A theoretical study of the spectrophysics and photochemistry
of formaldehyde
Citation for published version (APA):
Kemper, M. J. H. (1980). A theoretical study of the spectrophysics and photochemistry of formaldehyde. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR153278
DOI:
10.6100/IR153278
Document status and date: Published: 01/01/1980 Document Version:
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A THEORETICAL STUDY OF THE
SPECTROPHYSICS AND
PHOTOCHEMISTRY OF FORMALDEHYDE
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. IR. J. ERKELE~S, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP
VRIJDAG 21 NOVEMBER 1980 TE 16.00 UUR
DOOR
MARTIN JOZEF HUBERT KEMPER
GEBOREN TE HEERLEN
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOREN
PROF. DR. H.M. BUCK EN
CONTENTS
I. Introduction
II. Coupled potential surfaces and unimolecular photochemistry.
II.1. The calculation of coupling elements II.2. Ab-initia calculation on the
photo-chemistry of formaldehyde. The search for a hydroxycarbene intermediate.
J. Amer. Chem. Soc. 1978,100,7841 II!. A theoretica! study on the reactivity and
spectra of H2
co
and HCOH. A dimeric model for formaldehyde photochemistry.IV.
v.
J. Amer. Chem. Soc. submitted
The calculation of radiative transitions. IV.1. Ab-initio Cl calculation of single
vibronic level fluorescence emission spectra and absolute radiative life-times of H2
co (
1A2).
J. Chem. Phys. 1979,70,2854
IV.2. A comparitive study of theoretica! methods for calculating forbidden transitions.
Chem. Phys. submitted Some future developments. Summary Samenvatting Levensloop Dankwoord 7 12 13 17 23 72 73 78 94 98 100 102 103
I. INTRODUCT ION
In principle, quantum mechanics can predict all physical and chemical phenomena, which occur after the excitation of a molecule to a higher electronic state (e.g.
s
0 + hv----111-81). What is needed for such a description is shown in Scheme I. Using an ab-initio or semi-empirica! computer program, the Schrödinger equation for the electrons in a fixed nuclear frame iS solved. This gives wave functions and eigenvalues (energies) for the ground and excited states. If one repeats the calcula-tion for a large set of geometries, potential energy surfaces are obtained. The minima and saddle points on a specific sur-face represent (meta)stable structures and reaction paths, respectively, on the surface; in other words, they describe the thermal chemistry. From the potential surfaces force con-stants can be calculated; these concon-stants can be transformed into infra-red and Raman frequencies. The surfaces can also be used to calculate in a numerical way the anharmonic vibration functions. From the electron wave functions of ground and excited state, electronic transition moments and non-Born-Oppenheimer (BO) couplings are calculated. Together with the vibration functions this gives the total transition moment
(a measure for the probability of a radiative transition), and the total coupling between the ground and excited state. With these total couplings one describes radiationless transitions (e.g. s
1
1"1.1V-t>-~). The total transition moments can be used for the calculation of the vibrational structure of UV-absorption and -emission spectra. Also, radiative lifetimes can be calcu-lated. Another important phenomenon in photochemistry is energy transfer according to the Förster/Dexter mechanism. The total transition moments are needed for this purpose also.The practical elaboration of this seemingly simple Scheme is far from being trivial and straightforward. The prediction of stable molecular structures is the only subject in the Scheme, which can be done routinely; quantum mechanica! cal-culations being what they are however, even this is only true for not too extraordinary molecules. The calculation of coupling elements between potential energy surfaces has only recently become possible. A quantitative theory of radiationless tran-sitions was deve1oped by van Dijk et al1- q . In addition to
this, UV-absorption spectra and i.r. frequencies were calcu-lated3. These studies1-~ concentrated on the formaldehyde
molecule because of several reasons. Formaldehyde gives, after exci tation to the
s
1 state, all the phenomena related toScheme I: it has well-resolved absorption and fluorescence emission spectra; a radiationless transition depopulates the excited
s
1 state, and there are dissociation as well as addi-tion products. Moreover, from a theoretical point of view, this four-atom molecule is regarded as a suitable compromise between very computable, but photochemically "uninteresting;, two-atom molecules, and systems which have interesting reactions, but are much too large for reliable calculation. This thesis consists of a number of published and submitted papers on the related aspects of Scheme I; again, forma,ldehyde is the model compound. Chapter II concerns the calculation of non-BO couplings for several unimolecular reaction coordinates, and mentions, for the first time, the possibility of dimeric interactions. Such a dimeric model for formaldehyde photo-chemistry is developed in Chapter III, together with the cal-culation of i.r. and Raman spectra. Chapter IV concerns the calculation of radiative transitions. All papers carry their own abstract, introduction, and conclusions, to which the reader is referred for more information. A survey of the main c9nclusions and some possible future developments are given in Chapter V.Schrödinger equation for electrons electron
wave functions eigenvalues
electronic non 00
trans. moment coupling
vibration potential
1
... Ï "
-fllllctions surf aces total
trans. iroment
1
UV-absorption total couplings stable structures
& emission energy "radiationless i.r. and reaction paths
rad. lifetime transfer transitions" Raman "thermal chemistry"
IV v II III II, III, V
Sèheme I. Some aspects, needed for the description of ohotophysical and photochemical
~ behaviour. The Roman numerals indicate the Chapters which are related to these aspects.
A large number of methods used in this thesis are nowadays standard ones. Notably ab-initio calculations5 with the
GAUSSIAN programs6' 7 and ST0-3G8, 4-31G9 , and 6-31G*10 basis sets are well described and documented11 in the literature. Concerning these methods the reader is referred to the cited literature. The calculation of coupling elements however, is much less widely known. Therefore, Section II.1 contains a brief description of such a calculation, in order to facili-tate the understanding of the work presented in Section II.2. The papers in this thesis all carry more than one author's name; this is completely deserved, because these papers could not have been written in the present form without the work and knowledge of these colleagues. Of course, the full respon-sibility for the form and contents of these papers is carried by the author of this thesis.
REFERENCES
(1) van Dijk,J.M.F. Thesis, Eindhoven lhliversity of Technology 1977 (2) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.; Visser,G.J.
Olem. Phys. Letters 1978,54,353
(3) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M. J. Chem. Phys. 1978,69,2453
(4) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M. J. Chem. Phys. 1978,69,2462
(5) Any standard text on quantlllll chemistry, e.g.:
McWeeny ,R.; Sutcliffe ,B.1. "Methods of M::>lecular Quantum Mechanics", Academie Press, wndon 1969
(6) Hehre,W.J. et al Q:PE 1973,11,236 (7) Pople,J.A. et al Q:PE 1978, 11,368
(8) Hehre,W.J.; Stewart,R.F.; Pople,J.A. J. Chem. Phys. 1969,51,2657 (9) Ditchfield,R.; Hehre,W.J.; Pople,J.A. J. Chem. Phys. 1971,54,724 (10) (a) Hariharan, P.C.; Lathan,W .A.; Pople,J .A. Chem. Phys. Letters 1972,14,385; (b) Hariharan,P.C.; Pople, J.A. Chem. Phys. Letters 1972, 16,217; (c) Hariharan, P.C.; Pople,J.A. Theor. Chim. Acta 1973,28,213
(11) Lathan,W.A.; Curtiss,L.A.; Hehre,W.J.; Lisle,J.B.; Pople,J.A.
Progr. Phys. Org. Chem. 1974, 11, 175
II. COUPLED POTENTIAL SURFACES AND UNIMOLECULAR PHOTOCHEMISTRY
II.1 THE CALCULATION OF COUPLING ELEMENTS.
The Born-Oppenheimer approximation, which leads to separate wave functions for electrons and nuclei, has been extremely successful in molecular spectroscopy. Unfortunately, this success has given rise to the uneradicable misunderstanding that these electron and vibrational functions, and also the potential energy surf aces which are produced by standard quantum chemica! methods, really exist in nature1
• Actually
however, Born-Oppenheimer functions are merely the mathematica! results of the human incapability to solve in a direct way the complete Schrödinger equation for a molecule. (The same can be said for atomie orbi tals, molecular orbi tals, .etc.). This misunderstanding resulted in the fact, that it was not before
1968 that Jortner and co-wo.rkers2
- 5 showed that precisely these
non-BO couplings "cause" radiationless transitions. We will now briefly describe this theory, together with van Dijk's6
calculational method.
The interaction between a molecule and an electromagnetic field prepares the molecule into an excited state I~>. Due to the linewidth of the exciting light, this excited state is a linear combination of exact eigenfunctions: I~> ~ cm l~m>. These exact eigenfunctions can be expanded in a complete set of zero-order states {lun>}
The set {lun>} can be defined in many ways6'7• In the
adiabatic Born-Oppenheimer (ABO) formalism , which we will use throughout this section, the functions lun> are eigen-functions of
Ho H - TN
( 1)
H is the total Hamiltonian which describes electrons and nuclei; TN is the kinetic energy operator for the nuclei. Returning to equation (1), iu
0> carries oscillator strength to the ground state; in the formaldehyde case it is interpre-ted as the vibronic level in 1A2 (S1) of which the decay is described. The states lun> (n~O) are the vibronic levels,
s
0x.of the ground state. The fact that a linear combination of exact eigenfunctions is prepared gives rise to a time-dependent
(sharply decreasing) oscillator strength. This is because of the interfering phase factors: exp (-iEmt), where Em is the
ei~envalue of the exact eigenfunction ~m· Mathematically, the
decay of I~> is described by the time-evolution:
To quantify this theory, the coefficients am have to be calculated. They are obtained by diagonalizing the inter-action matrix of zero-order st~tes2• In other words, we have
to calculate the coupling elements vn
=
<u0 1TN1un>. Becauseof the ABO formalism we have 8 :
q, and
x
are electron and vibrational wave functions 1 ,respec-tive ly; q, depends explicitely on the set of electron coordinates q and parametrically on the set of nuclear coordinates Q. The subscripts n and m merely identify the functions. Using TN P2/2M, where M is the complete set of nuclear masses, we obtain for the coupling of a single vibronic level (4' 1x1i) in
s 1 with a high vibrational level (4'oXoj) in s0 :
where we neglected6the term with P2 • The subscripts q and Q
denote the integration variable. If P is expressed in
mass-weighted normal coordinates, we get:
!:
k
<~11 au/aQk l~o>
--~~~~~~~q a/aQk
EO E1
The summation is over the normal coordinates. U represents all potential energy terms: electron-electron repulsion, nuclear-nuclear repulsion, and electron-nuclear-nuclear attraction. The first term contributes nothing because it does not depend on Qk; the second term gives zero because of the orthogonality of ~O and
~1. This leaves
(3)
The summations e and n are over all electrons and nuclei, respectively. Zn is the nuclear charge; ren is the electron-nucleus distance:
j 1 x, y, z.
n e
sj' and qj' are the cartesian coordinates of nucleus n and electron e, respectively. Because we differentiate in
equation (3) to normal coordinates, we have to use the trans-formation
where the D's are elements of the transformation Jacobian between normal and cartesian coordinates. Now, equation (3) is easily6 transformed into:
Here, we have something that is computable: ~ (qj, - sj1)/r;n
is the j'-th component of the electric field operator for nucleus n. These integrals can be calculated routinely by several quantum chemical programs.
c
10(Q) is now a linear combination of these integrals. Finally, thec
10 function is integrated between the appropriate vibration functions (eq (2)).REFERENCES AND NOfES
(1) This misunderstanding is so widespread, that even at many places in this thesis such an incorrect impression is created.
(2) Bixon,M.; Jortner,J. J. Chem. Phys. 1968,48,715 (3) Jortner ,J.; Berry ,R. S. J. Chem. Phys. 1968 ,48,2757 (4) Bixon,M.; Jortner,J. J. Chem. Phys. 1969,50,3284 (5) Bi:xon,M.; Jortner,J. J. Chem. Phys. 1969,50,4061
(6) van Dijk,J.M.F. Thesis, Eindhoven University of Technology 1977 (7) van Dijk,J.M.F.; Kemper,M.J.H.; Buck,H.M. Chem. Phys. Letters
1976,44'190
(8) Born,M.; Huang,K. "Dynamical Theory of Crystal Lattices", Clarendon Press, Oxford 1954, Appendix VIII;
II. 2
Kemper, VOJI Dijk, Buck / Photoehemistry of Formaldehyde 7841 Ab Initio Calculation oh the Photochemistry of
Formaldehyde. The Search for a Hydroxycarbene Intermediate
M. J. H. K-per, * J. M. F. vu Dijll.l and H.M. Back
Contributi()ll /rom the Departmelll of Organic Chemistry, Eindhoven Unlversity of Ted1nalogy. Eindhoven. The Netherlands. Received April 28, 1978 •
Alonnct: Ab initio ca!culations on the H,CO-HCOH rearrangement have been performed. The electronic ooupling hetween the 81 and So surfacos, which can induce intesnal conversion. is calculated for this rearrangement and for the reaction coordi· nates leading direclly to radical and molecvlar products. The coupling is caleulated with true adiabatic Born-Oppenheimer functioml, i.e .• the wave functions and coupling integrals are explicilly calculated as functions of the nuclear geometry. The coupling for the hydro<ycarbene rearrangement tums out to be the largest one. This indicalés that the hydro<ycarhene can serve as an intermediate state in the formaldehyde photochemistry. We also report calculations on the bimolecular H,CO· HCOH reaf!•angemenl; lhis interaction givcs rise toa decrease of the energy harrier involved.
...
During the last decade there has been a growing interest in the pbotochemiatry of the formaldehyde molecule. The ex· perimental wor1c2-s clearly shows the increasing power of the techniques available today. One of the most striking experi· men tal results was obtained by Houst on and Moore. 5 They
found, under C<lllisionless ronditions, a time lag of at least 4 /IS between the decay of the fonnaldehyde S1 state and the appearance of the CO photoproduct. They rould not even ex· clude that, under collisionless ronditions, no photodissociation occurs at all. In view of this point it is interesting to no te that Y eimg and Moore4 found that the total ra te at which rollisions
remove moleeules from single vibronic levels of H2CO is as
much as ten timea the hard sphere rollision rate, thus indi<:ating
sornc long-range interaction between the excited molecule and its nc:ighbors. The ronclusion from their work is that some intermediate is involved in the photodissociation of forma!· dehyde, out of which the molecular and radical products are formed:
h•
H~O (So)...,. H2CO (S1l - X - products
of the obtained values for the HCOH sta tea, but very recently a large-scale Cl calculation by Lucchese and Schaefer12
showed that the results of Popte and Altmann are qualitatively correct and that the hydroxycarbene possibility is quite fea· sible. We also performed, as a continliation of oor study of the decay of the H2CO (S1) state, ab initio SCF and SCF-CI
calculations on the formaldehyde-hydroxycarbene rear-rangement. The emphasis in this study, however. does not lie on calculating reliable values for the varioos HCOH states. Just as important as the knowledge of the energiea of the local minima on the potential energy surface is the answer to the queation how the molecule can reach these local minima. The m<JSt attractive candidate for the intermediate X is the HCOH (So-lrans) state, which lies. according to oor results, about 20
kcal/mol below H~O (81). To reach this state, the H~O
(S1) molecule has to leave somewhere the S1 potential energy
surface. Although the roupling in the equilibrium state is too small to induce internal ronversion, as stated above, this sit· uation can, in principle, change further away on the reaction coordinate. So in section Il we calculate the electronic roupling elements between the S1 and So surfaces as functions of three reaction coordinates: leading to hydroxycarbene, direct radical dissociation. and direct molecul!tr dissociation, respectively. As we will sec in section II, the energy barrier between the So* state and the HCOH local minimum wilt be too high for a single molecule to reach this minimum. Thai is why we de-scribe in section 111 calculations of an interaction between a pair of formaldehyde molecules in order to investigate the possibility oflowering thisenergy harrier. The way the mole-cules interact in the model described in section 111 is inspired by the H2CO-HCOH reaction pathway; in sectfon IV we wil!
briefly discuss other kinds of interactions. One: of the main tasks of formaldehyde photochemistry is now
to unravel the nature of this intennediate state X. For this state several possibilities exist: in tbc first place. intemal ron-mo.i to an isoenergctic vibrational state, So*, of the electronic ground state. This So• state should then, onder collisionless ronditions, have a lifetime of at least 4 ,.s, after which disso-ciation to the pbotoproducts takes place. Recently we showed,
however, by mcans of an allCIU"ate ab initiocalculation,0--• that the roupling in the equilibrium state is too small to induce in· temal conversion. The second candidate is intersystem crossing to T1•. Apart from theexperimental findingsofTang etal.,9
which sbowed that the triplet state plays a negligible mecha·
nislic ro1e in the pbotochcmistry of the 224' (Si) level, it is not ll. 'I1le Unimolecular Reammgemat HiCQ-HCOH clear at all, from a theoretica! point of view, bow the T 1 state, A. Calculatioul Method. The calculational method is de·
which lies only 3000 cm-1 below Si. can give a level density scribed in detail elsewhere;7 we will here only repeat the main
for this fout-atomie molecule that is high enough to give an features. For the calculation of the electronic wave functions exponential decay. There exists. however, a third possibility of formaldehyde at the different points of the reaction roor-for the intermediate state: the hydroxycarbene HCOH. The dinates we used Clementi's IBMOL s program Il with a ron-fll'SI question that arises conceming this candidate involves the tracted Gaussian basis set given by Dunning: 14 for carbon and
energies of the different HCOH ronfigurations (So·trans, oxygen a (9s5p) [4s3p) set; for hydrogen a (4s) [2s) set. Fur-So-<;is, and T1·gauche) relative to the prepared H~O (S1) ther, we used Goscinski's transition operator method15 in order state. Calculations by Pople's group10 and Altmann et al.11 to describe the So and S
1 surfaces with the same accuracy. For
plai:e !hem below the H:tCQ (Si) state. These calculations were the ronfiguration interaction we included 175 configu.rations performed without ronfigu.ration interaction, leading among selected by the point system of Morokuma and Konishi. •6 The othen to a H~O So-T 1 energy gap much lower than the ex· electronic wave functions obtained are true adiabatic
Bom-perimental one. This result questions of rourse the reliability Oppenbeimer functions: they are explicitly calculated as
[Reprlnted from the Joumal of the American Chomical&ciety, 100. 7841 {1978).j Copyright @il 1978 by the American Chomical Society and reprinted by pennission of the copyright owner
7842 Journal of the American Chemica/ Society/ 100:25 / December6, 1978
Ol bJ C)
fipre I. Reaction coordinates(<I>. M,and R) leadingto(a) bydroxycar-bene formation: (b) direct molecular dissociation; and (c) direct radical dissociation. In (b) the variable M denotes the distance from"the carbon
to the midpoint of tbc H-H bond.
functions of tbe nuclear geometry, contrary to the conventional "Herzberg-Teller" -like approach, where one tries to include the dependence on the nuclear geometry by means of an ex-pansion around the equilibrium geomelry, i.e" an exex-pansion in crude Born-Oppenhcimer functions. The geometries which were used as an input in the SCF-CI calculations were ob-tained from a comf.!etely optimized, single-configuration 4-31 G calculation.' These optimizations were made for dif· ferent values of the three reaction coordinates depicted in Figure 1: (a) leading to the hydroxycarbene, (b) leading di-rectly to molecular products, and (c) leading directly to radical products. With the SCF-CI program we calculated both the So and S1 surfaces. With the single determinant Gaussian 70
program, however, no reliable S 1 calculations can be made for formaldehyde: the Si wave functions and geometries become unreliable because of spin contamînation from funetions of different multiplicity. Therefore we used for the S1 geometries the optimized T1 structures obtained from the Gaussian 70
program. The results of this procedure wil! be discussed in section II B.
18
The probability for the radiationless transition frorn S1 to .
So is determined by the coupling between the S1 and So
po-tential energy surfaces. This eoupling is caused by the impulse operator P of the nuclei. The electronic coupling.element is given by
C1o(Q) = {4>1(q.Q)IP/Ml<fio(q,Q))•P Here, q and Q denote the complete sets of electron and nuc!ear coordinates, respectively; <t>1 and <fio are the electronic wave functions of excited and ground state; M denotes the set of nuc!ear masses, while the subscript q denotes integration over the electron coordinates. This integral can be rewritten7 as a
linear combination of integrals of the electric field operator: C1o(Q)
~7 D'}kZ. (4>1(q.Q)I~ -(q}-sj·)/r •• 'l<fio(q.Q))0 <l>o(Q)- 4'1(Q) p
(11.I) Here, sj· and q} are the j'th Cartesian coordinate of nucleus n and eJectron e, respectively; z. stands for the charge of nu-cleus n; D'f. is an element of the Jacobian matrix, which
transforms the Cartesian coordinates to the normal coordinates
k, while <l>o(Q) and 4>1(Q) represent the adiabatic potential
energy surfaces. At this point the methods used here and the one used for the calculation of the "statie" S1-S0 internal
conversion 7 start to diverge. In the latter calculation the
stan-ing point was a formaldehyde molecule "reststan-ing" in some vi-hrational state, x11(Q), of the local minimum corresponding
to H2CO (S 1). In order to obtain the total coupling, u11,o1• bet ween the prepared state and an element of the coupling So•
manifold, the electronic coupling element C1o(Q) bas to be
integrated over Q:
v11.01 = (x,,(Q)IC1o(Q)lxo;(Q))e (11.2)
whcre x 11(Q) and X!\l(Q) denote the (anharmonic) Yibrational wave functions involved. for the statie situatÏQll, these vibra-tional wave functions, corresponding to the normal Yibrations, can be calculated from the potential energy surfaces +o(Q) and \ll1(Q). forthedynamksituation,however, where the molecule
does not just fluctuate around the equilibrium configuration, but instead wanders about on the potential energy surf ace. the vibrational part Of the coupling cannot be easily calculated. Therefore we only calculated at each point of the reaction coordinates the 12 integrals of the electric field operator:
Ej'n(Q) = (</>1(q,Q)lr'.
.
(qi - sj-)/r.,.311/>o(q,Q))q (11.3)As a measure of the electronic eoupling wc can choose for in· stance the length of the vector E, defined by
E2(Q) = Ê È ZnlEJ'•(Q)I' {11.4)
n=1r--1
We will return to this choice in the discussion in section llC.
Apart from an increasing E vector, the probability for the radiationless transition can also be enhanced becausc of the decreasingdistance, l\llo(Q) - 411(Q)I, between the potential energy surfaces. The total coupling due to electronic factors is then given by
vE(Q) = E(Q)/ll4>o(Q)- 4>1(Q)li (11.5)
B. Resulls. In Tables 1 and II we show the geometries and energies of the various formaldehyde states, For the sake of clarity we notc once more that we optimized the geometries with a single configuration 4-31 G program (method 1) and that · these gcometries were used as input in the large basis set + Cl calculation (method Il). No further geometry search was at-tempted in the Cl study performed here, in contradistinction
to what we did in a previoos paper7 for the H
2CO (So) and
H:iCQ (S1) states. The results from.ref 7 are also shown in Table 1 for comparison. The table soows that the H,CO (T1)
geometry from nn:thod I agrees reasonably well with the Cl optimization for H;iCO (S 1) from ref 7 and with the experi-mental data for H:iCQ (S1). The same hokls for the H;iCO (So)
geometries. This indicates that the procedure for choosing the geometry input for method Il works satisfactorily, at least in the starting points for the potential energy surf ace scan. Fur-tber we sec from Table 1 that the unimolecular rearrangement occurs in one plane for the So case, leading to the hydroxy· carbene trans configuration. For the rearrangcment in the T1
state we find an increasing out of plane angle 8, leading to the HCOH (T 1 )·ga uche configuration. Table II shows the energies of the various states, relative to the H;iCO (So) values obtained
by the same method. Concerning the value for H2CO (S1) we
have to distinguish between the 71.9 kcal/mol for the opti-mized Si structure (bent) and the value of9L7 kcal/mol for the S1 geometry which is reached by a vertical (franck-Condon) transition from theSoequilibriumgeometry. Using a complete optimization in the Cl calculation, van Dijk8 found for these energies 74.2 and 91.7 kcal/mol, respectively. This similarity gives another positîve affirmation for the procedure used. The potential energy surfaces for the H2CO-HCOH
rearrangement, obtained by method 11, are given in figure 2. In this figure the full lines represent the optimized So and Si surfaces, while the dotted lines, S0b and S1P, represent the So
surface with bent and the S1 surface with planar geometry, respectively. The energy harrier for the unimolecular rear-rangement on the S0 surface is !02 kcal/mol. We sec from
Table Il that the extension of method I to method Il dccreases this barrieronly by 8 kcal/mol. We do not expect thal a further geometry optimization in the Cl calculation wil! have a
sub-Kemper, van Dijk. Buck / Photochemistry of FQl'mofdehyde 7843
Table I. Optimized Bond Lengths (À) and Angles (deg) for H,CO, HCOH, and the Transition States (TS) for the Unimolecular Rearrangement
HCOH (So)·trans H,CO(So) method t• ref7• exp' H,CO (So)·TS method 1 method 1
co 1.204 1.23 1.2()8 co l.305 l.3211 CH =CH' l.081 l.10 l.116 CH' 1.087 1.098 LHCH' 116.2 116 ll6.5 CH l.266 1.936 fld 0 0 0 <!>'(• LHCO) 55 26.5 LH'CO 116.5 103.5 8 0 0 HCOH (T1)-gauche H2CO(T1) method 1 e•p H2CO (T1)·TS method 1 method 1
co l.367 , 1.307 co l.354 1.354 CH •CH' l.070 l.096 CH' l.072 1.072 LHCH' 121.0 118 CH l.448 l.782 e 32.3 37.9 l/>(=LHCO) 50 34.3 LH'CO 126.7 126.0 e 52.l 67.8
H,CO(S1) ref7 exp
co 1.36 1.325
CH =CH' l.06 1.095
LHCH' 112.S ll8
• Method 1: single configuration 4-3 IG. • Ascalculated in ref 7 with the (9s5p) [4s3p] basisset +Cl with geometry optimization. •· faper-imental data taken from ref 18. '8 deootes the out of plane angle. • <f> denotes the reaction coordinate for H2CO-HCOH. See Figure 1.
T.W. ll. Encrgies (kcal/mol) for the Various formaldehyde States. Relalive to the H2CO (Sol Value Obtained by the Same Method method 1• metbod n• othcr work HiCO(So) 0 (• -113.692 61)• O(• -113.86207) 0 ( • -113.863 54)1 H,CO{S,,)·TS' ll0.2 102.0 HCOH (S.,)-trans 51.2 52.5 51.712 H2CO(T1) 35.5 68.912 11,co (T1l-TS 100.9 HCOH !T1)-gauche 58.7 73.0" 71.9 (91.7)' 74.28 (91.7)• 153.4 123.7
• Method 1: singleconfiguration 4-JIG. • Method 11;(9s5p) (4s3p) +Cl, with the geometries from method 1.' TS ~ transition state. d The
absolute energies are given in atomie units. ~The value in parentheses is the vertical ( f'ranck-Condon) energy difference. See tut.
stantial effect. Tb is can be seen, for instance, f rom the absolute energies for H2CO ($o) given in Table Il (second and third column): they are the same within 1 kcal/mol. The harrier on the S 1 surf ace is a little lower: 81.5 kcal/mol.
The calculated electronic couplings, uE(Q) (see eq 11.5), for this rearrangement are given in Figure 3. The most important resull for the unimolecular rearrangemcnt is given in Figure 4. Here we compare the electronic roupling, vE( Q), for the first part of the three reactioo coordinates, starting from the S 1 equilibrium geometry. The calc;ulation for the two direct dis-sociations was done in the sa me way as for the H 2CO--HCOH rearrangement: calculate for sevcral values of the reaction coordinates Mand R (see Figure 1) the optimized triplet
ge-ometry and use this gege-ometry in the S1 calculation with the
large basis set +Cl program.
The direct dissociation paths have already been calculated on a Cl level by Hayes, Jaffe, and Morokuma. 19-2t Our 4-31G results for the radical dissociation are the same as theirs: for the dissociation on the T 1 potential energy surf ace the out of
plane angle increases remarkably; the leaving H atom is swung away from the rest of the molecule. For the direct molecular dissociation on the T 1 potential energy surface we also found
an increasing out of plane angle (the angle between the CO
bond and the HCH plane in the coordinate system we used in this case), while the two H atoms depart in a slightly asym-metrie way from the carbon alom. This asymmetry is mnch less dramatic, however, as found by Hayes, Jaffe, and Moro-kuma20·l1 for the So dissociation.
C. Analysis and Discussion. We start oor discussion with the
results given in Figure 4. We see there that the total coupling,
vE(Q), given by eq 11.5 is unequal to zero in the starting poinL Tbis is because of the following reasons. In the first place. the starting point is the $1 equilibrium geometry, which differs
from the So equilibrium structure. For this Jatter geometry the vibrational and translational components of the electronic coupling are zero because of symmetry reasons.7.S The most important contribution to the starting point coupling, however, comes from the rotational components. We conclude this from the following argumentation: as stated in section 1 IA, the electric field integrals (11.3) are transformed in the statie calculation from Cartcsian to normal coordinatcs by means of the Jacobian matrix elements DJk· lf the normal coordinate transformation is exactly known, it is possible7·' to distinguish
completely between the vibrational, rotational, and transla-tional components of the electronic roupling. In the calculation reported here, the movement of the molecules is too far away 19
7844 Journa/ of the American Chemica/ Society/ 100:15 / Deeember6, 1978
160
100
"' 80 •o 20
,
__
0F"tgure 2. Calculated potentiai energy surfaces (method ll) för the H;iCO-HCOH rearrangement; q, denolés the reaction çoordinate. Sob = S. with bents, geometry: S1• s, with planar S. geometry. The zero point on the energy s.cale çorresponds with -113.862 07 au (see Table
Il).
from the starting S1 equilibrium geometry to transform with
one single, constant Jacobian: we end up at a completely dif-ferent (hydroxycarbene) (:Ollfiguration. Although, because of this reason, it is not possible here to exactly distinguish between the various kinds of couplings, we can perform the transfor-mation of the integrals (11.3) for the first part of the three re-action coordinates in order to get an approximate insight into the relative importance of the components. The result of this transformation is given in Figure 5. We only give five of the
obtained nine curves because the translational vectors for the reaction coordinates (b) and (c) are almost the same as the one shown in the figure, while the rotational vectors become only slightly (<>< 10-4 au) larger for (b) and (c) at energies higher than l IO kcal/mol. So we see that the main difference between the couplings shown in Figure 4 is caused by the differences between the vibrational components for the three reaction coordinates. And only these eornponents can be responsible for înducing an internal conversîon. This is so because the trans-lational components have no physical relevance, being the consequence of keepîng the eleclron coordinates tixed while differentiating with respect to the translational coordinates.7
Concerning the rotational eornponents we note that, although they are dominant in the neighborhood of the S1 equilibrium geometry, they do not (:Olltribute much to the ra te of internal conversion. This is so because the electronic components have to be integrated between the vibrational and rotati<mal ei-genfunctions involved; see eq 11.2. This leads toa negligible contribution to the final coupling elements of the rotational components. 7 The result from these considerations is the conclusion that those electronic coupling components, which can effectively induce internal conversion, are larger for the H2CO-HCOH rearrangement than for the direct dissocia-tions. lt is hard to say exactly how much larger the possibility for internal conversion is for this rearrangement because of the
20
·-F"iguro 3. Calculated electronic oouplînp, v"(Q). for the H,CO-HCOH rcarrangement; tl> denoles the reaetion coon:lînatc.
uncertainties inherent in the method used; the obtaincd dif-ferences between the rearrangemenl and the direct dissoeia-tions are so systematic, however, that we have no doubt about the qualitative conclusîon made above. Unfortunately, tbisdoes not mean that the hydroxycarbene is the solution for the in-termediate state problem; we showcd earlier7 that the
mag-nitude of the total S,,-S1 coupling elements is so low that in the
statie situation there is not internal (:Ollversion at all. What we .have shown here is that the H~O-HCOH rearrangement leads to such a combination of normal mode movements that we have a favorable combination of coupling components. The increase of the coupling, relative to the statie calculation, is nol large enough, however, to explain the H2CO (S1) decay. So
we conclude that formaldehyde needs another molecule to induce the înternal conversion, a conclusion in agreement with the experimental findings mentioned before.5 Such a SC(:Olld
molecule is needed for another purpose too: as can be seen from Figure 2, the formaldehyde molecule wil! end up at the wrong side of the H2CO-HCOH energy barrier; it cannot reach the
HCOH (S,,) local minimum on the potential energy surface. In principle there are two ways to lower this barrier (the pos-sibility that the hydrogen tunnels through the harrier is men-tioned brietly in the next section). The first way is an extensioo of the calculational method: il is well known that equilibrium structures can be described satisfactorily at a lower level of calculational sophistication than transition states. So an ex-tension of the method might lower the barrier.34 The second way to achieve this is introducing a second molecule; Ibis possibility is treatcd in the next seetion.
111. The Bimoleeular Rearrangement H,CO-HCOH A. lntroductlou. As described above, the potential energy surfaces for both the So and S1 states show a large barrier for
the unimoleeular rearrangement H2CO-HCOH. A second
molecule is needed to lower the S,, harrier, in order to give the
H~O (So*) molecule the opportunity to reach the HCOH
($o) minimum. Moreover, a second molecule is needed already for inducing the s,-So internal conversion. lt cannot even be excluded that there will be a much larger medium effect. Re-member, for instance, the well-known HCN-CNH rear-rangement. Calculations22 show that there is a large harrier for this reaction, and yet il takes place almost immcdîately in the laboratory. The hydrogen isocyanide was observcd for the
Kemper, OQll Dijk, lhlck / Photochemutry of F<>rmaldehyde
Fiptt 4. Calculaled eleclronic oouplings, v"(Q), fOf (al H,CO-HCOH
rearra~ (b) direct molecular dissociation; and (c) direct radical dissociation. The cnergy scale is taken relativc to the H2CO (S,,) ener· gy.
first time in interstellar spacell where we have almost colli-siooless conditions; as soon as there is the possibility for colli·
sions one obtains the "normal" HCN. The same holds for vinyl alcohol. Althoogh a 4-3 IG calculation predicts a harrier of 85 kcal/mol for its unimolecular rearrangement to acetalde-hyde, 24 it was only recently possible to detect vinyl alcohol in
the gas phase.25 So for both the hydrogen isocyanide and the vinyl alcohol case we can expect a medium interaction which gives a large decrease of the harrier on the potential energy surface. The same may hold for formaldehyde.
B. MetW m Results. We treat the two formaldehydes as one super molecule using the Gaussian 70 program. We place the second formaldehyde as follows (see Figure 6 for the case where we try to lowerthe banier on the So surface): the oxygen
02 of the second molecule is placed on the line formed, in the unimolecular transition state, by C1 and the migrating hy· drogen H2• We then optimize on the STO-3G levelfor several
positions (4>) of H2 at, and in the neighborhood of, the
uni-molecular transition state (4>(TS)) the bond lengths C1 H2 and
C102, and the angle a describing the position of the second (catalyzing) molecule relative to the first (migrating) one. Some·tests showed that the total energy was minimized upon keeping c" Hz, 02, and C2 in one plane. The remaining
geo-metrical parameters were kept fixed at the 4-31G optimized values of the noninteracting molecules. With the optimized ST0-3G structures a 4-31G calculation was performed; a further 4-31 G optimization did not change anything consid· erably. We calculated at several positions.; in order to sec if the angle corresponding to the energy maximum shifts to an-other value, compared to the unimolecular case. This turned out not to be the case. We found the interaction bet ween H,CO · (TS) and H,CO to be attractive: !here is a shallo\v minimum in the potential energy curve as a function of the C,02 distance.
This attractive character is in contradistinction to the
(ST0-3G) curves for the H,CO-NH3 interaction;26 the situation
reported here resembles more the hydrogen bond between H2CO and H,021 and the H2CO-H system. 2s Prom the op-timized position of the catalyzing molecule, the obtained MOs, and MuUiken population analysis we found that the interaction
of the two molecules is mainly due to the interaction between
the migrating hydrogen H 2 and the n orbital of the oxygen 0,. In Table lil we show the main results of the calculalion and compare them to the unimolecular rearrangement. We note
7845
.,
"
,,
,.
•• 90 100 no ".".
Flpre 5. Lengtbs of vccton formed by !be vibrational oomponents for (a) H1CO-HCOH rearrangemcnt; (b) direct molec•lar dissnciat;..,; and (c) direct radical dissociatioo. Thè rotalional. R. and translational. T. vcctors for (a} are glven for comparison. The cnergy scale is taken rdative to the H,CO IS.)energy. "•'-. c.,7To, /r(tp!TSI "2 . ·. "' ·~/"' c,
\
H3Fiprt 6. Configuration used for calculatîng harrier 1owering, Sec text.
that the interaction does not lead toa hydrogen abstraction froll) the migrating to the catalyzing molecule: the C 1H2
dis-tance is increased relative. to the unimolecular case, bilt the hydrogen H2 stays with its original molecule. In Figure 7 we
give as an illustration the obtained nel atomie charges for the
T1 (migrating) + S0 (catalyzing) case; the other situations
reported in Table 111 give the sa me picture. As can be seen from Figure 7, the amount of charge transfer between the molecules is negligible ("'0.02 electrons). Table lil shows that there is. indeed a harrier lowering effect; this effect, bowever, is rela· tively small, 6.5- IO kcal/mol. So we sec that we still have an
energy harrier in the rearrangement: the unimolecular sin· gle-determinant harrier is l l0.2 kcal/mol; configuration in-teraction (sec Table Il) results in 102.0 kcal/mol, while the bimolecular interaction reported in this section gives a further
lowering, resulting in a harrier of approximately 95 kcal/mol. Tuis is still aboul 2S kcal/mol above the vibrationless S1 level. The qualilative key to the solution of this kind of problem is of course tunneling. The problem with this mechanism, how-ever, is the fact that the calculated tunneling probabilities are
7846 J®roa/ oftlte American Chemica/ Society/ 100:25 / December6, 1978 •192 H "'51 -321 c=O H/ ",92 +184 " ~20 -593 c=o
\
" •389 " b H"''86 .fi1&2~1ey",,
\ "' +l~l T1 lmlgr!+ S0 leatj Flgure 7. Calcula1ed ( 4- 31 G) net atomie charges 110-1 electrons).extremely sensitive to the parameters involved (potentialen-ergy curves, en(potentialen-ergy of the state involved, etc.).29.30 So in principle it is probably possible to adjust or parametrize the (calculated) parameters in s11eh a way that the observed H,CO decay and also the differences between H,CO and D,CO are explaîned, but one never knows how reallstic such a treatment will be. These argumentations concerning tunneling hold, of course, for the unimolecular rearrangement too.
IV. Summary and Concluslon
The H2CO-HCOH rearrangement shows a large barrie• on both the So and S 1 potential energy surfaces. For the single determinant calculation with modest basis set this result was obtained already by Altmann et al.; 11 we showed that extension toa larger basis set+ Cl only slightly decreases this harrier. One of the main results of this work is the tinding that internal conversion to So* is more probable for the hydroxycarbene rearrangement than for the direct dissociation mechanisms. This is due to the fact that those coupling components which can effectively induce the radiationless transition are larger for the rearrangement than for the direct mechanisms. This indicates that the hydroxycarbene can serve as an intermediate state in the formaldehyde photochemistry. lnteractions with other molecules will be needed, however, to effect this lransi-tion and probably also to reach the intermediate state. The inclusion of a second molecule in the process complicates the description because of the numerous ways the molecules can interact. Apart from the possibility reported in section 111, which only leads toa relatively small decrease of the barrier, we can mention, for instance, hydrogen abstraction leading to HCO + H2COH. Another interesting possibility is a hydrogen exchange between two (excited) H2CO molecules leading to two hydroxycarbenes as indicated in a schematic way below: H,CO + OCH2 ' HCOH + HOCH
The energy harrier for this process might be lower than for the single hydrogen abstraction, in analogy with the bifunctional eatalyzed [ 1,3] hydrogen shift in propenel2 and the simulta-neously moved hydrogen atoms leading to double wel! poten·
22
Tûle 111. Calculated 4-3 JG Resolts for the lnteraction between a
"Migmtin&''and a "Catalyzing" H,CO Molecule
migrating catalyzing harrier• c,tt" A• c,o" A a, deg
So So So T1 T1 T, So So 110.2 99.9 102.5 65.4 59.0 1.266 1.391 4.002 116 1.319 3.361 118 1.448 1.472 3.754 112
0 In kcal/mol relative to two noninteracting molecules in their
equilibrium OOJ'l:figuration. b Parameters from Figure 6.
tials in the guanine-cytosine pair and the formic acid dimer.33
Our final conclusion is that there area number of indications that the hydroxycarbene structure can play a key role in the H2CO (S1) decay, but that a lot of experimental and
theoret-ica! work bas still to be done to come toa satisfactory under-slanding of the photochemistry of this seemingly simple mol-ecule. This future work might focus on the direct experimental contirmation of the hydroxycarbene structure and both ex-perimental and theoretica! work on interactions between formaldehyde and other quenching molecules.
References and Notes
(11 PlilllpsResear<hl.abor_E,_,The_
(2) DoGralf, B. A.; C41vert, J. G. J. Am. Chem Soc. 1"7, 89, 2247. (3) McOulgg. R. O.; C..!vert, J. G. J. Am. Chem. Soc. 1989, 91, 1590. (4) Y"""9. E. S.; Moore, C, B. J. Chem. Phys, 1973, 58, 3988.
(5) Housloo. P. L.; Moore, C, B. J, Chem Phys. 1178, 65. 757. (8) van Oljk, J, M. F.; Kemper, M. J, H.; Kerp, J. H.M.; Viiser, G. J.; Buck, Il
M. Chem PhJ!s, l.ell. 1978, 54, 353.
(71 van Dijk, J, M. F.; Kemper, M. J. H.; Kerp. J. H. M.; Buok, H. M. J. Chem.
PllJis"lnpreso.
(81 """Dijk, J, M. F. Thesis, Eindhoven University o1 Teclvlology, Eindhoven.
T h e - . 1 9 7 7 .
(9)
=·
K. Y.; Fairchild, P. W.; lee, E. K. C. J, Chem. Phy$. 1977, 66,(10) l.ahn, W. A.; Curtlss, L. A.; ._.,,W. J.; Lisle, J. B.; Poplo, J. A. !'rog, Phys, 0rg. Chem. 1974, 11, 175.
(11) -.J. A.;Csizmadla, l.G.; Yates,K.;Ya .... P.,J.(;hem, PllJis. 1977, 116,298.
(121 Lucchese, R. R.;
-ter
UI. H. F. J. Am. Chem. Soc. 1978, 100, 298. (13) The BCIL5)fpad<agewasde"9loped by Or. E. Clemenll andoo-workers;the fOW'*lnde• tt~ prO(J'am was wrllten by Dt- Me van Hemert.
WettlankOr.P.E.S.--ol~~kl<maklng
._prog<amsandOr. G.J. V'....,..kl< adaptionoflheseprogramo lolhe
BurrougN 87700 compufer.
{14) lluMlng. T, H J. Chem. PflJis, 19711. 53, 2823.
( 15) Goscinski, O. and co-workers, u cbd in ref 7. (16) - - K.; KonJsh;, H. J. Cl>em, ,,,,,., 1971, 55, 402,
{17) - W. J. "al Gausslan 70, frwom 236. Qimlum Chemlslry ~
Exohange, - . a l.Wv<nily. llloomington. lnd. (18) Moule. 0. C.; Walsh, A.D. Chem. Rev. 1175, 75. 67. (19) Hayos, D. M.; - K. Chem Phys. Lolt. 1112, 12. 53&.
{21)) Jallo. R. L; Hayo$, D. M.; - - K. J. Chem. ,,,,,._ 1974, 8(1, 5\08,
{21) Jaffe. R. L; - K. J. Chem Phys, 1976, 6•, 4381. (22) Pea1soo, P. K.; Scilaefer lU, Il F. J. Chem Phys, 1975, 62, 350. (23) - · L E . ; 8'ill, 0. Bull. Am. Astron. Soc. 1971, 3, 388. (24) - W. J,; Popplnger. O . ; - . L. J. - · Chem. Soc. 1977, 99.
6443.
(25) Sailo, S, Chem Phys. Lolt. 1978, •2. 399.
{26) Mmaraj, U.; Csl!madia, I. G.; Wlnnlk, M. A. J. Am. Cl>em. Soc. 1977, 99,
946,
(27) lwata, S.; Moro1wma. K. J. Am. Chem. Soc. 1973, 95, 7563. (28) Mizutanl, K.; lzumi. T.; - · S. Bull. Chem. Soc. Jpn. 1977, 511.
2113.
{29} SrickmaM, J.: Zimtnermann, ... J. Chem. Pflys. 1Ht, 50, 1608.
(30) Harmony. M.O. Chem, Soc. - - 1972, 1. 211.
(31) Cllill<, J, H.; Moora, C, B.; Nogar, N. S. J. Chem. Phys. 1178, 68, 1264.
(32) Niemayer, H. M.; Gooclnold. 0.; Ahlbefg, P. T e - 1175, 31.
1899.
(33) Clementl, E.; Mehl. J.; von Nlessen, W. J. Chem Phr.J. 1971, 54, 503.
(34) Aft8' lh8 monusorlpt was llnlshed a study oo 1he ~
rearrangement _ . . , {l)yl<Wa, C. E.; SChaefer Hl, H F. J, Am. Chem.
Soc.1978, 100, 1378). TheaulllcrtshowthotforUVs,___in.
duSiOnolpofaritatlonluncllcnsiS-.tequally~as~
·-·
III. A THEORETICAL STUDY ON THE REACTIVITY AND SP~CTRA OF HzCO and HCOH.
A DIMERIC MODEL FOR FORMALDEHYDE PHOTOCHEMISTRY.
A THEORETICAL STUDY ON THE REACTIVITY AND SPECTRA OF H2CO AND HCOH. A DIMERIC MODEL FOR FORMALDEHYDE PHOTOCHEMISTRY
*
M.J.H. Kemper , C.H. Hoeks, and H.M. Buck
Contribution from the Department of Organia Chemistry, Eindhoven University of Teahnology, Eindhoven, The Netherlands.
Abstract The reactivity and spectra of formaldehyde isomers and dimeric complexes between them are studied with ab-initio
methods. A large number of complexes between H2co, HCOH-trans, and HCOH-cis is calculated, and the suitability of minimal basis sets for this purpose is discussed. Infrared and Raman spec.tra of (H 2Co) 2 are calculated with relatively simple methods using spectroscopie masses and scaled force constants.
In this way, the structure of dimers in matrices can be deduced. Hydroxycarbene, HCOH, plays a key role in a model that expJains a large number of experimental facts of formaldehyde photochem-is try. Hydroxycarbene forms complexes with H2CO; the
stabilization is due to hydrogen honds. HCOH is a new
example of an ambiphilic carbene. Addition products are formed from HCOH ... H2co complexes. The calculations show that, in agreement with matrix experiments, glycoaldehyde and methanol are easily formed. The formation of HCOH-trans occurs through a dimeric interaction with the shifting hydrogen. This bimolec-ular process is 9.6 kcal/mol (6-31Gx) in favour of the uni-molecular conversion. HCOH-cis might be formed via a non-planar transition state, where also stabilization at the carbenic center is possible. When higher concentrations of HCOH are available, a hydrogen exchange mechanism easily transfers hydroxycarbene back to H2co. Several experiments are suggested in this paper; notably molecular beam and isotopic-mixture experiments will give useful information. The involvement of HCOH in the light-induced formose reaction is suggested.
1. Introduction
During the last decade the study of the formaldehyde molecule has taken a central place in fundamental molecular photo-chemistry and photophysics. Formaldehyde owes this position to the fact that, on the one hand it can behave as a proto-type for the photochemistry and photophysics of larger mole-cules, and on the othev hand, it is amenable to detailed and well defined spectroscopie and theoretical studies.
The experimental studies revealed a large number of phenomena. The overall process is seemingly simple: formaldehyde is pre-pared to the
s
1 state by light absorption, and the final products are molecular and radical fragments:h
-c
H2+ COH7COISol
~
t-tiCOIS,)H + HCO
The detailed mechanism, however, is still a tantalizing problem. We will not try to discuss here in an extensive way all the existing literature on this subject. We will only mention in the following section some main results in order to define clearly the problem we are concerned with in this paper: the role of hydroxycarbene in formaldehyde photo-chemistry.
2. The problem
2.1. Gasphase and matrix experiments
The experiments on formaldehyde that are of interest here, can be placed in two categories: gasphase and matrix experi-ments.
An important result in gasphase experiments is the finding by Houston1 and Zughul2 that a time lag is involved in the
formation of CO photoproduct. At energi'es less than 1500 cm- 1 above the
s
1 origin, the appearance time of CO light absorption is much langer than the corresponding decay time ofs
1 formal-dehyde fluorescence. The appearance time is hardly dependenton the formaldehyde isotope or the vibrational energy. Extra-polation of the results indicates that the zero pressure inter-cept of the formation rate T~6 is at most 0.2 µsec-1. This suggests that photochemistry cannot occur without collisions. As remarked by Weisshaar3
, it is difficult to reconcile these results with the conclusions that have to be drawn from
collisionless (p < 1 mTorr) decay experiments. At these low pressures a rapid collision-free decay channel is observed. This fast decay can be explained3
, in principle, by a
se-quential coupling mechanism. The prepared single rotational level in
s
1 is coupled with the set of high vibrational levels ofs
0• Theses
0!t levels are broadened to a "lumpy" continuumbecause of coupling with the continuum of H2+CO dissociative levels. A level shift technique involving a uniform
ex-ternal electric field enabled Weisshaar to obtain quantitative information about the molecular parameters that determine intramolecular decay rates. H is encouraging to see that the coupling elements obtained by this elegant method are in agreement with the calculations of van Dijk4 and Heller5•
Weisshaar's conclusion is3 that the only way to reconcile low and high pressure results is to claim that the
s
1 state can be quenched to a non-fluorescing intermediate state, X, which requires a subsequent collision to give products:P=O
/ (1) ...
s,
co
. , 12) ...
P > 0.2 torr
The quenching (2) must dominate the collision-free channel (1) for pressures above ~ 0.2 Torr.
One of the main tasks of fundamental photochemistry is to unravel the nature of this intermediate state. Candidates are in short supply: high vibrational levels of the electronic
ground or triplet state (s
0
~ or T1
~. respectively), and the hydroxycarbene isomer HCOH. It is difficult to dismiss definitively one of these possibilities; all of them have arguments pro and con. Moreover, the experimentally observed phenomena in formaldehyde photochemistry are so numerous and divers, that it is unlikely to find just one simple mechanism to explain everything. In this paper we concentrateon the involvement of the hydroxycarbene isomer, and we will only make some remarks'on the other possibilities. More de-tails , including the extensive literature on this topic, can be found in Weisshaar's work8
• From a theoretical point of
view, r
1
~ has always been considered an unlikely candidate, because its vibrational level density near the s1 level ismuch too low. Experimentally, Tang6 et al. showed, by exciting
triplet perturbed
s
1 levels, that the triplet state plays no mechanistic role in the photochemistry of the 2341 and 2241 levels of formaldehyde. The recent and rather unusual results3of quenching experiments on D2
co
renewed the interest in this possibility. The main difficulty with s0
~ is probably the explanation of the time lag. It is hard to imagine how a very high vibrational state (28000 cm- 1) can resist energy re-laxation and randomization for one microsecond.Before going to the third candidate, HCOH, we have to mention the other type of experiment which is of interest here: photolysis of formaldehyde in low temperature matrices. These matrix experiments are complementary to gasphase work. It is for instance possible to study in a direct way in an inert-gas matrix the differences between monomeric and dimeric formaldehyde. Particularly, the work of Lee's group has to be mentioned here1
-9• Diem7 photolyzed H2
co
in an Ar matrix. Infrared absorption before and after the photolysis showed that the dissociation of formaldehyde is effected by the cage dimer. The amount of photoproducts, CH 30H plus CO, paralleled the amount of dimer present before photolysis. Surprisingly, the monomer peaks did not decrease at all after photolysis. So, matrix isolated H2co
is not photochemicallydissociated. (Recall, that it is not yet clear at this moment, whether or not photoproducts are formed in gasphase experiments
for p + 0. Extrapolation to zero-pressure has only given an
upper limit for
TëÓ)·
In more highly concentrated matrices, Sodeau8 observed the formation of glycoaldehyde, methanol andcarbon monoxide. Also some evidence for hydroxyketene, (CH(OH)CO), was reported. The intermediacy of hydroxycarbene in the formation of these addition products'was suggested. In the next section we will put together all these experimental facts and offer a model to explain them.
2.2. Hydroxycarbene
Houston and Moore1 mentioned for the first time trans-hydroxycarbene as a possible intermediate in formaldehyde photochemistry. Extensive calculations by Goddard10 and
Pople11 place HCOH (8
0) at energies of 52.8 and 56.6 kcal/mol, relative to the formaldehyde ground state. So, the local s 0-minimum which corresponds to HCOH is, in principle,
accessible from the first excited singlet of H2
co
(Es1=
80.6 kcal/mol). In an earlier paper12, we reported calculations onthe electronic coupling elements between the s 1 and s 0 surfaces. These elements, which induce s 1 "\J'V+ S~ internal conversion,
increase as the molecule is distorted towards a HCOH-like geometry. The increase of the coupling elements for the
reaction coordinates leading directly to molecular and radical products is much less dramatic. This suggests, that the
H2
co
+ HCOH reaction path is important, because it gives the molecule a maximal opportunity to leave the s 1 potential energy surface. We also showed12 that bimolecular interactionbetween two H2
co
molecules lowers the energy harrier to HCOH rearrangement.In order to be acceptable as an intermediate in formaldehyde photochemistry, HCOH must give reasonable explanations for the main findings mentioned in Section 2.1:
- The explanation for the time-lag is, of course, obvious. Just as T1 would do, HCOH gives the formaldehyde molecule 28
a place to wait a while before giving photoproducts.
- In gasphase experiments molecular and radical products are formed. This process can be induced by collisions; zero-pressure dissociation is uncertain.
- Mainly the matrix experiments show that the unimolecular formation of HCOH either must be very difficult or it must be a very rapid reversible one.
- Cage dimers of H2
co
must lead, via HCOH, to the addition products glycoaldehyde and methanol.This can be put together in Scheme I. Here, M is a second matrix
~COIS
1
1 + M--IHiCO···MI HCOH···M-products""/. ( 11 12)
wf
131!
gasphase ___..,H2 M + HCOH lS01-_.H
Scheme I+co
+ HCOformaldehyde molecule in its electronic ground state. We will also pay some attention to CO, H2
o,
and H2 as a quencher. In the next three sections we give the results of a large numberof ab-initio calculations on this model. In Section 3 we give
calculated bimolecular complexes between molecules of tt2
co
and HCOH. These complexes are used in Section 4 as a starting point for step (2) of the model: the formation of addition-products. In Section 5 we discuss the steps (1) and (3): the formation of hydroxycarbene.
Finally we note that the reverse reaction (4) involves a larger energetic problem than transition (3). This is illustrated very schematically in Figure 1. The harrier to HCOH lies slightly above ihe
s
1 origin13• As will be discussed in Section 5 tunneling and/or bimolecular interactions give an effective lowering of this harrier beneath thes
1 origin. If we start, however, with a Fischer-type transition metal-carbene complex like:the carbene ligand can split off from the metal. Then imme-diately a hydrogen shift occurs14, yielding an aldehyde; there is no trace of RCOH at all. As remarked by Lucchese15, this
indicates that HCOH + H2
co
must be very easy. The carbene ligand might have some internal energy after the split off, but part of the HCOH molecules will relax to the vibrationless:::::84 80.6 (3) E H2CO 1511 (kcal/mol l 52.8
f
HCOH ISol 0 H2CO 1501Figure Energies (kcal/mol) involved in the rearrangernent HzCO <---> HCOH-trans
level at 52.8 kcal/mol. From there no unimolecular escape to H2
co
is possible because the energy harrier of ~ 31 kcal/mol is too high. However, no HCOH is detected at all. The way to escape is a bimolecular one and will be discussed in Section 5. 2.All ab-initio calculations with ST0-3G and 4-31G basis sets
were done with the GAUSSIAN 70 program16
; for the 6-31G:t
calculations the GAUSSIAN 76 program17 was used. A large
number of the calculations in Sections 3-5 concern interaction energies; i.e. a calculated dimer energy minus the energies of the non-interacting molecules. In Table I we give all the energies which are taken as a reference.
Table I. Calculated energies (a.u.), 'Which serve as a reference level a / a SI'0-3G 4-31G SI'0-3G 4-31G 6-31G11/ 4-31G 6-31G* H2CO -112.35435 -113.69171 -113.69262 -113.86555 -113.86633 l:IXl:l-trans -112.27841 -113.60763 -113.61107 -113.78168 -113.78351 , HCOO-cis -112.26909 -113.59684 -113.60005 -113.77253 -113.77449
a) SI'0-3G
=
geometry optimized with ST0-3G basis set; 4-31G/SI'0-3G = 4-31G calculation in ST0-3G optimized structure, etc.3. Complexes of H6CO-isomers and their spectra 3.1. The complexes
In Table II we give the stable, dimeric complexes between formaldehyde isomers. All calculations were done with the ST0-3G basis-set; all intra- and intermolecular geometrical parameters were optimized with respect to the total energy of the system. The effect of optimizing intramolecular para-meters instead of holding them at their monomeric values is relatively small in case of weakly bonded complexes. If there is. however, a strong interaction or even a complete reaction between two molecules (as in Section 4), reoptimization is, of course, necessary. In order to treat all systems in an equivalent way, we decided to optimize all geometrical para-meters throughout this work. The intermolecular parapara-meters are elucidated in Figure 2. Some remarks can be made for all
Table II. Sf0-3G calculated complexes between H2CO isomers. The inter-molecular parameters are shown in Figure 2.
H-atoms R 1fi1 w2 +1 +2(kcal/mol) Energya HzCO + HzCO 1 1234 3.72 70 70 0 0 -0.94 (A -0.95)b "v (D -0.63)b 2 1234 3.59 53 71 0 90 -0.87 1\, (C -0.61)b 3 1234 3.44 0 180 0 0 -0.66 '\, 4 1234 4.07 101 48 0 0 -1.04 '\, (B -1.04)b 5 1234 4.19 107 43 0 0 -1.04 1\, (E -0.44)b 6 1234 3.92 54 54 90 90 -0.63 1\, H2
co
+ fl:(lf-trans 7 1238 4.06 74 56 0 0 -0.32 '\, 8 1238 3.91 65 46 90 0 -0.56 '\, 9 1247 5.93 0 0 0 0 -0. 15 '\, 10 1238 5.94 0 0 90 0 -0.11 '\,'\, 11 1247 4.51 191 322 90 0 -0.21 '\,I\, 12 1238 3.89 44 282 90 0 -4.41 '\,I\,u
1247 4.14 54 18 0 0 -3.33 H2CO + HCOH-cis 14 1248 3.47 66 282 90 0 -3.24 '\,I\,.u
1237 4.48 9 51 0 0 -6.14 16 1237 4.59 8 50 90 0 -4.71 1\,1\, 17 1248 4.53 32 304 0 0 -5.24 '\,I\, 18 1248 3.67 125 128 0 0 -1.54 '\,I\, 19 1248 3.55 176 116 90 0 -0.86 1\,1\, 20 1237 3.54 120 264 90 0 -0.82 '\,I\, HC(lf-trans + HC(lf-trans 21 1674 2.77 68 68 0 0 -19.88 1\,1\, 22 2754 3.31 70 70 90 90 -0.77 1\,1\,a)Relative to the sum of energies of the non-interacting molecules as given in Table I.
b)Related complexes and energies as given in ref. 18
