J. Phys. Chem. 1993,97, 1152-1 157
1152
Complexes between Formic Acid and Carbon Monoxide: An ab Initio Investigation Jan Lundell' and Markku RbPnen Department of Physical Chemistry, University of Helsinki, SF-001 70 Helsinki, Finland Zdzislaw Latajka Institute of Chemistry, University of Wroclaw, SO- 383 Wroclaw, Poland Received: August 4, 1992
The structure and energetics of the complexes formed between formic acid and carbon monoxide have been investigated by a b initio molecular orbital theory. Six minima were found for the trans-formic acid/CO complex and two minima for the cis-formic acid/CO complex, with interaction energies ranging from 6.5 to 18.5 kJ mol-' at the MP2/6-3 1Gs*level of theory. The most stable complexes are formed via a nearly linear hydrogen bond. The importance of electron correlation calculated at the MP2 level is especially notable due to the correlationinduced sign reversal of the dipole moment of carbon monoxide. Both HF and MP2 levels of theory predict a relatively strong hydrogen-bond formation, yielding a substantial perturbation of the vibrational spectrum of formic acid. Especially large shifts are found for the OH stretching and torsional vibrations. This is in accord with the experimental results.
Introduction Molecular complexes are pervasive in molecular science, and a great amount of experimental and theoretical information has become available.14 It is unnecessary to underline the importance of hydrogen-bond interactions, numerous chemical compounds interacting attractively through noncovalent or nonionic interactions. Owing to the small size of CO and its ability to weakly bind to countless molecular species as well as its importance in nature, many interaction investigations exist on CO. Connected with the present study, a number of investigationsare worth noticing. Reported complexesinclude interplays with hydrogen halides2-12 cyclobutadiene,13J4methanol,15J6and acetylene.17J8 Furthermore, an extensive theoretical investigation of weakly bound complexes containing carbon monoxide by Parish et al.I9 reveal one especially significant feature in weak binding of CO: its electrical polarization. The electrical response properties of CO play a major role in complexation. This poses a challenge for the theoretical capabilities in the case of the hydrogen bond when consideringwhich end of CO is acting as a better proton acceptor. SCF calculations constantly give the wrong sign for the dipole moment of CO, and only the inclusion of electron correlation is able to ensure the correct sign corresponding to the structure of c-o+.2c-22
Recent development of theoretical methods and computer facilities have made it possible to handle the interactions between largesubunits by meansofabinitio molecular orbital calculations. Interactions of formic acid have been one target of these studies: with amines using standard STO-3G and 4-3 1G basis sets,23s24 with water at the HF/4-31G level,25and with methyl chloride at the MP2/6-31+G* level of theory.26 Despite the extent of theoretical work done on 1:l complexes of formic acid, only relatively few experimental observations of formic acid complexation e ~ i s t . ~ 'Assignments .~~ in argon matrix of infrared spectrum of photodecomposition products of oxalic acid contain some fundamental vibrations for 1:1 formic acid/carbon dioxide supermolecule. In addition to these studies dimerization of carboxylic acids has been the subject of many theoretical investigations. Formic acid dimer has been studied with ab initio calculations using Hartree-Fock and configuration interaction appro ache^^^*^^ and molecular mechanic^.^' The structure of formic acid dimer has been experimentally revealed by the early microwave s t ~ d i e s and ~ ~ infrared - ~ ~ studies in the gas phase35.36 0022-3654/93/2097- 1 152304.00/0
and in a nitrogen matrix36showing the ability of formic acid to strong hydrogen-bonded interactions. Following in the footsteps of these investigations, we have performed ab initio molecular orbital study on formic acid-carbon monoxide complex in order to obtain information about the structures, energetics, and nature of the interactions between these two monomers. By using the electron correlation method we are able to aid the experimental studies by providing relatively reliable information on the infrared spectrum and intensities of the complex. The investigationof these complexes was stimulated by the existence of these complexes as photodecomposition products of formic acid anhydride3' isolated in rare-gas matrices. Also, the possibility of CO existing as an impurity in matrices can create a distortion of pure monomeric vibrations via complexation. The calculated equilibrium geometries and vibrational spectra are given for six complexesof trans-formic acid and for two cis-formic acid. Energy decomposition analysis of the interaction energies have been performed for all complexes.
Details of Calculations All calculations were performed within the framework of the ab initio closed shell approximation using the GAUSSIAN 9038 package of computer codes. Electron correlation was considered via Maller-Plesset perturbation theory39v40to the second order, including explicitly all electrons. Applied basis sets were the standard, split-valencetype, double-f 4-31G4' and 6-3 lG**,42-44where p and d functions are added on the first- and second-row atoms. According to the findings of Reynolds26 and the recommendation of Hobza et al.4S on improvement of computational level, the 6-3 1+G*46-48basis set was applied, introducing d-type functions and a diffuse sp shell on heavy atoms. The harmonic frequencies for each complex were calculated numerically at the MP2/6-3 1G** level, and the approximate assignments were done according to normal-coordinate analysis using the ab initiocalculated Cartesian forceconstants as input.49 Interaction energies were calculated as the difference of total energy between the complex and the monomers at infinitedistance. Energy Decomposition Analysis. One of the most commonly used energy decomposition schemes is the analysis proposed by Morokuma et al.50351 among a variety of schemes proposed during the last couple of decade^.^^-^^ Calculation of components using Q 1993 American Chemical Society
Formic Acid and Carbon Monoxide Complexes
The Journal of Physical Chemistry, Vol. 97, No. 6, 1993 1153
the monomer-centered basis set (MCBS) corresponds to the scheme of Morokuma, and it decomposes the interaction energy into the following contributions: electrostatic (Ea), exchangerepulsion (Eex),polarization (Epl),and charge transfer (&). In addition to Morokuma’s scheme also the dispersion energy (EDISP) is calculated. The energy decomposition scheme applied in this paper is similar to the schemes recently proposed in the l i t e r a t ~ r e employing ~~,~~?~~ the supermolecule approach and obtaining the monomer wave functions in thedimer-centered basis set (DCBS). In this scheme the sum of the electrostatic and exchange repulsion, Le., contributions of the first-order correction in the perturbation method, is defined as the Heitler-London (A&) interaction is removed from the SCF interaction energy energy. When MHL (USCF), the SCF delocalization energy can be accessed, representing the effect of the mutual deformationof the electronic charge clouds in the SCF calculations for molecular complexes. Le., to the E,, and E,I Further decomposition of ~ESCF, components, should be refused to avoid the possible collapse of the valence electrons of one monomer into the occupied core orbitals of its partner, resulting in a violation of the Pauli exclusion principle. The original Morokuma scheme suffers from this violation.63”s The electron correlation contribution at the MP2 level is calculated according to the definition of Chalasinski et al.6769 dividing the correlation interaction into second-order uncoupled Hartree-Fock dispersion energy (defined by Jeziorski et al.70), second-order intrasystem correlation correction of the electrostatic effect, induction correlation, and exchange terms. In the MCBS the interaction energy components are affected by the basis set superposition error (BSSE).54.58s61*65 The BSSE is calculated as the difference between the energy of isolated monomers in the MCBS and the energy of isolated monomers in the DCBS. This method corresponds to the counterpoise correction (CC) proposed by Boys and Bernardi7’ aimed to minimize the BSSE in all of the interaction energy components. A full description of this scheme has been published previously.72J3 Calculationswere carried out on VAX 8650 and Convex C220 computers and a CRAY X-MP EA/432 supercomputer at the Centre for Scientific Computing (Espoo, Finland).
Results and Discussion Six minima, I-VI, for the tram-formic acid + CO complex and two minima, VII-VIII, for the cis-formic acid CO complex were found using several levels of theory, presented in Figures 1 and 2, respectively. Structures I and I1 describes hydrogenbonded complexeswith an almost linear O-H-.(CO) arrangement where the carbon monoxide is attached to the 0-H tail of tramformic acid either from the carbon end or oxygen end of the monomer. Structures V and VI represent similar arrangements as in the first two complexes with the exception that now the complexation occurs on the formyl group hydrogen. Complexes I11 and IV show a different kind of interaction between the two subunits corresponding to a van der Waals complex where CO is in the CIOzHl plane between the lone electron pairs of the oxygen atom. The two structures involving cis-formicacid (VII, VIII), correspond to structures I and I1 again with a nearly linear O-H.-(CO) arrangement. Optimizations for cis-formic acid starting from structures similar to V and VI resulted always in structures VI1 and VIII, the potential energy surface always showing a diminishing energy path toward these two minima. Examination of the properties of the isolated subunits was performed analogically to the complexes. The reader is referred to a selected list of examples of various monomer properties in refs 74-83. However, the electrical properties of carbon monoxide are worth some consideration. Because of the well-known importance of electrostatic effects in the treatment of molecular intera~tions,8~-~~ the correct reproduction of dipole moment and
+
Z
ZJ
I I
03
* c2
I
111
IV
V
VI
Figure 1. Calculated structures for tram-formic acid 01
II
/=’-
o2 \
82
+ CO complexes.
01
II
% ,-
03
c2*
O2\
82
81
81 \ \
\ \
VI1
\
VIIl
Figure 2. Calculated structures for cis-formic acid
O3*C2
+ CO complexes.
dipole polarizability are crucial. At the SCF levels the dipole moments are consistentlypositive. The same was found even for correlatedlevelslikeMP2/4-31G (0.1086D)andMP2/6-31G** (0.2020 D). The inclusion of spdiffuse functions produced a negative dipole moment of 4.4383 D, which is much larger than the experimental value, 4.122 D.87 As noted, the magnitude of MP2/4-31G and MP2/6-31G1* calculationsis correct, but only added diffuse functions can reproduce the real electric structure of c-o+. Geometry and Interaction Energy of Complexes. The results of geometry optimizationsof tram- and cis-formic acid complexes at the electron correlated levels are collected in Tables I and 11, respectively. It has been shown that electron correlation plays a critical role in reproducing interacting systems with good accuracy, and the 6-31G** and 6-31+G* basis sets represent a good compromise of efficiency and completeness for a study of weak interaction^.^^^^^^^^ However, the introduction of a diffuse sp shell diminishes the total energyby 0.3-3.8 kJ mol-’ depending on the structure in question. Reynolds found this energy lowering to be 2.1 kJ mol-’ for the formic acid-methyl chloride system.26 Bond lengths calculated at the H F level are shorter than those at correlation levels. This is a result of poorer description of interactions. An exception to this is the HF/6-31G** basis set resulting constantly to a stronger complex bond than any other basis set. Compared with the MP2/6-31G** values, overestimation for hydrogen-bonded species ranges from 0.076 to 0.15 5 A. The same values are 0.032 and 0.161 A for structures I11 and IV, respectively. In addition, a difference of almost 0.2 A in the interaction bond length between structures I11 and IV is caused by the additional attraction toward the hydrogen atom of the C I - H ~bond. Likewise, in structure VI, the attraction of the carbon tail to the carbonyl oxygen might cause the distortion of the linear CI-H~.-03 bond. Within the framework of correlated level of calculations, a diverse variation of bond lengths is noticed. Going from MP2/ 4-3 1G to MP2/6-3 I+G*, a stabilization of parameters is achieved
Lundell et al.
1154 The Journal of Physical Chemistry, Vol. 97, No.6, 1993
TABLE I: Optimized Geometrical Structuree of tf8nsFormic Acid + CO Complex' Ill
I1
I
MP2 4-31G MP2 6-31G** MP2 6-31+G* MP2 4-31G MP2 6-31G** MP2 6-31+G* MP2 4 3 1 G MP2 6-31G** MP2 6-31+G* 1.242 1.215 1.218 1.240 1.213 1.217 1.238 1.212 1.215 0 2 4I 1.379 1.344 1.348 1.382 1.347 1.350 1.390 1.351 1.354 H1-02 0.990 0.975 0.985 0.986 0.97 1 0.982 0.986 0.972 0.982 H241 1.090 1.093 1.096 1.090 1.092 1.095 1.089 1.091 1.095 C2-03 1.168 1.148 1.148 1.172 1.151 1.151 1.172 1.150 1.151 C ~ * * - H I 2.145 2.216 2.260 2.147 2.225 2.172 0 s .HI 3.261 3.298 3.396 C2' * - 0 2 01C102 125.3 125.5 125.3 125.2 125.4 125.1 124.9 125.1 125.0 H102C1 110.9 106.5 107.8 111.1 106.5 107.4 110.8 106.1 107.1 H2C102 109.6 109.7 110.0 109.3 109.5 109.9 108.9 109.3 109.8 C2H102 170.1 163.9 180.3 159.3 163.9 176.0 03H102 0yC2H1 172.5 162.4 172.5 150.3 139.7 164.0 C203H1 110.4 110.6 113.7 C202CI 74.1 74.4 72.6 03c202 CI-01
IV
VI
V
MP2 4-31G MP2 6-31G** MP2 6-31+G* MP2 4-31G MP2 6-31G** MP2 6-31+G* MP2 4-31G MP2 6-31G** MP2 6-31+G* C1-01 OrCl H1-02 H241 C2-03 Cy * 0 2 Cy * *H2 0,. * *H2 01C102 H102C1 H2C102 C202Cl 03C202 C~H~CI 03H2C1 O3C2H2 C203H2 0
1.239 1.391 0.986 1.079 1.171 3.197 124.7 110.6 108.6 85.5 114.4
1.212 1.352 0.972 1.091 1.151 3.145
1.216 1.354 0.982 1.095 1.151 3.203
124.8 106.0 109.3 94.0 107.7
124.9 107.O 109.8 96.8 105.9
1.240 1.390 0.986 1.088 1.171
1.213 1.351 0.971 1.090 1.149
1.217 1.354 0.982 1.094 1.150
2.507
2.703
2.798
124.4 110.4 109.3
124.7 105.9 109.6
124.7 107.0 110.0
177.1
177.1
176.9
180.5
178.8
178.8
1.239 1.385 0.986 1.089 1.172
1.213 1.348 0.972 1-091 1.151
1.216 1.35 1 0.982 1.095 1.151
2.691 125.0 110.8 109.5
2.697 125.1 106.1 109.7
2.805 125.0 107.1 109.9
111.2
112.8
111.9
125.6
118.0
129.0
Bond lengths in angstroms and angles in degrees.
TABLE II: Optimized Geometrical Structures of &Formic Acid + CO Complex' VI1 CI-01
024I H1-02
c2-03
VI11
MP2 4-31G
MP2 6-31G**
MP2 6-31+G*
MP2 4-31G
MP2 6-31G**
MP2 6-31+G*
1.235 1.382 0.983 1.100 1.169 2.153
1.208 1.349 0.969 1.001 1.147 2.224
1.21 1 1.354 0.979 1.103 1.148 2.273
1.233 1.386 0.980 1.100 1.173
1.207 1.352 0.966 1.100 1.151
1.209 1.356 0.976 1.103 1.152
2.112 122.5 112.5 113.9
2.170 122.9 108.8 113.4
2.171 122.5 109.6 113.9
180.5
176.7
176.8
188.9
183.5
183.6
Cy**Hl 03.* *HI OIC102 122.8 123.1 122.7 Hi02C1 112.5 108.8 109.7 HzCiOz 113.9 113.4 113.9 C2H102 179.7 178.2 182.4 03H102 03C2H1 183.7 183.3 184.9 C203H1 a Bond lengths in angstroms and angles in degrees. between the two largest basis sets, MP2/4-31G showing some
dispersion. This also indicates that it is not really useful to use double-{wave functionsbeyond H F calculations. In general, the structures are almost unperturbed and nearly identical to those of isolated monomers. However, depending on the site of complexation, bond lengths and an les change clearly. A lengthening of the bond to 1.15 for each species exceeds the experimental value of 1.101 As9 for the CO monomer. For the trans-formic acid species the carbonyl bond lengthens compared to theexperimentalvalueof 1 .202A.76 On thecontrary, in the cis-formic acid species this bond length diminishes upon complexation from 1.22S79to 1.21 A. The energetics for various complexes of different levels is collected in Table 111. The energy of structure I is given in atomic
R
units and all the others relative to it. The energy difference between structures I and I1 is twice as large as given by Latajh et al.16 for similar structures between carbon monoxide and methanol. The CO rotational energybarriers between structures I and 11, calculated at the MP2/6-31G** level, are shown in Figure 3. The rotational angle of CO was scanned, keeping all other parameters at their values as in structure I. This rotation occurs in the plane of formic acid monomer because an out-ofplane rotation should implicitly overcome a rotational barrier of almost 100 times greater. Furthermore, our experimentalstudies show rotation of the CO subunit when argon matrix is annealed,17 which presents a strong evidence for a relaxation process from I1 to I involving a rotation 'in-plane". The calculated interaction energies of SCF and the electron
Formic Acid and Carbon Monoxide Complexes
The Journal of Physical Chemistry, Vol. 97, No. 6, 1993 11%
201
h 3
0
TABLE VI: Compoaents of Interaction Energy Calculated io the Dimer h i s Set (DCBS).
1
,
I
4-
\
!
H...CO
H...CO
0 120
60
0
180
240
I1 I11 IV V VI VI1 VI11
\I I
300
TABLE IIk Calculated Total Energies (84dRelative Energy Differences (W mol-') between the Various Complexes
+ CO
HF/4-31G HF/6-31G** MP2/4-31G MP2/6-31G** MP2/6-31+G*
IV
v
VI
-301.034 579 1 -1.24 10.98 9.51 10.46 7.46 -301.512 514 2 1.49 7.84 7.47 7.69 4.98 -301.603 655 3 12.14 14.41 18.60 12.82 18.18 -302.306081 4 8.24 11.30 13.09 11.94 11.38 -302.309 544 5 5.60 8.56 9.86 9.18 9.31 C-HCOOH
+ CO
basis set
VI1
VI11
HF/4-31G HF/6-3 1G* MP2/4-31G MP2/6-3 1G** MP2/6-31+GS
29.67 25.46 26.10 23.51 21.37
27.59 26.61 39.41 32.57 28.13
TABLE Iv: Calculated Intenctioa Energks (W mol-') at Difiemt Levels of Theory u1 the Mffenaces in Total Energy between the Complex dthe Isolated Moaowrs at Infinite Distance 4-31G
I I1 111 IV V VI VI1 VI11
6-31G**
Emsp -7.284 -5.527 -3.728 -1.728 -2.502 -4.581 -5.481 4.134
strengths are almost equal to structures I and 11. Additionally, the interaction energies ranging from 4.7 to 15.9 kJ mol-! are of the same magnitude than those reported for formic acid-methyl chloride complexes (from 8.9 to 21.0 kJ mol-l).26 Even though the stronginteractions, the energy barriers between the non-hydrogen-bonded and hydrogen-bonded complexes are somewhat small, and thus the vdW species are probably not very stable in low-temperature matrices. The hydrogen-bonded species have been studied and structures I and I1 have been identified in argon m a t r i ~ . 3The ~ ab initio predictions of the frequency shifts compare well with the experimentalobservations for the H1-bondedspecies. The results will be discussed in the forthcoming paper.j7 Search for the complexes of cis-formic acid in matrices is in progress in our laboratory. The leading idea is that it might be possible to trap cis-formic acid as a complex in the matrix. From creation of formic acid in the excited states, relaxation to the ground state could lead to trapping of the higher energy species and provide an opportunity to overcome the high barrier between cis- and trans-formic acid. The calculated relative energy difference between the trans- and cis-formic acid complexes, 21.4 and 28.1 kJ mol-!, for structuresVI1andVIIIcompared with I, respectively, are similar to the theoretical value of 18.7 kJ mol-' given by Goddard et al.77 for the two conformers of formic acid. Furthermore, these cis-formic acid complexes are located in a potential energy well deep enough to be stabilized in the matrix. Ewrgy Decomposition Analysis. Table V presents the results of the energydecomposition analysiscarried out for all complexes with 6-31G** basis set. Optimized geometries are used, and the standard method by Morokuma et al.,50,51where the monomers are calculated in the monomer centered basis set, is employed. All components are therefore affected by the BSSE given in the last column of Table V. Also the SCF interaction energy (MSCF) is deformed by the BSSE. For all structures the largest contributions come from the electrostatic (E-) and exchange-repulsion (Eex)components. For structures where the complexation occurs via the carbon end of CO, the exchange-repulsion starts to dominate the negative electrostatic component resulting to a repulsive Heitler-London interaction energy (aHL). Due to the repulsive MHL, the dominant attractive contribution to the SCF interaction energy is thecharge-transfer component. Also the&, term for structures I and VI1 is twice as large as for structures I1 and VI11 resulting
I.
I11
%& -3.707 -6.761 -1.310 -2.151 -0,184 -2.682 -4.481 -9.297
bonded interaction between trans-formic acid and CO. A similar
+
I1
&&:
-7.607 -3.527 -0.670 -0.205 -1.138 -1.435 -7.150 -3.782
L
case is with the cis-formic acid/CO where the hydrogen bond
of carbon monoxide in trowformic acid CO complex in the plane of the planar formic acid monomer. The x axis displays the rotational angle of CO as the deviation from the nearly linear hydrogen bond in structure
t-HCOOH
H
3.900 -3.234 -0.640 -1.946 0.954 -1.247 2.669 -5.514
The BSSE is removed from the energy components. All values are given in kJ mol-'. MP2/6-31G** level is used.
360
Rotational angle (degrees)
I
~
&X
25.552 12.171 5.904 1.339 6.213 8.146 20.020 8.703
~
Figure 3, Calculated (MP2/6-31G**) energy barriers for the rotation
basis set
Ea -21.652 -15.405 -6.544 -3.284 -5.259 -9.393 -17.351 -14.217
6-31+G*
SCF
MP2
SCF
MP2
MP2
-16.74 -17.98 -5.76 -7.23 -6.28 -9.28 -15.15 -17.23
-25.19 -13.05 -10.78 -6.61 -12.37 -7.01 -26.23 -12.92
-9.12 -7.63 -1.28 -1.65 -1.43 -4.14 -8.54 -9.69
-18.41 -10.17 -7.11 -5.32 -6.47 -7.03 -18.49 -9.43
-18.41 -9.00 -6.04 474 -5.42 -5.29 -15.90 -9.14
comlationcontribution (MP2) are presented inTable IV. Using MP2/6-31G** and MP2/6-31+G* levels, a larger correlation contributionresults, being more than a half of the total interaction energy. This is a net effect of the dominating perturbation term and the correct orientation of the dipole moment of CO, which stabilize the systems compared with H F calculations. The large interactions for structures I and 11, indicate a strong hydrogen-
TABLE V Componeots of Interaction lhergy Calculated in the Monomer Basis Set (MCBS). I I1 111
IV V VI VI1 VI11
E,
Eel
-16.242 -12.690 -5.100 -2.849 -4.054 -7.238 -13.422 -12.694
19.376 8.385 3.720 0.686 4.908 5.109 15.820 7.138
~
H
3.134 -4.305 -1.380 -2.163 0.854 -2.130 2.397 -5.556
L
EPI
E,,
MSCF
-3.238 -1.870 -0,318 -0,138 -0.377 -0.757 -3.728 -2.180
-9.168 -4.276 -2.372 -1.490 -2.653 -3.623 -7.456 -2.941
-9.272 -10.452 4 0 71 -3.795 -2.171 -6.510 -8.782 -10.678
EDISP -5.104 -4.293 -2.996 -1.531 -2.017 -3.582 -3.979 -3.376
#The BSSE is not removed from the energy components. All values are given in kJ mol-'. MP2/6-31G** level is used.
BSSE 5.866 3.694 2.761 1.632 1.987 3.833 4.305 1.381
Lundell et al.
1156 The Journal of Physical Chemistry, Vol. 97, No.6, 1993 TABLE VII: Calculated Wavenumber Shift8 (cm-') at the MP2/631C** Level for hw-HCOOH
+ CO
~~
monomers
complexes
t-HCOOH-CO
exP
I
I1
111
IV
V
VI
3808.0 3181.7 2125.1 1843.6 1445.2 1334.6 1153.6 1074.4 710.8 626.3
3570.0" 2943.8' 2138.6b 1776.2" 1387.0" 1223.0" 1105.4" 1033.4" 641.8' 625.4"
-68.2 -10.7 +21.8 -10.0 +8.1 +35.6 +31.3 +5.8 +86.9 +23.6 176.4 161.9 131.8 78.3 44.9
+5.2 -2.8 -2.4 -3.6 +3.9 +12.1 12.2 +2.8 +28.3 +10.1 103.2 95.9 88.5 46.6 43.4
-2.1 +13.5 -0.4 +0.3
-2.1 +19.3 +3.2 -3.4 -3.8 -9.0 -4.7 +7.5 -4.3 -0.8 115.1 73.6 72.7 39.0 28.6
-0.9 +27.3 +6.2 -6.4 +13.1 -3.5 -2.8 +29.8 +3.2 -0.7 121.8 79.0 66.2 50.6 17.8
-1.4 +10.3 -1.7 -4.7 +o. 1 +3.2 +3.6 +8.5 +2.9 +2.2 90.6 78.4 65.2 61.1 32.9
0.0 -5.8 -3.6 +3.1 -3.2 -0.8 75.2 60.4 49.9 42.4 18.2
+
From ref 74. From ref 83.
TABLE VIII: Ab Initio MP2/6-31C** Calculated Wavenumbers (cm-I) and Approximate Vibrational Assignments for the Two cl4HCOOHICO Complexes monomers struct VI1 struct VI11 C-HCOOH-CO 3872.1 3078.7 2125.1 1881.1 1472.2 1297.7 1145.4 1054.9 656.4 525.9
exP
2138.6'
freq 3818.1 3068.1 2147.6 1877.0 1473.6 1346.1 1175.0 1059.1 670.3 639.7 147.4 145.9 116.1 62.6 39.0
approx assignm YO-H
VC-H VCEO VC=o
OCH def &OH VC-0
CH wag y p C-O torsion CH rock b H - C
0-H torsion VH...C
C = O wag oop 8H-CsO
freq 3883.1 3073.4 2122.7 1880.7 1473.2 1320.2 1161.0 1057.1 663.3 583.1 103.5 89.5 69.4 39.5 23.2
approx assignm YO-H VC-H
VC=O
vc-4 OCH def kOH VC-0
CH wag oop CH rock C-O torsion VH ...O
0 - H torsion b-H-0
C=O wag oop 8 H ...M
From ref 83.
from the electron density radius of CO being greater at the C end that at the 0 end. This is connected with exchange-repulsion favoring structures I1 and VI11 more than I and VII. The DCBS calculated components of interaction energy are collected in Table VI. Here a BSSE correction has been made on all components. Compared with the values given in Table V, one can notice a clear rise in the two major components, Le., E , and Eex. However, the relationship between these components is similar to that calculated in the MCBS: For the complexes detached from the C end of CO the ~ E H shows L repulsive nature. It is noteworth that the mutual deformation of the electron clouds, AEz;: reaches energies of -7.6 and -7.2 kJ mol-' for structures I and VII, which are twice as large as for the other complexes. Both structures are bound from the OH tail of the formic acid monomer to the CO carbon. This is probably a consequence of the favorable linear arrangement of the dipole moments of both subunits as well as stronger overlap between wave functions of both subunits, as is additionally indicated by the E,, term. The dispersion energy, E D I S Prepresents , the most important contribution among the correlation terms. By describing the subunit wave functions in DCBS, the resulting dispersion is maximized. The largest E ~ l s pis found for structure I, -7.3 kJ mol-', and the lowest for one of the other vdW structures, -3.7 kJ mol-'. In the formic acid CO complexes the dispersion energy corresponds to one third of the total interaction energy. Even though E ~ l s pis essential for the description of interaction energy, it shows great distance dependence. A careful study for the H F dimer has been performed presenting strong evidence for this.'* As a conclusion the present results on the formic acid species lead to a rough approximation: the shorter the interaction
+
distance, the larger the dispersion attraction resulting to a stronger complexation. This could be justified by the argument that the electron clouds of the two monomers would be closer together and would allow a larger delocalization of the electrons between the occupied and vacant orbitals. Vibrational Frequencies. As observed in experimental studies'5J7,37small amounts of CO induce changes in the IR spectra of methanol or formic acid in an argon matrix. Table VI1 gives the MP2/6-31G** calculated wavenumbers for CO and trunsformicacid as well as the complexationshifts for various complexes between CO and HCOOH. The spectra for cis-formic acid and its complexes, as well as the approximate assignments for each vibrational mode, are collected in Table VIII. Potential energy distributions (PED) with full assignments will be published separately with the experimental spectra. In accordance with the studies on methanol + CO complex,I5J6 considerable wavenumber shifts areobserved in the OH stretching, bending,and torsional bands, when almost linear hydrogen-bonded complexes are formed. For the trans-formic acid a red-shift as large as 68 cm-1 for VOH is predicted. This correlates with the experimental value of 80 6311-1.3' Only structure I1 gives a quite small blue-shift for this mode. Also VC-H shows shifting into the red for structures I and 11,all the others giving shifts into the blue varying between 10 and 27 cm-1. All other modes are predicted to be close to the monomer fundamentals, being, however, easily measurable in matrices. For the cis-formic acid species the complex absorptions are randomly blue or red shifted. Most significant differences in complexation shifts can be found for VOH, OH, and T O H . The largest relative shift is found for CH rocking mode in structure VII, a blue shift of 114 cm-I.
Formic Acid and Carbon Monoxide Complexes The intermolecular, low-frequency modes are probably quite anharmonic, and the calculated harmonic wavenumbers give an approximate picture of them. In all structures involving the OH tail, the OH torsion mode is naturallycoupled to the intermolecular torsions serving as a possible and thereby also as an important energy relaxation channel. Due to the large shifts of the OH torsions the suggestion for a strong interaction between formic acid and carbon monoxide is justified, and in accordancewith the energetics presented.
Conclwion In the present study we present strong calculational evidence for significant interactions between formic acid and carbon monoxide. The inclusion of electron correlation is essential, not more or less due to the correlation-inducedsign reversal of the COdipolemoment. The6-31G** basisset representsa reasonable compromise between the efficiency, completeness, and accuracy in reproduction of molecular properties for complexes such as I-VIII. Furthermore, this basis set was applicablefor every step of investigation, and for the sake of consistency the use of a variety of basis sets was not attempted. The minimization of the BSSE plays a significant part for molecular complexes: A small BSSE eliminates the distortion of the potential energy surface. For both conformers of formic acid the most favored structures are nearly linear hydrogen-bonded arrangements. Upon complexation the largest shifts are found in the vibrational spectra of the hydrogen-bonded structures. The most affected are the vibrational modes close to the site of the complexation, Le., OH stretching and torsion modes, indicating a strong hydrogen bond. Perturbation of other vibrational modes is relatively modest.
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