station and Hondo. In RelatiVistic and Electron Correlation Effects in Molecules and Clusters; Malli, G. L., Ed.; NATO ASI Series; Plenum Press: New York, 1992. (13) Dunn, K. M.; Morokuma, K. J. Chem. Phys. 1995, 102, 4904.

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Ab Initio Study of the Photochemical Dissociation of Methylamine - The

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