Multireference Configuration Interaction Study of Bromocarbenes

ARTICLE pubs.acs.org/JPCA

Multireference Configuration Interaction Study of Bromocarbenes Jean M. Standard,* Rebecca J. Steidl, Matthew C. Beecher, and Robert W. Quandt Department of Chemistry, Illinois State University, Normal, Illinois 61790-4160, United States ABSTRACT: Multireference configuration interaction (MRCI) calculations of the lowest ~ (1A00 ) state have ~ (1A0 ) and triplet ~a(3A00 ) states as well as the first excited singlet A singlet X been performed for a series of bromocarbenes: CHBr, CFBr, CClBr, CBr2, and CIBr. The MRCI calculations were performed with correlation consistent basis sets of valence triple-ζ plus polarization quality, employing a full-valence active space of 18 electrons in 12 orbitals (12 and 9, respectively, for CHBr). Results obtained include equilibrium geometries and harmonic vibrational frequencies for each of the electronic states, along with ~a(3A00 ) r ~ (1A00 ) r X ~ (1A0 ) transition energies. Comparisons have been made with previous computational and ~ (1A0 ) singlet-triplet gaps and A X experimental results where available. The MRCI calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the bromocarbenes.

I. INTRODUCTION It has long been known that chlorine-containing hydrocarbons have large ozone depletion potentials (ODPs) due to considerable release rates and long atmospheric lifetimes.1 It would be expected that bromine-containing halocarbons, with release rates and atmospheric lifetimes that are generally much smaller than their chlorine-containing counterparts, would have negligible ODPs. However, unstable reservoir molecules and synergistic effects with chlorine lead to much greater than expected ODPs for these species.2 Indeed, it has been estimated that, on a per atom basis, bromine is almost 60 times more destructive to ozone than chlorine.3 These larger than expected ODPs have led to a renewed interest in bromine-containing hydrocarbons in recent years. It has been found that, in addition to better known sources such as Halons and methyl bromide, bromoform is a significant source of reactive bromine in the stratosphere.4-6 Depending upon the excitation wavelength, photodissociation of bromocarbons such as bromoform can follow two different routes: dissociation into atomic bromine and a substituted methyl radical or dissociation into molecular bromine and a singlet carbene. For example, McGivern et al. observed that at 193 nm the primary photoproduct was atomic bromine.7 They also observed secondary dissociation of the excited photoproduct, CHBr2*, to form CBr and HBr. Xu et al. observed the formation of atomic halogen in both the 2P1/2 and 2P3/2 spin states upon excitation at 234 and 267 nm.8 They also found significant formation of molecular bromine with branching ratios into that channel of 0.16 and 0.26 at 267 and 234 nm, respectively. Quandt and co-workers recently studied the 2 193 nm photodissociation of CBr4 and CHBr3 via photoproduct emission.9 Observed emission was attributed to the Swan system (d3Πg f a3Πu) of C2, which was formed via reaction of electronically excited radicals, CH(A2Δ) and CBr(A2Δ). In addition, formation of CBr2 (or CHBr) and Br2 was implied by secondary evidence. A computational study of this dark channel was undertaken, and the results showed the presence of three transition states and an ion-pair isomer intermediate for both CBr4 and CHBr3 dissociation. r 2011 American Chemical Society

A number of previous computational studies have been performed on bromocarbenes. A comprehensive study of the lowest ~ (1A0 ) and triplet ~a(3A00 ) states of all halocarbenes was singlet X carried out by Schwartz and Marshall in 1999 in which equilibrium geometries, harmonic vibrational frequencies, and ~a(3A00 ) ~ (1A0 ) singlet-triplet gaps obtained at the QCISD/6-311GrX (d) level were reported.10 A few years later, Drake et al. employed CISD, CASSCF, and CASPT2 methods along with basis sets of ~ (1A00 ) r DZP quality to determine geometries and adiabatic A ~ (1A0 ) and first excited ~ (1A0 ) transition energies for the ground X X ~ (1A00 ) singlet states of a series of bromo- and iodocarbenes.11 In A particular, the CASPT2(18,12)/DZP method was shown to provide a good balance of computational cost and predictive accuracy for the ~ (1A0 ) transition energies.11 CASSCF and ~ (1A00 ) r X adiabatic A CASPT2 calculations also have been employed in other studies of the bromocarbenes CFBr 12 and CBr2 13 in order to obtain equilibrium geometries, harmonic vibrational frequencies, and other spectroscopic parameters for the ground and first excited singlet states as well as the lowest triplet state. Higher level multireference configuration interaction (MRCI) calculations have been previously completed only for CHBr,14,15 CFBr,12 and CClBr.16 In work by Yu et al.,14 MRCI calculations were carried out on CHBr with a cc-pVTZ basis set using state-averaged full-valence active space CASSCF reference functions. Equilibrium geometries and a detailed analysis of the potential surfaces of the ~ (1A00 ) singlet states as well the lowest ~ (1A0 ) and excited A ground X 3 00 ~a( A ) triplet state of CHBr were presented. In recent work by Burrill and Grein,15 a TZP basis set with polarization and diffuse functions was employed in order to carry out MRCI calculations on the lowest six singlet and triplet electronic states of CHBr. For CFBr, the MRCI method with an active space of two electrons in two orbitals, MRCI(2,2), and a TZP quality basis set was employed to ~ (1A00 ) singlet state.12 For CClBr, a study only the first excited A similar MRCI(2,2) study was carried out to determine the geometry Received: August 13, 2010 Revised: December 31, 2010 Published: January 31, 2011 1243

dx.doi.org/10.1021/jp107688v | J. Phys. Chem. A 2011, 115, 1243–1249

The Journal of Physical Chemistry A and spectroscopic parameters of the first excited singlet state as ~ (1A0 ) transition energy.16 The ~ (1A00 ) r X well as the adiabatic A generally excellent agreement between the MRCI results and available experimental results for these systems, particularly for transition energies, suggests that this is a method of choice for the study of bromocarbenes. In this work, we report the results of MRCI calculations of the ~ (1A0 ) and triplet ~a(3A00 ) states as well as the first lowest singlet X ~ (1A00 ) state for a series of bromocarbenes with excited singlet A formula CXBr, where X = H, F, Cl, Br, or I. These compounds are the expected photoproducts from one channel in the dissociation of various bromocarbons. The results presented include equilibrium geometries and harmonic vibrational frequencies of each of ~ (1A0 ) singlet-triplet the electronic states, along with ~a(3A00 ) r X 1 00 1 0 ~ ~ gaps and adiabatic A ( A ) r X( A ) transition energies. While various aspects of each of these compounds have been studied previously using a wide range of theoretical methods, the calculations presented here are intended to provide a comprehensive series of results at a consistent high level of theory for all of the bromocarbenes.

II. METHODS Internally contracted MRCI calculations17,18 of the bromocarbenes were performed using a full-valence active space of 18 electrons in 12 orbitals (12 and 9, respectively, for CHBr). The Davidson correction19 was applied to obtain the final electronic energy of each state. The initial wave functions for the MRCI calculations of the CXBr molecules were based upon CASSCF reference functions, and the set of active molecular orbitals was constructed from the valence atomic orbitals of C (2s2p), X (1s for X = H; nsnp for X = F, Cl, Br, or I), and Br (4s4p). For ~ (1A0 ) state, for example, this resulted in calculations of the ground X a reference space consisting of 1316 configuration state functions (CSFs) for CHBr and 8029 CSFs for CIBr, and the total number of contracted configurations in the MRCI calculations ranged from ∼276 000 for CHBr to ∼2 400 000 for CIBr. The calculations were performed using standard all-electron correlation-consistent basis sets of triple-ζ quality with polarization functions, cc-pVTZ, for hydrogen, carbon, fluorine, and bromine.20,21 A similar basis set including tight-d functions, cc-pV(Tþd)Z, was employed for chlorine.22 For iodine, a relativistic effective core potential along with the corresponding ccpVTZ basis set was employed.23 For CHBr, additional calculations were performed using the cc-pVnZ (n = D, T, Q, and 5) basis sets in order to investigate convergence properties of equilibrium geometries and transition energies. ~~ (1A0 ) and A The ground and first excited singlet states, X 1 00 ( A ), respectively, as well as the lowest triplet state, ~a(3A00 ), of all of the bromocarbenes were investigated. Full geometry optimizations were performed and stationary points were verified by calculation of harmonic vibrational frequencies. The harmonic vibrational frequencies were determined from force constants computed numerically using a second-order finite difference approximation. The results obtained by employing the methods described above will generally be referred to in this paper using the notation MRCI/cc-pVTZ for equilibrium geometries and frequencies or MRCIþDav/cc-pVTZ for singlettriplet gaps or singlet-singlet transition energies. All calculations were performed using the MOLPRO software package24 running on local Linux workstations or at the National Center for Supercomputing Applications.

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Table 1. Optimized Geometries of Bromocarbenes, CXBr a carbene

R(X-C), Å

R(C-Br), Å

CHBr CFBr CClBr CBr2 CIBr

Ground Singlet State 1.112 [1.110, 1.116] b 1.870 [1.857, 1.854] b 1.291 1.949 1.720 1.912 1.903 [1.865] c 1.903 [1.865] c 2.128 1.899


1.083 1.313 1.679 1.844 2.048


1.086 1.306 1.663 1.834 [1.796] c 2.047

Triplet State 1.825 1.864 1.847 1.844 1.843 Excited Singlet State 1.796 1.900 1.839 1.834 [1.796] c 1.833

— X-C-Br, deg

101.3 [101.0, 102.6] b 107.0 109.9 110.3 [110.7] c 111.3 126.9 124.2 128.8 129.5 130.9 130.6 125.3 131.5 131.7 [131.3] c 132.3

a Available experimental results are listed in square brackets. b References 25 and 26. c Reference 27 (excited-state geometry extrapolated from ground-state values).

III. RESULTS AND DISCUSSION A. Equilibrium Geometries. The calculated equilibrium bond lengths and angles of the bromocarbenes computed at the MRCI/cc-pVTZ level are listed in Table 1 for the ground ~ (1A00 ) singlet states as well as for the ~ (1A0 ) and first excited A X 3 00 lowest triplet state, ~a( A ). Available experimental results are also included in the table.25-27 To avoid confusion, it should be noted that all bromocarbenes with the formula CXBr are nonlinear triatomic molecules with connectivity X-C-Br. As expected on the basis of size considerations, the X-C bond lengths (X = H, F, Cl, Br, I) of the bromocarbenes increase monotonically from H to I for all of the electronic states studied. The C-Br bond length is shortest for CHBr and longest for CFBr and then decreases monotonically from F to I. The X-C-Br bond angle is smallest for the ground singlet state of each of the bromocarbenes, ranging from 101 to 111, reflective of the fact that, in the ground singlet states, the two nonbonded electrons of the carbon occupy an in-plane sp2-like orbital. The X-C-Br bond angles of the triplet states are slightly smaller than those of the corresponding excited singlet states, but in all cases the bond angles of the triplet and excited singlet states are similar, ranging from 124 to 132. The larger bond angles of the triplet and excited singlet states relative to those of the ground singlet states are a result of the removal of at least one electron from the in-plane sp2-like orbital and placement in an outof-plane p-type orbital on carbon. No experimental geometrical data are available for comparison with the triplet-state geometries. However, experimental geometries are available for the ground singlet states of CHBr 25,26 and CBr2 27 and for the excited singlet state of CBr2, extrapolated from ground-state values.27 The calculated C-Br bond lengths are slightly longer than the experimental values by 0.02-0.04 Å in those cases. For CHBr, the calculated H-C bond length of the ground singlet state brackets the experimental values, as does the H-C-Br bond angle. For CBr2, the calculated Br-C-Br bond angles of the ground and excited singlet states are very close to the experimental values (within 0.4). Geometries of all compounds obtained in the current work are in generally good agreement with the myriad of previous 1244

dx.doi.org/10.1021/jp107688v |J. Phys. Chem. A 2011, 115, 1243–1249

The Journal of Physical Chemistry A

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Table 2. Equilibrium Geometry of CHBr as a Function of Basis Set R(H-C), Å

basis set

R(C-Br), Å

Table 3. Harmonic Vibrational Frequencies of Bromocarbenesa carbene

ω1, cm-1

CHBr

1161 [1118] b

ω2, cm-1

ω3, cm-1

— H-C-Br, deg Ground Singlet State

Ground Singlet State

2851 [2902] d

773 [666] 631 [628]

f

CBr2

627 [607]

g

CIBr

542

CHBr

953 [930] h

743 [758] h

3195

CFBr CClBr

734 604

356 263

1291 950

1.1322

1.8895

101.08

cc-pVTZ cc-pVQZ

1.1120 1.1102

1.8696 1.8632

101.28 101.46

CClBr

cc-pV5Z

1.1095

1.8606

101.56

TQ extrapolation

1.1088

1.8585

Q5 extrapolation

1.1089

1.8578

experiment

1.110,a 1.116b

1.857,a 1.854b

CFBr

361 [350]

e

1252 [1166] e

287 [263]

f

756 [772] f

219 [200]

g

646 [680] g

173

627

Triplet State 101.0,a 102.6b

Triplet State cc-pVDZ

1.1004

1.8436

126.41

CBr2

551

206

873

cc-pVTZ

1.0833

1.8255

126.90

CIBr

476

178

837

cc-pVQZ cc-pV5Z

1.0822 1.0819

1.8196 1.8177

126.87 126.85

TQ extrapolation

1.0814

1.8153

CHBr

883 [829] i

764 [770] h

3151 [3100] h

1.0816

1.8156

301 [304]

e

Q5 extrapolation

579 [494]

e

1267 [1134] j

533 [536]

k

265 [243]

k

942 [961] l

CBr2

487 [474]

m

208 [185]

m

849

CIBr

430

Excited Singlet State CFBr CClBr

Excited Singlet State

a

675 [676] b,c

e

cc-pVDZ

cc-pVDZ

1.1048

1.8166

129.29

cc-pVTZ

1.0860

1.7955

130.63

cc-pVQZ

1.0848

1.7888

130.83

cc-pV5Z TQ extrapolation

1.0845 1.0839

1.7866 1.7840

130.92

Q5 extrapolation

1.0842

1.7842

b

Reference 25. Reference 26.

computational studies of bromocarbenes carried out in recent years using a variety of theoretical methods.10-16,28-31 It is observed that C-Br bond distances are generally shorter by 0.01-0.04 Å and bond angles slightly larger by less than 1 (and closer to available experimental results) for calculations employing triple-ζ plus polarization quality basis sets compared to results obtained using double-ζ plus polarization basis sets. To explore the source of the small discrepancies between the calculated and experimental geometries, particularly for C-Br bond lengths, additional MRCI calculations were performed for CHBr using cc-pVnZ, n = D, T, Q, and 5, basis sets. Results are presented in Table 2 for the ground and excited singlet states and the lowest triplet state of CHBr. Extrapolations32 to the complete basis set (CBS) limit are also included in the table. The largest changes observed in the geometry of CHBr as a result of basis set effects occur from the cc-pVDZ to cc-pVTZ level: the H-C and C-Br bond distances decrease by about 0.02 Å, and the H-C-Br bond angle increases by as much as 1.3. As expected, the geometrical changes observed when the basis set is increased from cc-pVTZ to cc-pVQZ or from cc-pVQZ to cc-pV5Z are much less pronounced. For example, the C-Br distance exhibits an additional decrease of 0.006-0.007 Å from cc-pVTZ to cc-pVQZ, but a decrease of only 0.002-0.003 Å from cc-pVQZ to cc-pV5Z. Extrapolations to the CBS limit for the C-Br bond length of CHBr yield results that are within 0.001-0.004 Å of the experimental bond length for the ground singlet state; thus, it appears that the major source of the discrepancy between the calculated and experimental geometries may be attributed to the use of the cc-pVTZ basis set rather than a larger basis set. B. Harmonic Vibrational Frequencies. The calculated harmonic vibrational frequencies of the bromocarbenes obtained at

178

803

Experimental results are listed in brackets. In the table, ω1 corresponds to the CXBr low-frequency stretch (or CBr2 symmetric stretch), ω2 corresponds to the bend, and ω3 corresponds to the CXBr highfrequency stretch (or CBr2 antisymmetric stretch). b Reference 33. c Reference 34. d Reference 35. e Reference 36. f Reference 37. g Reference 38. h Reference 31. i Reference 26. j Reference 12. k Reference 39. l Reference 40. m Reference 41. a

the MRCI/cc-pVTZ level are presented in Table 3 along with available experimental results.12,26,31,33-41 In the results presented, the harmonic frequency ω1 corresponds to the CXBr low-frequency stretch (or CBr2 symmetric stretch), ω2 corresponds to the bend, and ω3 corresponds to the CXBr high-frequency stretch (or CBr2 antisymmetric stretch). In some cases, as will be elaborated further, the reported experimental frequencies include anharmonic effects while the calculated results are harmonic; therefore, in those cases the calculated harmonic frequencies are generally expected to be higher by about ∼5-10% compared to the experimental anharmonic frequencies. For the ground singlet state, experimental results are available for all of the compounds except CIBr.33-38 For CClBr and CBr2, the harmonic vibrational frequencies of the ground singlet state computed in this work are in excellent agreement with experimental harmonic values,37,38 exhibiting differences of less than 35 cm-1. For CHBr, the computed value of the bending mode ω2 is within 1 cm-1 of the experimental anharmonic value (the anharmonicity is expected to be low in this case),33,34 while the calculated harmonic stretching modes ω1 and ω3 differ from the anharmonic experimental frequencies33,35 by about 40-50 cm-1; however, these differences correspond to less than 4% for ω1 and less than 2% for ω3. The largest discrepancies between the present results and experiment occur for CFBr. The calculated value of ω3 is high by 86 cm-1 compared to the experimental anharmonic result36 (1252 vs 1166 cm-1), and the calculated value of ω1 is high by 108 cm-1 (773 vs 665 cm-1); in contrast, the calculated value of ω2 is within 11 cm-1 of experiment (361 vs 350 cm-1). In contrast, the present MRCI/ccpVTZ results for ω2 and ω3 for the ground singlet state of CFBr are close to previous computational results obtained at the CASPT2(18,12)/cc-pVTZ level.12 In that work, harmonic frequencies of 345 1245


The Journal of Physical Chemistry A and 1258 cm-1 were obtained for ω2 and ω3, respectively, which are within 20 cm-1 of the present results. On the other hand, our computed value of ω1 is high compared to the CASPT2(18,12)/ccpVTZ value (773 vs 642 cm-1). For the other bromocarbenes, good agreement is observed between the harmonic vibrational frequencies of the ground singlet states obtained in this work and previous computational results.10,12-14,16 For the triplet states, there are no experimental results available for harmonic frequencies except for ω1 and ω2 of CHBr,31 but the calculated results for those modes are within 25 cm-1 of experiment. When compared with previous computational results determined at the QCISD/6-311G(d,p) level,10 the harmonic vibrational frequencies of the triplet states of the bromocarbenes obtained in the present work are higher by 30-100 cm-1, with differences primarily due to the scaling of the QCISD results by 0.954. The only exception is the ω1 value of CHBr, which is lower than the QCISD result by 23 cm-1. Experimental results are available for the vibrational frequencies of the first excited singlet states of all compounds except CIBr.12,26,31,36,39-41 In comparing the results from the present work with experiment, trends are observed similar to those for the ground singlet states. For CClBr and CBr2, the calculated harmonic vibrational frequencies of the excited singlet state are in excellent agreement with the harmonic experimental values,39-41 with differences of less than 25 cm-1. For CHBr, the computed value of the bending mode ω2 is within 6 cm-1 of the experimental anharmonic value,31 while the stretching modes ω1 and ω3 differ from the anharmonic experimental values by about 50 cm-1 each.26,31 For CFBr, the calculated value of ω1 is high by 85 cm-1 compared to the experimental result, the calculated value of ω3 is high by 133 cm-1, and the calculated value of ω2 is within 3 cm-1 of experiment.12,36 These discrepancies are in part a result of the relatively high sensitivity of the CFBr excited-state potential surface to the basis set/level of theory primarily as a result of the flatness of the CFBr singlet excited state potential energy surface.12 On the other hand, the present MRCI/cc-pVTZ results for the harmonic frequencies of the excited singlet state of CFBr are very close to previous computational results obtained at the CASPT2(18,12)/cc-pVTZ level.12 In that work, harmonic frequencies of 577, 326, and 1260 cm-1, respectively, were obtained, which are all within 25 cm-1 of the present results; frequency calculations with larger basis sets may produce results in closer agreement with experiment. Finally, it should be noted that good agreement between the harmonic vibrational frequencies of the bromocarbene excited singlet states obtained in this work and previous computational results is also observed.12-14,16 C. Singlet-Triplet Gaps. Adiabatic singlet-triplet gaps for ~ (1A0 ) transition of the bromocarbenes determined the ~a(3A00 ) r X at the MRCIþDav/cc-pVTZ level and corrected for zero-point vibrational energies are presented in Table 4 along with recent computational and experimental results. Experimental singlet-triplet gaps are available only for CHBr and CBr2.34,42,43 For CHBr, the singlet-triplet gap computed in the present work is lower than recent experimental results from emission spectroscopy by about 340 cm-1.34,42 On the other hand, the computed singlet-triplet gap for CBr2, 5688 cm-1, is very far from the reported experimental gap of 700 ( 1000 cm-1, obtained from negative ion photoelectron spectroscopy.43 However, high-level computational predictions of singlet-triplet gaps for these systems are generally expected to be more accurate than the experimentally determined singlet-triplet gaps due to the difficulty in interpretation of experiments involving negative ion photoelectron spectroscopy.44 This is certainly expected

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Table 4. Singlet-Triplet (S-T) Gaps for the ~a(3A00 ) r ~ (1A0 ) Transition of Bromocarbenes X calculated S-T gap, cm-1 experimental carbene

this work

CHBr

1669

2006 ( 8,c 2005d

1670,a 1809b a

CFBr CClBr

11418 6279

CBr2

5688

5270a

4826

a

CIBr

S-T gap, cm-1

lit.

11050 6030,a 6593e 700 ( 1000f g

h

4080, 4770, 3640

a

Reference 10, QCISD(T)/6-311þG(3df,2p)//QCISD/6-311G(d,p) level. b Reference 14, MRCI/cc-pVTZ level. c Reference 42. d Reference 34. e Reference 16, CBS extrapolation from CCSD(T) calculations with cc-pVnZ basis sets (n = D, T, Q, 5). f Reference 43. g Reference 45, CCSD(T)/ 6-311þþG(3df,2p) with Stuttgart ECP for iodine. h Reference 45, MR-SDCI/6-311þþG(3df,3pd) with Davidson correction.

to be the case for CBr2, for which the experimentally determined singlet triplet gap was reported with a large uncertainty in the measurement.43 The calculated singlet-triplet gaps of the bromocarbenes cover a fairly large range, from 1669 cm-1 for CHBr to 11418 cm-1 for CFBr. The singlet-triplet gaps increase as the electronegativity of the substituent X (H, I, Br, Cl, F) increases. A previous computational study of singlet-triplet gaps of halocarbenes at the QCISD(T) level demonstrated a near-linear dependence of the singlet-triplet gaps on the electronegativity of the X substituent,10 which also is observed for the present results. The increase in the singlet-triplet gap as the electronegativity of the X substituent increases may be attributed to additional stabiliza~ (1A0 ) singlet state by the presence of the electrotion of the X negative substituent, possibly either through an increase in s character of the carbon lone pair orbital or through electron donation into the empty p orbital on carbon.10 All of the singlet-triplet gaps determined in this work at the MRCIþDav/cc-pVTZ level are in reasonable agreement with recent computational values reported in the literature.10,14,16,45 For CHBr, the singlet-triplet gap determined in this work, 1669 cm-1, is similar to or slightly lower than the previous computational values of 1670 and 1809 cm-1,10,14 and for CClBr, the present result for the singlet-triplet gap, 6279 cm-1, brackets previous computational values of 6030 and 6593 cm-1.10,16 For CFBr and CBr2, the singlettriplet gaps determined in this work, 11 418 and 5688 cm-1, respectively, are higher than previous computational results by about 300-400 cm-1, and for CIBr, the previous computational results vary rather widely,10,45 though the result obtained in this work is within 60 cm-1 of the value from a previous CCSD(T) calculation.45 Additional MRCI calculations were performed for CHBr using the cc-pVnZ, n = D, T, Q, and 5, basis sets in order to explore basis set effects on the convergence of the singlet-triplet gap. These results, obtained using the MRCIþDav method and corrected for vibrational zero-point energies, are presented in Table 5 along with extrapolations to the complete basis set (CBS) limit. The results indicate that use of larger basis sets leads to an increase in the singlet-triplet gap from 1669 cm-1 at the cc-pVTZ level to 1922 cm-1 at the ccpV5Z level. CBS extrapolations provide a prediction for the CHBr singlet-triplet gap of ∼1990 cm-1, which is about 320 cm-1 larger than the cc-pVTZ result and within 15-20 cm-1 of the experimental values.34,42 It should be noted that the singlet-triplet gap of CHBr is the smallest of any of the bromocarbenes, and thus corrections due to 1246



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Table 5. Singlet-Triplet (S-T) Gap as a Function of Basis ~ (1A0 ) Transition of CHBr Set for the ~a(3A00 ) r X basis set

S-T gap,a cm-1

basis set

cc-pVDZ

1185

cc-pVTZ cc-pVQZ

1669 1854

cc-pV5Z

1922

Table 7. Adiabatic Transition Energies, T00, as a Function of ~ (1A0 ) Transition of CHBr ~ (1A00 ) r X Basis Set for the A

S-T gap,a cm-1

basis set

T00,a cm-1

basis set

TQ extrapolation

1988

cc-pVDZ

12 880

TQ extrapolation

11 676

Q5 extrapolation experiment

1993 2006 ( 8,b 2005c

cc-pVTZ cc-pVQZ

12 008 11 816

Q5 extrapolation Experiment

11 670 11 972 b

cc-pV5Z

11 744

a

Calculated S-T gaps include vibrational ZPE correction determined at the MRCI/cc-pVTZ level. b Reference 42. c Reference 34.

~ (1A00 ) Table 6. Adiabatic Transition Energies, T00, for the A 1 0 ~ r X ( A ) Transition of Bromocarbenes calculated T00, cm-1 experimental T00, cm-1

carbene

this work

lit.

CHBr

12 008

12 470 a

11 972 b

CFBr

23 437

18 190 c

23 271 d

CClBr

16 447

15 868 e

16 197 f

CBr2

15 354

15 237 g

15 279 h

CIBr

13 482

13 158 i

a

Reference 14, MRCI/cc-pVTZ level. b Reference 25. c Reference 12, CASPT2(18,12)/cc-pVTZ level. d Reference 36. e Reference 16, CBS extrapolation from EOM-CCSD calculations with cc-pVnZ basis sets (n = D, T, Q, 5). f Reference 39 g Reference 13, MRCI(2,2)/cc-pVTZ with Davidson correction. h Reference 46. i Reference 11, Te value, CASPT2(18,12)/DZP level.

basis set effects on them have a much more significant impact on the magnitude of the singlet-triplet gap than is expected to be the case for other bromocarbenes. For example, in a previous study of CClBr,16 the singlet-triplet gap differed by less than 40 cm-1 when the basis set was varied from cc-pVTZ to cc-pV5Z. The computed results do not include some additional corrections that are expected to have a small effect on the predicted singlet-triplet gap, including core-valence correlation, scalar relativistic, and spin-orbit corrections. For example, in a recent study of CClBr, the core-valence correlation, scalar relativistic, and spin-orbit corrections were determined to have a net impact on the singlet-triplet gap of about 100 cm-1.16 ~ 1A00 ) r X( ~ 1A0 ) Transition Energies. Table 6 D. Adiabatic A( reports the calculated adiabatic transition energies, T00, for the ~ (1A0 ) transition of the bromocarbenes obtained at ~ (1A00 ) r X A the MRCIþDav/cc-pVTZ level (including vibrational zeropoint corrections) along with recent experimental and computational results. Experimental values are available for all the bromocarbenes except CIBr.25,36,39,46 The experimental T00 value for CFBr listed in Table 6 is based on a recent reanalysis ~ (1A0 ) transition, which led to an increase in ~ (1A00 ) r X of the A the band origin from the previous value of 20 906 cm-147 to the value of 23 271 cm-1.36 Also, for CBr2, the experimental result of 15 279 cm-1 for T00 reported in Table 6 is based on a ~ 1A0 system,46 which increased ~ 1A00 -X reassignment of the A the band origin relative to the previous experimental value of 15 093 cm-1.27 As was the case with the singlet-triplet gaps, the calculated ~ (1A0 ) transition energies of the bromocarbenes increase ~ (1A00 ) r X A as the electronegativity of the substituent X increases. The calculated ~ (1A0 ) transition energies range from 12 008 cm-1 for ~ (1A00 ) r X A CHBr to 23 437 cm-1 for CFBr. The relationship between transition

T00,a cm-1

a

Calculated transition energies include vibrational ZPE correction determined at the MRCI/cc-pVTZ level. b Reference 23.

energy and electronegativity does not appear to be linear in this case, however. The calculated T00 values from the present work are all in very good agreement with the most recent experimental measurements.25,36,39,46 The T00 result for CHBr from the present work is very close to the experimental measurement by Sears and coworkers, within 36 cm-1.25 For CFBr, the T00 value (23 437 cm-1) from the present work is only 166 cm-1 higher than the most recent experimental result (23 271 cm-1)36 and is in much better agreement with experiment than a previous computational result obtained at the CASPT2/cc-pVTZ level,12 which underestimated the T00 value by about 5000 cm-1. For CClBr, the T00 value of 16 447 cm-1 from the present work is only 250 cm-1 higher than the experimental result of 16 197 cm-1,39 and in similar agreement with experiment as a literature result obtained at the EOM-CCSD level.16 For CBr2, the present result of 15 354 cm-1 for T00 is within 75 cm-1 of the most recent experimental measurement of 15 279 cm-1,45 and in excellent agreement with a previous computational result (15 237 cm-1),13 also determined at the MRCI/cc-pVTZ level with Davidson correction but with an active space of only two electrons in two orbitals. Finally, while no experimental result is available for CIBr, the T00 value calculated in this work (13 482 cm-1) is in very good agreement with a previous computational result of 13 158 cm-1 for Te, computed at the CASPT2(18,12)/DZP level, with a vibrational zero-point correction estimated to be less than 40 cm-1.11 ~ (1A00 ) r X ~ (1A0 ) transition energies Basis set effects on the A were explored by performing additional MRCI calculations for CHBr using the cc-pVnZ, n = D, T, Q, and 5, basis sets. Results for the adiabatic transition energies, T00, obtained using the MRCIþDav method and corrected for vibrational zero-point energies, are presented in Table 7 along with extrapolations to the complete basis set (CBS) limit. The results suggest that a ~ (1A0 ) transition energy is ~ (1A00 ) r X slight decrease in the A observed for larger basis sets. For example, the computed ccpVTZ value is lower than the cc-pV5Z value by about 260 cm-1. ~ (1A00 ) r X ~ (1A0 ) A similar decrease of about 320 cm-1 in the A transition energy computed using cc-pVTZ and cc-pV5Z basis sets was observed in a recent study of CClBr.16 CBS extrapola~ (1A0 ) ~ (1A00 ) r X tions provide a prediction for the CHBr A -1 transition energy of ∼11 670 cm , which is about 340 cm-1 lower than the experimental value.23 As was also the case for the singlet-triplet gaps, the computed ~ (1A0 ) transition energies do not include core-va~ (1A00 ) r X A lence correlation, scalar relativistic, or spin-orbit corrections; these corrections may be expected to lead to a small decrease in the predicted transition energies. For example, in a recent study on CClBr, the core-valence correlation, scalar relativistic, and spin-orbit corrections were determined to have a net impact on ~ (1A0 ) transition energy of about -90 cm-1.16 ~ (1A00 ) r X the A 1247



IV. CONCLUSIONS In this work, results from high-level MRCI calculations employing correlation consistent basis sets have been presented for the ground and excited states of bromocarbenes. The goals of the study were to obtain a complete set of high-quality ab initio results for the equilibrium geometries and harmonic vibrational frequencies of the lowest triplet state along with the ground and first excited singlet states of a series of bromocarbenes: CHBr, CFBr, CClBr, CBr2, and CIBr. In addition, singlet-triplet gaps ~ (1A0 ) transition and adiabatic transition for the ~a(3A00 ) r X 1 00 ~ (1A0 ) transition, including vibra~ energies for the A ( A ) r X tional zero-point corrections, were determined. The equilibrium geometries of the bromocarbenes are reasonably well described using a wide variety of theoretical methods, and the MRCI(18,12)/cc-pVTZ results presented in this work provide bromocarbene geometries that are in good agreement with previous computational and available experimental geometries. Calculated harmonic vibrational frequencies also agree well with previous computational results and with available experimental data, with most results within 5% of experimental values for frequencies above 400 cm-1 or within 25 cm-1 for frequencies below 400 cm-1. A paucity of quality experimental singlet-triplet gap data ~ (1A0 ) exists for the bromocarbenes. For CHBr, the ~a(3A00 ) r X singlet-triplet gap predicted in this work is in excellent agreement with previous computational work and with experimental results from emission spectroscopy. No experimental singlettriplet gap data are available for CFBr, CClBr, or CIBr, and the only experimental data for CBr2 are from negative ion photoelectron spectroscopy, which is generally known to give unreliable results for these systems.44 Thus, the singlet-triplet gaps presented in this work are expected to provide a consistent quality set of values for the entire series of bromocarbenes. ~Finally, good agreement is observed between adiabatic A 1 00 1 0 ~ ( A ) r X( A ) transition energies calculated in this work at the MRCIþDav/cc-pVTZ level and experimental values for all of the bromocarbenes except CIBr, for which no data are available. The present results also appear to be in much closer agreement with experimental results than the majority of previous computational results and provide a consistent set of high-quality data for ~ 1A0 transition energies. ~ 1A00 r X bromocarbene adiabatic A ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT J.M.S. and R.W.Q. acknowledge the National Center for Supercomputing Applications, Champaign, IL, for partial support of this work through awards of supercomputer time (Grants TG-CHE060076 and TG-CHE090123). ’ REFERENCES (1) Molina, M. J.; Molina, L. T.; Kolb, C. E. Annu. Rev. Phys. Chem. 1996, 47, 327–367. (2) Yung, Y. L.; Pinto, J. P.; Watson, R. J.; Sander, S. P. J. Atmos. Sci. 1980, 37, 339–353. (3) Wayne, R. P. Chemistry of Atmospheres, 3rd ed.; Oxford University Press: New York, 2000. (4) Sturges, W. T.; Oram, D. E.; Carpenter, L. J.; Penkett, S. A.; Engle, A. Geophys. Res. Lett. 2000, 27, 2081–2084.

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Multireference Configuration Interaction Study of Bromocarbenes

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