An ab initio study of the electronic structure of the boron oxide neutral (BO), cationic (BO+), and anionic (BO−) species Ilias Magoulas and Apostolos Kalemos Citation: The Journal of Chemical Physics 141, 124308 (2014); doi: 10.1063/1.4895820 View online: http://dx.doi.org/10.1063/1.4895820 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in First principles study of cobalt hydride, CoH, and its ions CoH+ and CoH− J. Chem. Phys. 137, 034309 (2012); 10.1063/1.4734595 Ab initio many-electron study for the low-lying states of the alkali hydride cations in the adiabatic representation J. Chem. Phys. 136, 124304 (2012); 10.1063/1.3695997 Giant Renner–Teller vibronic coupling in the BF 2 radical: An ab initio study of the X ̃ A 2 1 and A ̃ Π 2 electronic states J. Chem. Phys. 133, 064304 (2010); 10.1063/1.3477765 An accurate first principles study of the geometric and electronic structure of B 2 , B 2 − , B 3 , B 3 − , and B 3 H : Ground and excited states J. Chem. Phys. 132, 164307 (2010); 10.1063/1.3389133 An ab initio study of the lowest electronic states of yttrium dicarbide, YC 2 J. Chem. Phys. 122, 084323 (2005); 10.1063/1.1853375
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THE JOURNAL OF CHEMICAL PHYSICS 141, 124308 (2014)
An ab initio study of the electronic structure of the boron oxide neutral (BO), cationic (BO+ ), and anionic (BO− ) species Ilias Magoulas and Apostolos Kalemosa) Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Athens 15771, Greece
(Received 17 June 2014; accepted 5 September 2014; published online 25 September 2014) The BO neutral, cationic, and anionic molecular species have been painstakingly studied through multireference configuration interaction and single reference coupled cluster methods employing basis sets of quintuple cardinality. Potential energy curves have been constructed for 38 (BO), 37 (BO+ ), and 12 (BO− ) states and the usual molecular parameters have been extracted most of which are in very good agreement with the scarce experimental data. Numerous avoided crossings appear on more or less all of the studied states of the neutral and cationic species challenging the validity of the Born Oppenheimer approximation. Finally, all excited states of the anionic system lie above the ground state of the neutral BO system and are therefore resonances. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4895820] I. INTRODUCTION
Boron oxide (BO) is a small 13 electron system that was first observed by Lord Rayleigh in 1913 during the reaction of BCl3 with N2 . He observed a bright greenish blue flame whose spectrum showed many clearly defined bands (see Ref. 2), but Jevons1 who identified two distinct band systems, α (6370–3370 Å) and β (3256–2140 Å), inadvertently ascribed them to BN. Some years later, in 1925, Mulliken2 correctly attributed the system to BO and extended Jevons previous measurements providing also for the first time a complete verification of the vibrational isotope effect and the existence of zero point energy in what is now considered to be a paper of historical importance. Jenkins3 has shown that the rotational structure of the observed bands belongs to a 2 –2 transition (a band system) with the 2 state being inverted (A2 i ). Jenkins and McKellar4 in a tour-de-force study extended significantly Scheib’s5 α band system’s data and provided molecular parameters for both lower (X2 (+) ) and upper (A2 i ) electronic states. Interestingly enough, a perturbation was found in the rotational levels of 2 1/2 (v = 4) caused by its interaction with the levels of 2 + (v = 17). The β system was shown by Lagerqvist et al.6 to be due to a B2 –X2 electronic transition. Besides these two distinct α and β systems, a third electronic transition (γ system) was discovered by Chrétien7 in 1950 that was shown by Mal’tsev et al.8 and Kuzyakov et al.9 a decade later to involve a (C)2 excited state. Clyne and Heaven10 reported the first laser induced fluorescence spectra of the BO(A–X) system extended up to the v = 11 level while Dunn and Hanson11 recorded and analyzed the 0–2 band of the same α system. Coxon et al.12, 13 and Mélen et al.14 presented accurate constants of the X2 + , A2 , and B2 + electronic states for both 10,11 BO isotopic species which are particularly useful a) [email protected]
0021-9606/2014/141(12)/124308/10/$30.00
for the calculation of accurate Rydberg–Klein–Rees (RKR) potential curves and Frank–Condon factors. Mélen et al.14 have also found a previously unreported perturbation in the (v =)8–(v =)1 band of the A–X system. In this band, the 2 3/2 substate of the v = 8 level shows a perturbation in the Q11 and P12 branches with a maximum at J = 21.5. From extrapolation of the ground state energy levels it was found that this perturbation is due to the v = 20 (2 + 1/2 ) level. Thirty six bands of the γ (C–X) system were rotationally analyzed by Mélen et al.15 resulting in better constants for the C2 state that was also shown to be a regular one. Strong perturbations are found in the spectra due to more than two perturber states. Curiously enough the B18 O species remained unexplored until very recently. Bojovi´c et al. reported a vibrational16 and rotational17 analysis of the β system of B18 O for the first time. All of the above concern three band systems, α, β, and γ , between four electronic states, i.e., X2 + , A2 i (α), B2 + (β), and C2 r (γ ). In an effort to shed some light on new electronic states of the neutral BO system Bredohl et al.18 recorded the absorption spectrum of BO between 2400 and 300 Å. A new electronic transition (X2 + → D2 + ) has been observed and vibrationally analyzed. Moreover, nine Rydberg states have also been observed and classified into Rydberg series converging to four electronic states of BO+ (X1 + , A1 , B1 + , and C1 + ). This work remains up to date the only source of experimental evidence on excited electronic states lying above the C2 r one. Over the years the molecular constants of the X2 + state have been refined through microwave19 and infrared laser spectroscopy.20–22 This is grosso modo all we know about BO from an experimental point of view. The situation is not that much better at the theoretical level. Although there are several theoretical papers on neutral BO,23 they are at a low computational level making them unsuitable for a serious comparison with experiment. There are nevertheless four studies which we feel they deserve to be mentioned explicitly. The first one
141, 124308-1
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being a MRDCI/[6s5p1d] study by Karna and Grein24 who studied 16 stable states of 2 ± , 2 , 2 , 4 ± , 4 , and 4 symmetry with four of them being of Rydberg nature. Their goal was to help understand the experimentally observed perturbations and to report unobserved states. The second study is a 2009 paper by Wang et al.25 who constructed MRCI/augcc-pV(T,Q,5)Z potential energy curves (PEC) for the X2 + and A2 BO states. The third one is a 2010 MRCI/cc-pV5Z investigation of its four lowest X, A, B, and C states by Shi et al.26(a) recently extended to include nine more valence states.26(b) The cationic BO+ species is extremely poorly known. We are aware of only four papers dealing with this system. The very first one is a 1967 experimental observation by Kataev and Mal’tsev on an electronic transition 1 + –1 + (at 3.47 eV).27 The second one is a MRDCI/[5s3p1d] study by Karna and Grein28 on 24 BO+ states with only 9 of them being bound. The third one is an exhaustive study on only two of its states (X1 + and 23 ) by using a series of correlation consistent basis sets with both contracted and uncontracted MRCI calculations.29 The final one is a low resolution VUV absorption spectrum of BO18 that recorded four electronic states of BO+ of 1 + and 1 symmetry. The anion BO− is also very poorly studied. All but one study is devoted to the determination, experimentally or theoretically, of the electron affinity (EA) of the neutral BO. The only work pertaining to its electronic structure, both ground and excited states, is a complete active space self-consistent field (CASSCF) study30 on its three lowest states of 1 + , 1 , and 1 symmetry. Potential energy curves and the associated molecular constants are also reported. We are aware of only three experimental papers dealing with the EA. A value of EA = 2.84 ± 0.09 eV was first reported in 1971 by Srivastava et al.31 based on the equilibrium constant of the BO + Cl− → BO− + Cl reaction, that is also consistent with a lower limit of 2.48 eV assigned by Jensen.32 The second experimental study is a negative ion photoelectron spectrum of 11 BO− to form BO (X2 + ).33 The origin of the band observed is at 2.508 ± 0.008 eV, this value has been accepted as the EA of 11 BO. A hot band of weak intensity is also observed corresponding to the anion vibrational frequency of ωe (11 B16 O− ) = 1665 ± 30 cm−1 . A D0 0 (BO− ) = 9.39 ± 0.15 eV and re = 1.236±0.010 Å are also given. The last experimental study pertaining to the EA is a vibrationally resolved photoelectron spectroscopy of 10 BO− .34 The measured value is EA = 2.510 ± 0.015 eV with a vibrational frequency ωe (10 BO− ) = 1725 ± 30 cm−1 . From a theoretical point of view the accurate computation of the BO EA has been a computational endeavor since 1976.35 The most accurate values obtained so far are EA = 2.50 eV (CCSD(T)/d-aug-cc-pV6Z),35(g) 2.52 eV (MRCI(TQ)+Q/aug-cc-pVTZ),35(h) 2.507(32) eV (OUDQMC/FSGO–SGG),35(i) in perfect agreement with the latest experimental values of 2.508 ± 0.008 eV33 and 2.510 ± 0.015 eV.34 It is clear that all three species, i.e., BO0,+,− , have not received the painstaking and thorough attention they deserve and with this report we aim at filling the gap of knowledge on their electronic structure. To this end we have constructed
J. Chem. Phys. 141, 124308 (2014)
PECs of 38(BO), 37(BO+ ), and 12(BO− ) 2S+1 states at the internally contracted multireference configuration interaction (icMRCI) level of theory employing large basis sets. We strongly believe that such a study will prove particularly invaluable to the experimentalists in deciphering the observed perturbations and in the prediction of potential new ones.
II. COMPUTATIONAL DETAILS
For both B0,+,− and O0,+,− atoms we have employed the Dunning augmented correlation consistent polarized valence quintuple zeta (aug-cc-pV5Z = A5ζ ) basis set (15s9p5d4f3g2h)36(a), 36(b) generally contracted to [7s6p5d4f3g2h] comprising a total of 254 spherical Gaussian functions. For core–valence (CV) correlation and scalar relativistic effects, the appropriately optimized aug-ccpCV5Z36(c) (=AC5ζ ) and aug-cc-pV5Z-DK36(d) (A5ζ -DK) basis sets have been used. Our zeroth-order wavefunction is of the CASSCF type and results from the distribution of 7(BO), 6(BO+ ), and 8(BO− ) electrons in the active space of 11(BO)/[(2s+2p+3s+3p)B + (2p)O ], 7(BO+ )/[(2s+2p)B +(2p)O ], and 7(BO− )/[(2s+2p)B +(2p)O ] orbitals. For the construction of the PECs that capture correctly the valence, Rydberg, and ion-pair mixing we have optimized our zeroth-order wavefunction within the state average (SA) CASSCF ansatz. Valence correlation (9e− for BO, 8e− for BO+ , and 10e− for the BO− ) was extracted through single and double excitations out of all configuration functions (CF) of the reference space within the internally contracted icMRCI scheme37 and through the restricted coupled cluster + single + double + perturbative connected triplets (RCCSD(T))38 computational methods. Core–valence correlation effects (13e− for BO, 12e− for BO+ , and 14e− for BO− ) were considered at the RCCSD(T) computational level while scalar relativistic effects at the second order Douglas–Kroll–Hess (DKH2) approximation.39 Size nonextensivity errors amount to ∼5 mEh (BO), ∼2 mEh (BO+ ), and ∼18 mEh (BO− ) and are practically cancelled out at the +Q Davidson correction level.40 All calculations were performed under C2v symmetry and equivalence restrictions with the MOLPRO 2012.1.12 program.41
III. RESULTS AND DISCUSSION
Table I presents numerical data on 29 states of the 11 B16 O isotopic species while the PECs of all constructed (38) BO states are displayed in Figure 1. In Table II we report the molecular parameters of 29 states of the 11 B16 O+ cationic species with its PECs (37) shown in Figure 2. Finally results on the 11 B16 O− anionic states (11) are gathered in Table III and its PECs (12) are presented in Figure 3. The molecular states are tagged either with a number representing their ascending energy order or with a letter when they are spectroscopically known. In what follows we will discuss the X2 + , A2 , and B2 + BO, the X1 + , 23 , and A1 BO+ , and the X1 + BO− molecular states. The remaining of them will be detailed in the supplementary material42 of this paper.
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J. Chem. Phys. 141, 124308 (2014)
TABLE I. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), dipole moments μ (D), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of twenty nine 11 B16 O states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
X2 +
99.897375 (99.914074) 99.909368c 100.023734e 99.968184f
193.4 (195.4) 192.9c 194.4e 192.7f [193.63]h 123.0 (125.9) 125.6c 126.2e 125.5f [125.30]j 114.6 (117.9) [115.34]k 63.52 (65.46) 50.16 (53.07) 41.84 (45.07) 36.90 (41.67) 36.37 (40.87) 30.51 (38.80) [35.39]m 53.36 [53.43]n
D2 +
99.601950
1.2095 (1.2086) 1.2080c 1.2045e 1.2079f [1.2045531(45)]g 1.3517 (1.3618) 1.3587c 1.3541e 1.3585f [1.353471]i 1.3112 (1.3139) [1.305527]i 1.4013 (1.4024) 1.4170 (1.4168) 1.4325 (1.4346) 1.4296 (1.4305) 1.4305 (1.4316) 1.3303 (1.3106) [1.319747]l 1.3742
114
99.583276 (99.594629) 99.572959 (99.594944) 99.563844 (99.585789) 99.540579
1.3710 (1.3659) 1.4641 (1.4542) 1.4936 (1.4690) 1.2092
99.522409 99.510820 (99.525475)
1.2229 2.0404 (2.0585)
99.486783 (99.499912) 99.508244 (99.531099)
1.3060 (1.3069) 1.3058 (1.3182)
G2
99.494748
1.2868
194
99.493833 (99.511260)
2.0558 (2.0900)
99.484230 (99.497656) 99.490199 99.488332 (99.505961) 99.484247
1.3075 (1.3082) 1.323 2.0910 (2.1255) 1.244
A2
99.785093 (99.804643) 99.802160c 99.915100e 99.861162f
B2 +
99.700242 (99.719152)
44 +
99.690021 (99.706603) 99.668716 (99.686832) 99.655471 (99.674109) 99.647935 (99.668867) 99.647058 (99.667630) 99.637113 (99.665007)
54 64 − 72 − 82 C2
122 132 E2 + 152 + 164 +
F2
202 214 222
μb − 2.201 − 2.311c,d − 2.296d,e − 2.302d,f 0.850 0.836c,d 0.859d,e 0.838d,f 1.523
− 0.391 − 0.674 − 0.757 − 0.894 − 0.852 − 2.078
− 0.152 − 0.018
35.23 (40.55)
0.264 0.282
50.86 [45.3]p 39.46 31.95 (34.70)
3.994 − 4.504 0.444
− 0.882 − 3.036
ωe
ω e xe
ae × 102
D¯ e × 106
Te
1873.96 (1868.58) 1880.58c 1891.37e 1879.68f [1885.4712(27)]g 1280.86 (1238.17) 1244.86c 1252.23e 1244.16f [1260.782(28)]i 1274.77 (1239.94) [1283.318(60)]i 1223.95 (1264.87) 1112.25 (1205.35) 1055.03 (1085.23) 1102.77 (1154.34) 1090.29 (1144.29) 1296.59 (1294.85) [1315.75(14)]l 1363.45 [1517(1.2)]o 1182.86 (1158.45) 830.53 (968.84) 714.84 (892.63) 1860.46
11.91 (9.32) 11.57c 11.51e 11.56f [11.7734(65)]g 9.50 (16.61) 7.36c 6.67e 7.32f [11.1914(82)]i 9.76 (5.23) [11.562(21)]i 20.82 (28.88) 2.28 (36.17) 1.87 (7.75) 6.08 (8.94) 10.62 (17.00) 12.15 (6.32) [11.125(21)]l 16.86 [19.4(6)]o 6.97 (3.45) 32.39 (37.25) 36.76 (44.45) − 12.23
1.63 (1.69) 1.63c 1.65e 1.64f [1.65699(78)]g 1.85 (1.89) 2.04c 2.13e 2.04f [1.8523(40)]i 1.98 (2.05) [2.2021(80)]i 1.38 (1.55) 1.43 (1.61) 1.52 (1.73) 1.90 (1.85) 1.73 (1.75) 1.89 (2.58) [1.8042(94)]l 1.83
6.02 (5.70) 6.33c 7.12e 6.76f [6.3489(40)]g 7.45 (5.12) 4.40c 7.00e 6.28f [6.935(18)]i 7.18 (7.12) [8.392(23)]i 3.76 (5.27) 5.72 (7.06) 7.31 (3.97) 6.84 (6.52) 6.66 (3.83) 5.05 (6.27) [5.080(99)]l 5.65
0.0 (0.0) 0.0c 0.0e 0.0f [0.0] 70.46 (68.67) 67.27c 68.17e 67.16f [68.325]i 123.71 (122.32) [123.44]i 130.12 (130.19) 143.49 (142.60) 151.80 (150.58) 156.53 (153.87) 157.08 (154.65) 163.32 (156.29) [158.24]l 185.38 [185.35]o 197.10 (200.45) 203.57 (200.26) 209.29 (206.00) 223.89 [230.2]o 235.29 242.57 (243.85)
1.47 (1.71) 4.85 (4.07) 5.98 (5.27) 5.48
3.32 (9.28) 14.4 (11.6) 16.0 (13.4) − 0.55
3.84 0.17 (0.06)
7.18 4.70 (2.84)
1.84 (1.67) 0.26 ( − 0.98)
3.89 (3.78) 6.19 (0.62)
1768.79 650.26 (606.88) Local minimum 1465.01 (1475.24) 1528.23 (1434.18)
33.10 8.21 (5.19)
647.08 (573.11) Local minimum 1432.58 (1454.42)
11.80 (3.84)
0.50 (0.24)
4.29 (2.44)
8.25 (10.98)
1.75 (1.82)
7.66 (6.31)
641.95 (589.77)
12.81 (4.75)
0.92 (0.50)
4.42 (3.16)
− 2.714 21.31 (25.82)
− 0.342
− 0.801
17.91 (22.58)
− 0.696
257.65 (259.89) 244.18 (240.32) [233.3]o 252.65 [240.5]o 253.23 (252.77)
255.5 256.68 (256.09) 259.2
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J. Chem. Phys. 141, 124308 (2014)
TABLE I. (Continued.) State 236 + 242 254 262 272
282 -
294 +
−E
re
De a
99.483288 (99.497250) 99.482496 (99.494576) 99.481854 (99.495406) 99.480211 (99.492330) 99.477105 (99.492416)
1.8120 (1.8110) 1.3136 (1.3133) 1.3087 (1.3087) 1.3139 (1.3141) 2.4477 (2.4465)
14.97 (17.40)
99.474400 (99.487523) 99.476453 (99.491866)
1.3155 (1.3113) 2.4371 (2.4114)
99.471309 (99.484890) 99.446349 (99.461334)
1.3192 (1.3131) 1.2363 (1.2375)
μb 2.356 − 0.563 − 0.718 − 0.504
10.84 (14.05)
− 0.556
− 0.538 10.43 (13.72)
− 0.600
− 0.528 − 3.710
ωe
ω e xe
ae × 102
D¯ e × 106
Te
498.41 (508.63) 1477.81 (1461.00) 1449.47 (1455.21) 1470.07 (1456.31) 478.59 (495.25) Local minimum 1508.14 (1470.06) 441.58 (472.53) Local minimum 1501.75 (1464.39) 1700.00 (1681.49)
10.93 (9.81) 13.91 (12.44) 13.38 (11.81) 13.78 (12.68) 12.89 (8.20)
2.30 (1.99) 1.90 (1.89) 1.68 (1.87) 1.92 (1.89) 1.08 (0.76)
6.69 (7.22) 7.46 (6.32) 4.01 (5.60) 6.80 (6.49) 0.20 (0.75)
259.84 (261.56) 260.34 (263.24) 260.74 (262.72) 261.77 (264.65) 263.72 (264.59)
12.69 (7.96) 11.90 (9.79)
1.82 (1.64) 0.74 (0.42)
6.18 (3.29) 2.36 (4.06)
264.13 (264.94)
9.37 (6.93)
1.57 (1.62) 2.30 (2.20)
2.97 (7.05) 5.81 (7.12)
283.02 (284.10)
a
De with respect to the adiabatic products. μ calculated as expectation values. The origin is on the center of mass with the O atom along the positive z axis. In classical electrostatics the dipole moment vector points to the positive charge. c RCCSD(T)/A5ζ results. d μ calculated by the finite field approach, field strength ranging from −5 × 10−5 to 5 × 10−5 a.u. e C-RCCSD(T)/AC5ζ results. f RCCSD(T)-DK/A5ζ -DK results. g Reference 22. h Reference 45. i Reference 14. j De (A2 ) = De (X2 + ) − Te (A2 ← X2 + ), Refs. 14 [Te (A2 ← X2 + )] and 45 [De (X2 + )]. k De (B2 + ) = De (X2 + ) + EO (1 D ← 3 P) − Te (B2 + ← X2 + ), Refs. 14 [Te (B2 + ← X2 + )], 43 [EO (1 D ← 3 P)], and 45 [De (X2 + )]. l Reference 15. m De (C2 ) = De (X2 + ) − Te (C2 ← X2 + ), Refs. 15 [Te (C2 ← X2 + )] and 45 [De (X2 + )]. n De (D2 + ) = De (X2 + ) + EO (1 D ← 3 P) − Te (D2 + ← X2 + ), Refs. 18 [Te (D2 + ← X2 + )], 43 [EO (1 D ← 3 P)], and 45 [De (X2 + )]. o Reference 18. p De (E2 + ) = De (X2 + ) + EB (4 P ← 2 P) − Te (E2 + ← X2 + ), Refs. 18 [Te (E2 + ← X2 + )], 43 [EB (4 P ← 2 P)], and 45 [De (X2 + )]. b
A. BO
In this study we have considered molecular states dissociating to the ground B(2 P) + O(3 P) → BO 2,4 ( + , − [2], [2], ), first B(2 P) + O(1 D) → BO 2 ( + [2], − , [3], [2], ), and second B(4 P) + O(3 P) → BO 2,4,6 ( + [2], − , [2], ) excited dissociation channels lying 1.967(1.942)[1.958] and 3.529(3.620)[3.551] eV above of the ground state fragments at the MRCI(+Q)[exp]43 level; see Fig. 1. The X2 + state correlates adiabatically to B(2 P, M = ±1) + O(3 P, M = ∓1) while its equilibrium CF and MRCI Mulliken population analysis (valence electrons are only counted) are |X2 + ∼ = 0.903σ 2 4σ 2 5σ 1 1πx2 1πy2 , with 3σ ∼ (0.34)2s[B] + (0.32)2pz [B] + (0.93)2s[O], 4σ ∼ (0.55)2s[B] + (0.40)2pz [B] − (0.32)2s[O] − (0.87)2pz [O], 5σ ∼ (0.76)2s[B] − (0.69)2pz [B] + (0.27)2pz [O], 1π ∼ (0.41)2pπ [B] + (0.90)2pπ [O], and 2s 0.90 2pz0.53 2px0.38 2py0.38 /B 2s 1.91 2pz1.58 2px1.57 2py1.57 /O , qB = 0.79,
with qB being the Mulliken charge on the B atom. They both can be pictorially represented by the following valence-bondLewis (vbL) scheme44 (see Scheme 1). Its MRCI(+Q)[RCCSD(T), C-RCCSD(T), RCCSD(T)-DK] molecular (11 BO) parameters re = 1.2095(1.2086)[1.2080, 1.2045, 1.2079] Å, ωe = 1874.0(1868.6)[1880.6, 1891.4, 1879.7] cm−1 , ωe xe = 11.91(9.32)[11.57, 11.51, 11.56] cm−1 , and De = 193.4(195.4)[192.9, 194.4, 192.7] kcal/mol are in excellent agreement with the (latest) experimental values of re = 1.2045531(45) Å,22 ωe = 1885.4712(27) cm−1 ,22 ωe xe = 11.7734(65) cm−1 ,22 and De = 193.63,45 195.02 (=D0 0 + ωe /2 − ωe xe /4 = 192.3346 + 2.695422 − 0.008422 ) kcal/mol. The second excited B2 + state correlating to B(2 P, M = 0) + O(1 D, M = 0) is part of the β system6 and it is essentially described by a single CF, i.e., |B 2 + ∼ = 0.873σ 2 4σ 1 5σ 2 1πx2 1πy2 that can be considered as a single excitation from . . . 4σ 2 5σ 1 . . . (X) → . . . 4σ 1 5σ 2 . . . (B). Its MRCI Mulliken
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I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
atomic distributions 2s 1.55 2pz0.54 2px0.25 2py0.25 /B 2s 1.81 2pz0.98 2px1.74 2py1.74 /O , qB = 0.28 reveal a B(2 P/4 P) mixing through the avoided crossings at 4.6 bohr (D − E2 + ) and 4.2 bohr (B − D2 + ).42 Its MRCI molecular constants (cf. Table I) are in very good agreement with the experimental values.14 The A2 state, part of the α system, is the first excited state of BO lying experimentally14 at Te = 23,897.153 cm−1 (=68.33 kcal/mol) above the X2 + state. It correlates adiabatically to B(2 P, M = ±1) + O(3 P, M = 0) while at equilibrium it is nicely described by a single CF, i.e., |A2 ∼ = 0.953σ 2 4σ 2 5σ 2 1πx1 1πy2 that can be considered as a single excitation . . . 5σ 1 1π x 2 . . . (X) → . . . 5σ 2 1π x 1 . . . (A). The MRCI Mulliken analysis 2s 1.56 2pz0.63 2px0.11 2py0.20 /B 2s 1.90 2pz1.65 2px0.94 2py1.78 /O , qB = 0.38 alludes to the following pictorial representation (see Scheme 2). The calculated molecular constants are in very good agreement with the experimental ones (cf. Table I). One of the most interesting features is the existence of perturbations in the A2 (v = 44,12,13 and 814 ) levels due to the X2 + (v = 17 and 20) levels, respectively.
FIG. 1. Potential energy curves of all 38 BO states at the MRCI/A5ζ level of theory along with the MRCI/A5ζ PEC of the X1 + BO+ state.
TABLE II. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of twenty nine 11 B16 O+ states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
X1 +
99.422013 (99.434739) 99.431412b 99.544810c 99.490334d
127.5 (130.3) 132.9b 135.1c 132.7d
1.79 (1.79) 1.78b 1.79c 1.78d
99.400709 (99.411745) 99.391073 (99.401803)
1807.54 (1806.66) 1796.42b 1809.34c 1795.77d [1787]e 1462.41 (1465.53) 1487.54 (1492.79)
12.96 (12.96) 10.26b 10.45c 10.25d
23
1.2077 (1.2075) 1.2068b 1.2028c 1.2067d [1.2052]e 1.3086 (1.3083) 1.3092 (1.3095)
13.26 (13.58) 9.67 (11.16)
1.83 (1.85) 1.62 (1.60)
6.42 (5.29) 6.88b 7.74c 5.83d [7.06]e 8.21 (6.74) 8.04 (7.97)
11.21 (9.37) 6.27 (5.24) 13.01 (12.89)
2.03 (1.95) 1.23 (1.23) 1.59 (1.55)
6.46 (5.61) 5.59 (8.13) 4.77 (8.35) [6.33]e
13.37 (14.43) 19.42 (20.67) [6.18]f 61.95 (61.89) 69.96 (71.91) 81.05 (79.36) [82.88]f
4.79 (4.28)
1.69 (1.61)
10.8 (7.54)
117.02 (118.81)
A1
43 + 53 B1 +
71
99.323285 (99.336105) 99.310522 (99.320143) 99.292853 (99.308273)
1.2358 (1.2378) 2.1036 (2.1013) 1.1923 (1.1934) [1.1917]e
99.184944 (99.194542) 99.235535 (99.245396)
1.8614 (1.8665) 2.1256 (2.1132)
69.15 (70.63) 108.4 (110.0) 128.2 (130.7) 12.01 (12.74) 96.72 (102.0)
9.91 (10.86)
1678.62 (1656.37) 306.03 (306.66) 1979.35 (1987.69) [1952]e Local minimum 678.89 (666.93) 269.87 (282.32)
Te 0.0 (0.0) 0.0b 0.0c 0.0d
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124308-6
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
TABLE II. (Continued.) State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
Te
83
1.7663 (1.7695) 1.3849 1.6676 (1.7066) 1.4461 (1.4439) 1.9398 (1.9464) 1.5131 (1.5003) 1.5833 (1.5838) 1.5129 (1.5059) 1.6800 (1.6969) 2.3820 (2.4132) 2.2115 (2.1870) 1.9410 (1.9556) 2.3913 (2.3655) 1.6844 (1.6911) 1.8526 (1.8286) 3.5997 (3.7439) 3.6585 (3.8033) 1.7066 (1.6988) 1.8371 1.9645 (1.9713) 2.5082
50.82 (51.01) 95.15 50.28 (48.88) 40.65 (43.11) 35.23 (35.85) 34.76 (36.47) 32.41 (34.89) 30.04 (32.17) 24.10 (25.36) 14.51 (17.77) 8.89 (10.16) 3.77 (4.11) 1.05 (1.21) 42.64 (42.60) 12.16
709.35 (694.91) 1293.52 662.78 (638.27) 1001.11 (946.70) 498.00 (485.43) 820.08 (799.54) 773.81 (811.84) 802.06 (797.39) 603.97 (562.12) 371.06 (362.18) 371.49 (387.50) 228.71 (233.04) 119.32 (125.05) 674.12 (655.40) 514.51 (512.49) 159.66 (156.89) 133.98 (147.19)
4.93 (4.41) 10.17 6.88 (7.16) 20.45 (6.99) 0.59 (0.26) 17.67 (11.34) 12.93 (14.11) 14.25 (9.84) 7.07 (4.06) 4.69 (3.69) 9.09 (8.63) 9.66 (9.01) 9.17 (8.96) 7.11 (7.39) 3.58 (2.79) 3.73 (2.89) 2.85 (2.47)
0.25 (0.24) 1.52 1.63 (1.33) 3.16 (2.85) 0.34 (0.32) 2.72 (2.43) 2.29 (2.22) 2.69 (2.60) 2.25 (1.91) 0.77 (0.64) 1.26 (1.15) 3.95 (3.58) 4.70 (4.34) 1.50 (1.54) 0.23 (0.45) 0.50 (0.38) 0.49 (0.34)
5.13 (3.20) 6.76 5.26 (8.10) 6.34 (5.85) 5.30 (5.52) 9.70 (9.57) 6.77 (5.70) 8.37 (6.87) 7.28 (5.74) 3.83 (3.19) 4.92 (2.89) 28.6 (24.4) 63.9 (52.5) 5.62 (4.46) 7.04 (6.28) 1.91 (2.95) 3.49 (1.71)
283
99.200837 (99.210429) 99.198470 99.197950 (99.208151) 99.183768 (99.196487) 99.175992 (99.185783) 99.174915 (99.186602) 99.170540 (99.183206) 99.167460 (99.179985) 99.157427 (99.168555) 99.142218 (99.156748) 99.133217 (99.143958) 99.124953 (99.134775) 99.120603 (99.130155) 99.115127 (99.124662) 99.103226 (99.114924) 99.096319 (99.123059) 99.091538 (99.128304) 99.072748 (99.083358) 99.069260 99.062494 (99.072885) 99.051872
604.33 295.35 (279.82) 265.83 Local minimum
14.07 6.65 (8.25) 16.06
1.71 1.72 (2.13) 2.46
5.75 17.5 (15.2) 6.17
138.79 (140.76) 140.28 140.60 (142.19) 149.50 (149.51) 154.38 (156.22) 155.06 (155.71) 157.80 (157.84) 159.73 (159.86) 166.03 (167.03) 175.57 (174.44) 181.22 (182.47) 186.41 (188.23) 189.14 (191.13) 192.57 (194.58) 200.04 (200.69) 204.38 (195.58) 207.38 (192.29) 219.17 (220.49) 221.36 225.60 (227.07) 232.27
293
98.992384 (99.007638) 99.033180
1.5874 (1.6153) 1.535
93 + 105 113 121 131 141 153 163 175 181 195 + 205 213 223 235 243 253 263 273
4.96 (5.37) 4.25 (5.81) 15.70 (16.27) 14.15 9.28 (9.86) 3.17
(268.01) 244
a
De with respect to the adiabatic products. RCCSD(T)/A5ζ results. c C-RCCSD(T)/AC5ζ results. d RCCSD(T)-DK/A5ζ -DK results. e Reference 45. f Reference 18. b
B. BO+
We have studied all molecular states arising from B+ (1 S) + O(3 P) → BO+ (3 − , 3 ), B+ (1 S) + O(1 D) → BO+ (1 + , 1 , 1 ), B+ (1 S) + O(1 S) → BO+ (1 + ), B+ (3 P) + O(3 P) → BO+1,3,5 ( + , − [2], [2], ), B(2 P) + O+ (4 S) → BO+3,5 ( − , ), and B+ (3 P) + O(1 D) → BO+3 ( + [2], − , [3], [2], ), lying at 1.949(1.963)[1.958], 4.154(4.178)[4.180],
4.691(4.669)[4.631], 5.534(5.186)[5.320], and 6.650(6.579)[6.589] eV higher than the ground state channel at the MRCI(+Q)[exp]43 level. The first four electronic states of the neutral BO species are the X2 + , A2 (Te = 68.7 kcal/mol), B2 + (Te = 122.3 kcal/mol), and 44 + (Te = 130.2 kcal/mol). The ground state of BO+ , correlating adiabatically to the first excited dissociation channel, B+ (1 S) + O(1 D, M = 0), results primarily from the X2 + (BO) state by removal of a ∼2sB nature σ electron.
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124308-7
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
Its equilibrium configurations are surprisingly enough of multi reference character: |X1 + ∼ = 0.813σ 2 4σ 2 1πx2 1πy2 + 0.323σ 2 4σ 1 5σ¯ 1 1πx2 1πy2 + 0.313σ 2 4σ 2 1πx2 1π¯ y1 2πy1 + 1π¯ x1 2πx1 1πy2 .
FIG. 2. Potential energy curves of all 37 BO+ states at the MRCI/A5ζ level of theory.
The “0.81” component reflects clearly a triply bonded σ , π x , π y system, where the removed electron comes from the rear side (5σ ) of the B atom (see the discussion on the X2 + BO state). In the “0.32” component the charged species resulted when an electron was ejected from the σ bond (4σ ), while the “0.31” component mirrors the 44 + state42 of the neutral species. The bonding situation is a real hybrid of three different constituent parts pictorially represented by the following vbL schemes (see Scheme 3). It is quite revealing to contrast its MRCI(+Q) molecular constants with those of the X2 + BO state; re (BO+ ) = 1.208(1.208) Å vs re (BO) = 1.210(1.209) Å and ωe (BO+ ) = 1807.5(1806.7) cm−1 vs ωe (BO) = 1874.0(1868.6) cm−1 . This similarity reflects the “0.81” component of the X1 + state identical in bonding nature with the X2 + of the neutral BO, their difference is the non-bonding 5σ electron residing in the rear side of the B atom. The limited experimental data,45 re = 1.2052 Å and ωe = 1787 cm−1 , are in harmony with our calculated values (cf. Table II). The ionization energy (IE) is
TABLE III. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of eleven 11 B16 O− states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
X1 +
99.968225 (100.001693) 100.001431b 100.115685c 100.060224d
1.2521 (1.2428) 1.2400b 1.2365c 1.2399d [1.236±0.010]e 1.1996 (1.2113) (1.2034) 1.2159 (1.2167) 1.3200 (1.3098) 1.3517 (1.3657) 1.3510 (1.3541) 1.4627 (1.4354) 1.4686 (1.4409) (1.4824) (1.4850)
220.86 (217.47) 217.84b 219.20c 217.74d [216.54±3.46]e 143.57 (142.78) (141.31) 146.38 (139.48) 36.83 (76.38) 78.98 (70.63) 79.97 (71.11) 75.66 (67.92) 75.54 (67.89) (67.96) (62.96)
1687.72 (1716.61) 1709.75b 1720.04c 1709.19d [1665±30]e
10.11 (12.31) 10.75b 10.65c 10.75d
1.47 (1.67) 1.68b 1.71c 1.69d
6.92 (4.41) 8.93b 4.67c 9.43d
(1866.55)
(32.21)
(2.76)
(9.12)
1854.54 (1821.99)
10.23 (9.88)
1.56 (1.56)
5.96 (5.82)
(1791.25) 1288.03
(35.21) 13.42
(2.00) 1.62
(4.47) 5.08
1322.44 (1308.47) 874.76 (849.62) 880.53 (855.07)
19.03 (18.60) 12.23 (9.36) 12.29 (8.73)
1.88 (2.07) 1.87 (2.37) 1.72 (2.18)
5.68 (8.77) 11.4 (11.6) 8.65 (9.58)
23 31 43 + 51 + 61 73 81 91 103 113
99.842743 (99.881336) (99.879527) 99.849243 (99.876823) 99.674964 (99.776849) 99.740056 (99.766892) 99.741046 (99.766261) 99.735749 (99.762055) 99.735535 (99.761976) (99.761912) (99.753907)
Te 0.0 (0.0) 0.0b 0.0c 0.0d 78.74 (75.53) (76.66) 74.66 (78.36) (141.09) 143.18 (147.34) 142.56 (147.74) 145.88 (150.38) 146.02 (150.42) (150.46) (155.49)
a
De with respect to the adiabatic products. RCCSD(T)/A5ζ results. C-RCCSD(T)/AC5ζ results. d RCCSD(T)-DK/A5ζ -DK results. e Reference 33, the binding energy reported is a D0 0 value. b c
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124308-8
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
SCHEME 1.
SCHEME 2.
FIG. 3. Potential energy curves of all 12 BO− states at the MRCI+Q/A5ζ level of theory along with the MRCI/A5ζ PECs of the X2 + and A2 BO states.
found to be IE = 12.94(13.04)[13.01, 13.03, 13.00] eV at the MRCI(+Q)[CCSD(T), C-CCSD(T), DK-CCSD(T)] levels of theory while the latest experimental value of 12.849 eV18 is indeed very close to our calculated values. The first (23 ) and second (A1 ) excited states (see Fig. 2) are of identical bonding character, their energy difference is only E = 10 mEh , but they are related to different dissociation channels, i.e., the 23 dissociates to the ground state fragments while the A1 to the first excited one. Both result from the A2 BO state (see Fig. 1) by removing one electron from the σ frame (5σ orbital of primarily 2sB character). All their equilibrium features like CFs, Mulliken analysis, and molecular constants point to their similarity: |23 ∼ = 0.933σ 2 4σ 2 5σ 1 1πx1 1πy2 ,
SCHEME 3.
SCHEME 4.
|A1 ∼ = 0.943σ 2 4σ 2 5σ 1 1π¯ x1 1πy2 , 2s 0.89 2pz0.51 2px0.09 2py0.24 /B 2s 1.93 2pz1.57 2px0.90 2py1.71 /O , qB = 1.24, (similar for both states) re (2, A) = 1.309, 1.309 Å and ωe (2, A) = 1462.4, 1487.5 cm−1 . The above can be synopsized pictorially below (see Scheme 4).
SCHEME 5.
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124308-9
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
The difference between the 2 and A states is the spin coupling of the 5σ 1 1π x 1 electrons. We should note the complete disagreement between the only experimental value of Te (A– X) = 6.18 kcal/mol18 and our MRCI(+Q) calculated values of 19.42(20.67) kcal/mol (cf. Table II). We strongly believe that the former value is in error.
ACKNOWLEDGMENTS
C. BO−
A.K. thanks Dr. Hélène Lefebvre-Brion for reading and commenting on the manuscript.
We have constructed PECs for all states converging to B(2s2 2p1 ; 2 P) + O− (2s2 2p5 ; 2 P) → 1,3 ( + [2], − , [2], ). The ground state of the anion is of 1 + symmetry and inherently of closed shell character. Its equilibrium CFs and Mulliken atomic distributions |X1 + ∼ = 0.93|3σ 2 4σ 2 5σ 2 1πx2 1πy2 and 2s 1.38 2pz0.75 2px0.34 2py0.34 /B 2s 1.89 2pz1.63 2px1.61 2py1.61 /O both point to the following vbL scheme (see Scheme 5). It has a spectacularly high binding energy of De = 218(219) kcal/mol at the RCCSD(T)/A5ζ [CRCCSD(T)/AC5ζ ] level of theory in excellent agreement with the experimental value of D0 0 = 216.54 ± 3.46 kcal/ mol33 or De = D0 0 + ωe /2 = 218.92 ± 3.46 kcal/mol. It is indeed very close to the binding energy of the isoelectronic system N2 (D0 0 = 225.06 kcal/mol).45 The C-RCCSD(T)/AC5ζ re = 1.2365 Å, ωe = 1720 cm−1 , and EA = 2.502 eV values have practically converged to the experimental ones,33 i.e., re = 1.236 ± 0.010 Å, ωe = 1665 ± 30 cm−1 , and EA = 2.508 ± 0.08 eV. The MRCI EA value of 2.17 eV is rather low mainly due to size nonextensivity errors. The +Q Davidson correction changes it by +0.204 eV but it is still far from the experimental value. IV. CONCLUSIONS
We present for the first time high level ab initio MRCI(+Q), RCCSD(T), and C-RCCSD(T) results for a plethora of BO0,+,− states. We have constructed PECs for 38 (BO), 37 (BO+ ), and 12 (BO− ) states, and reported their molecular constants. We have analyzed and discussed the most salient features of their electronic structure and compared our theoretical findings to all existing experimental data. The ground states of BO0,+,− are of 2 + (De = 193.4 kcal/mol, re = 1.2095 Å, ωe = 1874 cm−1 ), 1 + (De = 127.5 kcal/ mol, re = 1.2077 Å, ωe = 1808 cm−1 ), and 1 + (De = 220.9 kcal/mol, re = 1.2521 Å, ωe = 1688 cm−1 ) symmetry, respectively, with first excited states the A2 (BO: De = 123.0 kcal/mol, re = 1.3517 Å, ωe = 1281 cm−1 ) and 23 (BO+ : De = 69.15 kcal/mol, re = 1.3086 Å, ωe = 1462 cm−1 ). The proximity of the low lying BO+ states is the root cause of the observed perturbations through spin orbit coupling. Perturbations are also observed in the neutral BO system (a band system) between the highly excited vibrational states of the X state with the low ones of the A state.
We believe that we offer the most concise and trusted road map to the experimentalists interested in the presently studied systems and especially in their highly perturbed spectra (see Ref. 15).
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124308-10
I. Magoulas and A. Kalemos
(2001); (h) P. Stampfuβ and W. Wenzel, ibid. 370, 478 (2003); (i) S.-I. Lu, J. Chem. Phys. 121, 10495 (2004); (j) D. Jana, D. Datta, and D. Mukherjee, Chem. Phys. 329, 290 (2006). 36 (a) T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989); (b) R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, ibid. 96, 6796 (1992); (c) D. E. Woon and T. H. Dunning, Jr., ibid. 103, 4572 (1995); (d) W. A. de Jong, R. J. Harrison, and D. A. Dixon, ibid. 114, 48 (2001). 37 H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988); P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514 (1988). 38 K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989); J. D. Watts, J. Gauss, and R. J. Bartlett, J. Chem. Phys. 98, 8718 (1993); P. J. Knowles, C. Hampel, and H.-J. Werner, ibid. 99, 5219 (1993); 112, 3106 (2000). 39 M. Douglas and N. M. Kroll, Ann. Phys. 82, 89 (1974); B. A. Hess, Phys. Rev. A 32, 756 (1985); 33, 3742 (1986). 40 S. R. Langhoff and E. R. Davidson, Int. J. Quantum Chem. 8, 61 (1974); E. R. Davidson and D. W. Silver, Chem. Phys. Lett. 52, 403 (1977).
J. Chem. Phys. 141, 124308 (2014) 41 H.-J.
Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz et al., MOLPRO, version 2012.1, a package of ab initio programs, see http://www.molpro.net. 42 See supplementary material at http://dx.doi.org/10.1063/1.4895820 for a detailed discussion and figures of a plethora of states of the BO0,+,− species. 43 A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database, version 5.0, 2012, see http://www.nist.gov. 44 A. Papakondylis, A. Mavridis, and A. Metropoulos, J. Phys. Chem. 99, 10759 (1995). 45 K. P. Huber and G. Herzberg, “Constants of diatomic molecules,” in NIST Chemistry WebBook, NIST Standard Reference Database Vol. 69, edited by P. J. Linstrom and W. G. Mallard (National Institute of Standards and Technology, Gaithersburg, MD, 20899), see http://webbook.nist.gov (retrieved May 19, 2014). 46 M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A. McDonald, and A. N. Syverud, JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985.
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THE JOURNAL OF CHEMICAL PHYSICS 141, 124308 (2014)
An ab initio study of the electronic structure of the boron oxide neutral (BO), cationic (BO+ ), and anionic (BO− ) species Ilias Magoulas and Apostolos Kalemosa) Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Athens 15771, Greece
(Received 17 June 2014; accepted 5 September 2014; published online 25 September 2014) The BO neutral, cationic, and anionic molecular species have been painstakingly studied through multireference configuration interaction and single reference coupled cluster methods employing basis sets of quintuple cardinality. Potential energy curves have been constructed for 38 (BO), 37 (BO+ ), and 12 (BO− ) states and the usual molecular parameters have been extracted most of which are in very good agreement with the scarce experimental data. Numerous avoided crossings appear on more or less all of the studied states of the neutral and cationic species challenging the validity of the Born Oppenheimer approximation. Finally, all excited states of the anionic system lie above the ground state of the neutral BO system and are therefore resonances. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4895820] I. INTRODUCTION
Boron oxide (BO) is a small 13 electron system that was first observed by Lord Rayleigh in 1913 during the reaction of BCl3 with N2 . He observed a bright greenish blue flame whose spectrum showed many clearly defined bands (see Ref. 2), but Jevons1 who identified two distinct band systems, α (6370–3370 Å) and β (3256–2140 Å), inadvertently ascribed them to BN. Some years later, in 1925, Mulliken2 correctly attributed the system to BO and extended Jevons previous measurements providing also for the first time a complete verification of the vibrational isotope effect and the existence of zero point energy in what is now considered to be a paper of historical importance. Jenkins3 has shown that the rotational structure of the observed bands belongs to a 2 –2 transition (a band system) with the 2 state being inverted (A2 i ). Jenkins and McKellar4 in a tour-de-force study extended significantly Scheib’s5 α band system’s data and provided molecular parameters for both lower (X2 (+) ) and upper (A2 i ) electronic states. Interestingly enough, a perturbation was found in the rotational levels of 2 1/2 (v = 4) caused by its interaction with the levels of 2 + (v = 17). The β system was shown by Lagerqvist et al.6 to be due to a B2 –X2 electronic transition. Besides these two distinct α and β systems, a third electronic transition (γ system) was discovered by Chrétien7 in 1950 that was shown by Mal’tsev et al.8 and Kuzyakov et al.9 a decade later to involve a (C)2 excited state. Clyne and Heaven10 reported the first laser induced fluorescence spectra of the BO(A–X) system extended up to the v = 11 level while Dunn and Hanson11 recorded and analyzed the 0–2 band of the same α system. Coxon et al.12, 13 and Mélen et al.14 presented accurate constants of the X2 + , A2 , and B2 + electronic states for both 10,11 BO isotopic species which are particularly useful a) [email protected]
0021-9606/2014/141(12)/124308/10/$30.00
for the calculation of accurate Rydberg–Klein–Rees (RKR) potential curves and Frank–Condon factors. Mélen et al.14 have also found a previously unreported perturbation in the (v =)8–(v =)1 band of the A–X system. In this band, the 2 3/2 substate of the v = 8 level shows a perturbation in the Q11 and P12 branches with a maximum at J = 21.5. From extrapolation of the ground state energy levels it was found that this perturbation is due to the v = 20 (2 + 1/2 ) level. Thirty six bands of the γ (C–X) system were rotationally analyzed by Mélen et al.15 resulting in better constants for the C2 state that was also shown to be a regular one. Strong perturbations are found in the spectra due to more than two perturber states. Curiously enough the B18 O species remained unexplored until very recently. Bojovi´c et al. reported a vibrational16 and rotational17 analysis of the β system of B18 O for the first time. All of the above concern three band systems, α, β, and γ , between four electronic states, i.e., X2 + , A2 i (α), B2 + (β), and C2 r (γ ). In an effort to shed some light on new electronic states of the neutral BO system Bredohl et al.18 recorded the absorption spectrum of BO between 2400 and 300 Å. A new electronic transition (X2 + → D2 + ) has been observed and vibrationally analyzed. Moreover, nine Rydberg states have also been observed and classified into Rydberg series converging to four electronic states of BO+ (X1 + , A1 , B1 + , and C1 + ). This work remains up to date the only source of experimental evidence on excited electronic states lying above the C2 r one. Over the years the molecular constants of the X2 + state have been refined through microwave19 and infrared laser spectroscopy.20–22 This is grosso modo all we know about BO from an experimental point of view. The situation is not that much better at the theoretical level. Although there are several theoretical papers on neutral BO,23 they are at a low computational level making them unsuitable for a serious comparison with experiment. There are nevertheless four studies which we feel they deserve to be mentioned explicitly. The first one
141, 124308-1
© 2014 AIP Publishing LLC
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124308-2
I. Magoulas and A. Kalemos
being a MRDCI/[6s5p1d] study by Karna and Grein24 who studied 16 stable states of 2 ± , 2 , 2 , 4 ± , 4 , and 4 symmetry with four of them being of Rydberg nature. Their goal was to help understand the experimentally observed perturbations and to report unobserved states. The second study is a 2009 paper by Wang et al.25 who constructed MRCI/augcc-pV(T,Q,5)Z potential energy curves (PEC) for the X2 + and A2 BO states. The third one is a 2010 MRCI/cc-pV5Z investigation of its four lowest X, A, B, and C states by Shi et al.26(a) recently extended to include nine more valence states.26(b) The cationic BO+ species is extremely poorly known. We are aware of only four papers dealing with this system. The very first one is a 1967 experimental observation by Kataev and Mal’tsev on an electronic transition 1 + –1 + (at 3.47 eV).27 The second one is a MRDCI/[5s3p1d] study by Karna and Grein28 on 24 BO+ states with only 9 of them being bound. The third one is an exhaustive study on only two of its states (X1 + and 23 ) by using a series of correlation consistent basis sets with both contracted and uncontracted MRCI calculations.29 The final one is a low resolution VUV absorption spectrum of BO18 that recorded four electronic states of BO+ of 1 + and 1 symmetry. The anion BO− is also very poorly studied. All but one study is devoted to the determination, experimentally or theoretically, of the electron affinity (EA) of the neutral BO. The only work pertaining to its electronic structure, both ground and excited states, is a complete active space self-consistent field (CASSCF) study30 on its three lowest states of 1 + , 1 , and 1 symmetry. Potential energy curves and the associated molecular constants are also reported. We are aware of only three experimental papers dealing with the EA. A value of EA = 2.84 ± 0.09 eV was first reported in 1971 by Srivastava et al.31 based on the equilibrium constant of the BO + Cl− → BO− + Cl reaction, that is also consistent with a lower limit of 2.48 eV assigned by Jensen.32 The second experimental study is a negative ion photoelectron spectrum of 11 BO− to form BO (X2 + ).33 The origin of the band observed is at 2.508 ± 0.008 eV, this value has been accepted as the EA of 11 BO. A hot band of weak intensity is also observed corresponding to the anion vibrational frequency of ωe (11 B16 O− ) = 1665 ± 30 cm−1 . A D0 0 (BO− ) = 9.39 ± 0.15 eV and re = 1.236±0.010 Å are also given. The last experimental study pertaining to the EA is a vibrationally resolved photoelectron spectroscopy of 10 BO− .34 The measured value is EA = 2.510 ± 0.015 eV with a vibrational frequency ωe (10 BO− ) = 1725 ± 30 cm−1 . From a theoretical point of view the accurate computation of the BO EA has been a computational endeavor since 1976.35 The most accurate values obtained so far are EA = 2.50 eV (CCSD(T)/d-aug-cc-pV6Z),35(g) 2.52 eV (MRCI(TQ)+Q/aug-cc-pVTZ),35(h) 2.507(32) eV (OUDQMC/FSGO–SGG),35(i) in perfect agreement with the latest experimental values of 2.508 ± 0.008 eV33 and 2.510 ± 0.015 eV.34 It is clear that all three species, i.e., BO0,+,− , have not received the painstaking and thorough attention they deserve and with this report we aim at filling the gap of knowledge on their electronic structure. To this end we have constructed
J. Chem. Phys. 141, 124308 (2014)
PECs of 38(BO), 37(BO+ ), and 12(BO− ) 2S+1 states at the internally contracted multireference configuration interaction (icMRCI) level of theory employing large basis sets. We strongly believe that such a study will prove particularly invaluable to the experimentalists in deciphering the observed perturbations and in the prediction of potential new ones.
II. COMPUTATIONAL DETAILS
For both B0,+,− and O0,+,− atoms we have employed the Dunning augmented correlation consistent polarized valence quintuple zeta (aug-cc-pV5Z = A5ζ ) basis set (15s9p5d4f3g2h)36(a), 36(b) generally contracted to [7s6p5d4f3g2h] comprising a total of 254 spherical Gaussian functions. For core–valence (CV) correlation and scalar relativistic effects, the appropriately optimized aug-ccpCV5Z36(c) (=AC5ζ ) and aug-cc-pV5Z-DK36(d) (A5ζ -DK) basis sets have been used. Our zeroth-order wavefunction is of the CASSCF type and results from the distribution of 7(BO), 6(BO+ ), and 8(BO− ) electrons in the active space of 11(BO)/[(2s+2p+3s+3p)B + (2p)O ], 7(BO+ )/[(2s+2p)B +(2p)O ], and 7(BO− )/[(2s+2p)B +(2p)O ] orbitals. For the construction of the PECs that capture correctly the valence, Rydberg, and ion-pair mixing we have optimized our zeroth-order wavefunction within the state average (SA) CASSCF ansatz. Valence correlation (9e− for BO, 8e− for BO+ , and 10e− for the BO− ) was extracted through single and double excitations out of all configuration functions (CF) of the reference space within the internally contracted icMRCI scheme37 and through the restricted coupled cluster + single + double + perturbative connected triplets (RCCSD(T))38 computational methods. Core–valence correlation effects (13e− for BO, 12e− for BO+ , and 14e− for BO− ) were considered at the RCCSD(T) computational level while scalar relativistic effects at the second order Douglas–Kroll–Hess (DKH2) approximation.39 Size nonextensivity errors amount to ∼5 mEh (BO), ∼2 mEh (BO+ ), and ∼18 mEh (BO− ) and are practically cancelled out at the +Q Davidson correction level.40 All calculations were performed under C2v symmetry and equivalence restrictions with the MOLPRO 2012.1.12 program.41
III. RESULTS AND DISCUSSION
Table I presents numerical data on 29 states of the 11 B16 O isotopic species while the PECs of all constructed (38) BO states are displayed in Figure 1. In Table II we report the molecular parameters of 29 states of the 11 B16 O+ cationic species with its PECs (37) shown in Figure 2. Finally results on the 11 B16 O− anionic states (11) are gathered in Table III and its PECs (12) are presented in Figure 3. The molecular states are tagged either with a number representing their ascending energy order or with a letter when they are spectroscopically known. In what follows we will discuss the X2 + , A2 , and B2 + BO, the X1 + , 23 , and A1 BO+ , and the X1 + BO− molecular states. The remaining of them will be detailed in the supplementary material42 of this paper.
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124308-3
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
TABLE I. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), dipole moments μ (D), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of twenty nine 11 B16 O states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
X2 +
99.897375 (99.914074) 99.909368c 100.023734e 99.968184f
193.4 (195.4) 192.9c 194.4e 192.7f [193.63]h 123.0 (125.9) 125.6c 126.2e 125.5f [125.30]j 114.6 (117.9) [115.34]k 63.52 (65.46) 50.16 (53.07) 41.84 (45.07) 36.90 (41.67) 36.37 (40.87) 30.51 (38.80) [35.39]m 53.36 [53.43]n
D2 +
99.601950
1.2095 (1.2086) 1.2080c 1.2045e 1.2079f [1.2045531(45)]g 1.3517 (1.3618) 1.3587c 1.3541e 1.3585f [1.353471]i 1.3112 (1.3139) [1.305527]i 1.4013 (1.4024) 1.4170 (1.4168) 1.4325 (1.4346) 1.4296 (1.4305) 1.4305 (1.4316) 1.3303 (1.3106) [1.319747]l 1.3742
114
99.583276 (99.594629) 99.572959 (99.594944) 99.563844 (99.585789) 99.540579
1.3710 (1.3659) 1.4641 (1.4542) 1.4936 (1.4690) 1.2092
99.522409 99.510820 (99.525475)
1.2229 2.0404 (2.0585)
99.486783 (99.499912) 99.508244 (99.531099)
1.3060 (1.3069) 1.3058 (1.3182)
G2
99.494748
1.2868
194
99.493833 (99.511260)
2.0558 (2.0900)
99.484230 (99.497656) 99.490199 99.488332 (99.505961) 99.484247
1.3075 (1.3082) 1.323 2.0910 (2.1255) 1.244
A2
99.785093 (99.804643) 99.802160c 99.915100e 99.861162f
B2 +
99.700242 (99.719152)
44 +
99.690021 (99.706603) 99.668716 (99.686832) 99.655471 (99.674109) 99.647935 (99.668867) 99.647058 (99.667630) 99.637113 (99.665007)
54 64 − 72 − 82 C2
122 132 E2 + 152 + 164 +
F2
202 214 222
μb − 2.201 − 2.311c,d − 2.296d,e − 2.302d,f 0.850 0.836c,d 0.859d,e 0.838d,f 1.523
− 0.391 − 0.674 − 0.757 − 0.894 − 0.852 − 2.078
− 0.152 − 0.018
35.23 (40.55)
0.264 0.282
50.86 [45.3]p 39.46 31.95 (34.70)
3.994 − 4.504 0.444
− 0.882 − 3.036
ωe
ω e xe
ae × 102
D¯ e × 106
Te
1873.96 (1868.58) 1880.58c 1891.37e 1879.68f [1885.4712(27)]g 1280.86 (1238.17) 1244.86c 1252.23e 1244.16f [1260.782(28)]i 1274.77 (1239.94) [1283.318(60)]i 1223.95 (1264.87) 1112.25 (1205.35) 1055.03 (1085.23) 1102.77 (1154.34) 1090.29 (1144.29) 1296.59 (1294.85) [1315.75(14)]l 1363.45 [1517(1.2)]o 1182.86 (1158.45) 830.53 (968.84) 714.84 (892.63) 1860.46
11.91 (9.32) 11.57c 11.51e 11.56f [11.7734(65)]g 9.50 (16.61) 7.36c 6.67e 7.32f [11.1914(82)]i 9.76 (5.23) [11.562(21)]i 20.82 (28.88) 2.28 (36.17) 1.87 (7.75) 6.08 (8.94) 10.62 (17.00) 12.15 (6.32) [11.125(21)]l 16.86 [19.4(6)]o 6.97 (3.45) 32.39 (37.25) 36.76 (44.45) − 12.23
1.63 (1.69) 1.63c 1.65e 1.64f [1.65699(78)]g 1.85 (1.89) 2.04c 2.13e 2.04f [1.8523(40)]i 1.98 (2.05) [2.2021(80)]i 1.38 (1.55) 1.43 (1.61) 1.52 (1.73) 1.90 (1.85) 1.73 (1.75) 1.89 (2.58) [1.8042(94)]l 1.83
6.02 (5.70) 6.33c 7.12e 6.76f [6.3489(40)]g 7.45 (5.12) 4.40c 7.00e 6.28f [6.935(18)]i 7.18 (7.12) [8.392(23)]i 3.76 (5.27) 5.72 (7.06) 7.31 (3.97) 6.84 (6.52) 6.66 (3.83) 5.05 (6.27) [5.080(99)]l 5.65
0.0 (0.0) 0.0c 0.0e 0.0f [0.0] 70.46 (68.67) 67.27c 68.17e 67.16f [68.325]i 123.71 (122.32) [123.44]i 130.12 (130.19) 143.49 (142.60) 151.80 (150.58) 156.53 (153.87) 157.08 (154.65) 163.32 (156.29) [158.24]l 185.38 [185.35]o 197.10 (200.45) 203.57 (200.26) 209.29 (206.00) 223.89 [230.2]o 235.29 242.57 (243.85)
1.47 (1.71) 4.85 (4.07) 5.98 (5.27) 5.48
3.32 (9.28) 14.4 (11.6) 16.0 (13.4) − 0.55
3.84 0.17 (0.06)
7.18 4.70 (2.84)
1.84 (1.67) 0.26 ( − 0.98)
3.89 (3.78) 6.19 (0.62)
1768.79 650.26 (606.88) Local minimum 1465.01 (1475.24) 1528.23 (1434.18)
33.10 8.21 (5.19)
647.08 (573.11) Local minimum 1432.58 (1454.42)
11.80 (3.84)
0.50 (0.24)
4.29 (2.44)
8.25 (10.98)
1.75 (1.82)
7.66 (6.31)
641.95 (589.77)
12.81 (4.75)
0.92 (0.50)
4.42 (3.16)
− 2.714 21.31 (25.82)
− 0.342
− 0.801
17.91 (22.58)
− 0.696
257.65 (259.89) 244.18 (240.32) [233.3]o 252.65 [240.5]o 253.23 (252.77)
255.5 256.68 (256.09) 259.2
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I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
TABLE I. (Continued.) State 236 + 242 254 262 272
282 -
294 +
−E
re
De a
99.483288 (99.497250) 99.482496 (99.494576) 99.481854 (99.495406) 99.480211 (99.492330) 99.477105 (99.492416)
1.8120 (1.8110) 1.3136 (1.3133) 1.3087 (1.3087) 1.3139 (1.3141) 2.4477 (2.4465)
14.97 (17.40)
99.474400 (99.487523) 99.476453 (99.491866)
1.3155 (1.3113) 2.4371 (2.4114)
99.471309 (99.484890) 99.446349 (99.461334)
1.3192 (1.3131) 1.2363 (1.2375)
μb 2.356 − 0.563 − 0.718 − 0.504
10.84 (14.05)
− 0.556
− 0.538 10.43 (13.72)
− 0.600
− 0.528 − 3.710
ωe
ω e xe
ae × 102
D¯ e × 106
Te
498.41 (508.63) 1477.81 (1461.00) 1449.47 (1455.21) 1470.07 (1456.31) 478.59 (495.25) Local minimum 1508.14 (1470.06) 441.58 (472.53) Local minimum 1501.75 (1464.39) 1700.00 (1681.49)
10.93 (9.81) 13.91 (12.44) 13.38 (11.81) 13.78 (12.68) 12.89 (8.20)
2.30 (1.99) 1.90 (1.89) 1.68 (1.87) 1.92 (1.89) 1.08 (0.76)
6.69 (7.22) 7.46 (6.32) 4.01 (5.60) 6.80 (6.49) 0.20 (0.75)
259.84 (261.56) 260.34 (263.24) 260.74 (262.72) 261.77 (264.65) 263.72 (264.59)
12.69 (7.96) 11.90 (9.79)
1.82 (1.64) 0.74 (0.42)
6.18 (3.29) 2.36 (4.06)
264.13 (264.94)
9.37 (6.93)
1.57 (1.62) 2.30 (2.20)
2.97 (7.05) 5.81 (7.12)
283.02 (284.10)
a
De with respect to the adiabatic products. μ calculated as expectation values. The origin is on the center of mass with the O atom along the positive z axis. In classical electrostatics the dipole moment vector points to the positive charge. c RCCSD(T)/A5ζ results. d μ calculated by the finite field approach, field strength ranging from −5 × 10−5 to 5 × 10−5 a.u. e C-RCCSD(T)/AC5ζ results. f RCCSD(T)-DK/A5ζ -DK results. g Reference 22. h Reference 45. i Reference 14. j De (A2 ) = De (X2 + ) − Te (A2 ← X2 + ), Refs. 14 [Te (A2 ← X2 + )] and 45 [De (X2 + )]. k De (B2 + ) = De (X2 + ) + EO (1 D ← 3 P) − Te (B2 + ← X2 + ), Refs. 14 [Te (B2 + ← X2 + )], 43 [EO (1 D ← 3 P)], and 45 [De (X2 + )]. l Reference 15. m De (C2 ) = De (X2 + ) − Te (C2 ← X2 + ), Refs. 15 [Te (C2 ← X2 + )] and 45 [De (X2 + )]. n De (D2 + ) = De (X2 + ) + EO (1 D ← 3 P) − Te (D2 + ← X2 + ), Refs. 18 [Te (D2 + ← X2 + )], 43 [EO (1 D ← 3 P)], and 45 [De (X2 + )]. o Reference 18. p De (E2 + ) = De (X2 + ) + EB (4 P ← 2 P) − Te (E2 + ← X2 + ), Refs. 18 [Te (E2 + ← X2 + )], 43 [EB (4 P ← 2 P)], and 45 [De (X2 + )]. b
A. BO
In this study we have considered molecular states dissociating to the ground B(2 P) + O(3 P) → BO 2,4 ( + , − [2], [2], ), first B(2 P) + O(1 D) → BO 2 ( + [2], − , [3], [2], ), and second B(4 P) + O(3 P) → BO 2,4,6 ( + [2], − , [2], ) excited dissociation channels lying 1.967(1.942)[1.958] and 3.529(3.620)[3.551] eV above of the ground state fragments at the MRCI(+Q)[exp]43 level; see Fig. 1. The X2 + state correlates adiabatically to B(2 P, M = ±1) + O(3 P, M = ∓1) while its equilibrium CF and MRCI Mulliken population analysis (valence electrons are only counted) are |X2 + ∼ = 0.903σ 2 4σ 2 5σ 1 1πx2 1πy2 , with 3σ ∼ (0.34)2s[B] + (0.32)2pz [B] + (0.93)2s[O], 4σ ∼ (0.55)2s[B] + (0.40)2pz [B] − (0.32)2s[O] − (0.87)2pz [O], 5σ ∼ (0.76)2s[B] − (0.69)2pz [B] + (0.27)2pz [O], 1π ∼ (0.41)2pπ [B] + (0.90)2pπ [O], and 2s 0.90 2pz0.53 2px0.38 2py0.38 /B 2s 1.91 2pz1.58 2px1.57 2py1.57 /O , qB = 0.79,
with qB being the Mulliken charge on the B atom. They both can be pictorially represented by the following valence-bondLewis (vbL) scheme44 (see Scheme 1). Its MRCI(+Q)[RCCSD(T), C-RCCSD(T), RCCSD(T)-DK] molecular (11 BO) parameters re = 1.2095(1.2086)[1.2080, 1.2045, 1.2079] Å, ωe = 1874.0(1868.6)[1880.6, 1891.4, 1879.7] cm−1 , ωe xe = 11.91(9.32)[11.57, 11.51, 11.56] cm−1 , and De = 193.4(195.4)[192.9, 194.4, 192.7] kcal/mol are in excellent agreement with the (latest) experimental values of re = 1.2045531(45) Å,22 ωe = 1885.4712(27) cm−1 ,22 ωe xe = 11.7734(65) cm−1 ,22 and De = 193.63,45 195.02 (=D0 0 + ωe /2 − ωe xe /4 = 192.3346 + 2.695422 − 0.008422 ) kcal/mol. The second excited B2 + state correlating to B(2 P, M = 0) + O(1 D, M = 0) is part of the β system6 and it is essentially described by a single CF, i.e., |B 2 + ∼ = 0.873σ 2 4σ 1 5σ 2 1πx2 1πy2 that can be considered as a single excitation from . . . 4σ 2 5σ 1 . . . (X) → . . . 4σ 1 5σ 2 . . . (B). Its MRCI Mulliken
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124308-5
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
atomic distributions 2s 1.55 2pz0.54 2px0.25 2py0.25 /B 2s 1.81 2pz0.98 2px1.74 2py1.74 /O , qB = 0.28 reveal a B(2 P/4 P) mixing through the avoided crossings at 4.6 bohr (D − E2 + ) and 4.2 bohr (B − D2 + ).42 Its MRCI molecular constants (cf. Table I) are in very good agreement with the experimental values.14 The A2 state, part of the α system, is the first excited state of BO lying experimentally14 at Te = 23,897.153 cm−1 (=68.33 kcal/mol) above the X2 + state. It correlates adiabatically to B(2 P, M = ±1) + O(3 P, M = 0) while at equilibrium it is nicely described by a single CF, i.e., |A2 ∼ = 0.953σ 2 4σ 2 5σ 2 1πx1 1πy2 that can be considered as a single excitation . . . 5σ 1 1π x 2 . . . (X) → . . . 5σ 2 1π x 1 . . . (A). The MRCI Mulliken analysis 2s 1.56 2pz0.63 2px0.11 2py0.20 /B 2s 1.90 2pz1.65 2px0.94 2py1.78 /O , qB = 0.38 alludes to the following pictorial representation (see Scheme 2). The calculated molecular constants are in very good agreement with the experimental ones (cf. Table I). One of the most interesting features is the existence of perturbations in the A2 (v = 44,12,13 and 814 ) levels due to the X2 + (v = 17 and 20) levels, respectively.
FIG. 1. Potential energy curves of all 38 BO states at the MRCI/A5ζ level of theory along with the MRCI/A5ζ PEC of the X1 + BO+ state.
TABLE II. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of twenty nine 11 B16 O+ states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
X1 +
99.422013 (99.434739) 99.431412b 99.544810c 99.490334d
127.5 (130.3) 132.9b 135.1c 132.7d
1.79 (1.79) 1.78b 1.79c 1.78d
99.400709 (99.411745) 99.391073 (99.401803)
1807.54 (1806.66) 1796.42b 1809.34c 1795.77d [1787]e 1462.41 (1465.53) 1487.54 (1492.79)
12.96 (12.96) 10.26b 10.45c 10.25d
23
1.2077 (1.2075) 1.2068b 1.2028c 1.2067d [1.2052]e 1.3086 (1.3083) 1.3092 (1.3095)
13.26 (13.58) 9.67 (11.16)
1.83 (1.85) 1.62 (1.60)
6.42 (5.29) 6.88b 7.74c 5.83d [7.06]e 8.21 (6.74) 8.04 (7.97)
11.21 (9.37) 6.27 (5.24) 13.01 (12.89)
2.03 (1.95) 1.23 (1.23) 1.59 (1.55)
6.46 (5.61) 5.59 (8.13) 4.77 (8.35) [6.33]e
13.37 (14.43) 19.42 (20.67) [6.18]f 61.95 (61.89) 69.96 (71.91) 81.05 (79.36) [82.88]f
4.79 (4.28)
1.69 (1.61)
10.8 (7.54)
117.02 (118.81)
A1
43 + 53 B1 +
71
99.323285 (99.336105) 99.310522 (99.320143) 99.292853 (99.308273)
1.2358 (1.2378) 2.1036 (2.1013) 1.1923 (1.1934) [1.1917]e
99.184944 (99.194542) 99.235535 (99.245396)
1.8614 (1.8665) 2.1256 (2.1132)
69.15 (70.63) 108.4 (110.0) 128.2 (130.7) 12.01 (12.74) 96.72 (102.0)
9.91 (10.86)
1678.62 (1656.37) 306.03 (306.66) 1979.35 (1987.69) [1952]e Local minimum 678.89 (666.93) 269.87 (282.32)
Te 0.0 (0.0) 0.0b 0.0c 0.0d
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124308-6
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
TABLE II. (Continued.) State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
Te
83
1.7663 (1.7695) 1.3849 1.6676 (1.7066) 1.4461 (1.4439) 1.9398 (1.9464) 1.5131 (1.5003) 1.5833 (1.5838) 1.5129 (1.5059) 1.6800 (1.6969) 2.3820 (2.4132) 2.2115 (2.1870) 1.9410 (1.9556) 2.3913 (2.3655) 1.6844 (1.6911) 1.8526 (1.8286) 3.5997 (3.7439) 3.6585 (3.8033) 1.7066 (1.6988) 1.8371 1.9645 (1.9713) 2.5082
50.82 (51.01) 95.15 50.28 (48.88) 40.65 (43.11) 35.23 (35.85) 34.76 (36.47) 32.41 (34.89) 30.04 (32.17) 24.10 (25.36) 14.51 (17.77) 8.89 (10.16) 3.77 (4.11) 1.05 (1.21) 42.64 (42.60) 12.16
709.35 (694.91) 1293.52 662.78 (638.27) 1001.11 (946.70) 498.00 (485.43) 820.08 (799.54) 773.81 (811.84) 802.06 (797.39) 603.97 (562.12) 371.06 (362.18) 371.49 (387.50) 228.71 (233.04) 119.32 (125.05) 674.12 (655.40) 514.51 (512.49) 159.66 (156.89) 133.98 (147.19)
4.93 (4.41) 10.17 6.88 (7.16) 20.45 (6.99) 0.59 (0.26) 17.67 (11.34) 12.93 (14.11) 14.25 (9.84) 7.07 (4.06) 4.69 (3.69) 9.09 (8.63) 9.66 (9.01) 9.17 (8.96) 7.11 (7.39) 3.58 (2.79) 3.73 (2.89) 2.85 (2.47)
0.25 (0.24) 1.52 1.63 (1.33) 3.16 (2.85) 0.34 (0.32) 2.72 (2.43) 2.29 (2.22) 2.69 (2.60) 2.25 (1.91) 0.77 (0.64) 1.26 (1.15) 3.95 (3.58) 4.70 (4.34) 1.50 (1.54) 0.23 (0.45) 0.50 (0.38) 0.49 (0.34)
5.13 (3.20) 6.76 5.26 (8.10) 6.34 (5.85) 5.30 (5.52) 9.70 (9.57) 6.77 (5.70) 8.37 (6.87) 7.28 (5.74) 3.83 (3.19) 4.92 (2.89) 28.6 (24.4) 63.9 (52.5) 5.62 (4.46) 7.04 (6.28) 1.91 (2.95) 3.49 (1.71)
283
99.200837 (99.210429) 99.198470 99.197950 (99.208151) 99.183768 (99.196487) 99.175992 (99.185783) 99.174915 (99.186602) 99.170540 (99.183206) 99.167460 (99.179985) 99.157427 (99.168555) 99.142218 (99.156748) 99.133217 (99.143958) 99.124953 (99.134775) 99.120603 (99.130155) 99.115127 (99.124662) 99.103226 (99.114924) 99.096319 (99.123059) 99.091538 (99.128304) 99.072748 (99.083358) 99.069260 99.062494 (99.072885) 99.051872
604.33 295.35 (279.82) 265.83 Local minimum
14.07 6.65 (8.25) 16.06
1.71 1.72 (2.13) 2.46
5.75 17.5 (15.2) 6.17
138.79 (140.76) 140.28 140.60 (142.19) 149.50 (149.51) 154.38 (156.22) 155.06 (155.71) 157.80 (157.84) 159.73 (159.86) 166.03 (167.03) 175.57 (174.44) 181.22 (182.47) 186.41 (188.23) 189.14 (191.13) 192.57 (194.58) 200.04 (200.69) 204.38 (195.58) 207.38 (192.29) 219.17 (220.49) 221.36 225.60 (227.07) 232.27
293
98.992384 (99.007638) 99.033180
1.5874 (1.6153) 1.535
93 + 105 113 121 131 141 153 163 175 181 195 + 205 213 223 235 243 253 263 273
4.96 (5.37) 4.25 (5.81) 15.70 (16.27) 14.15 9.28 (9.86) 3.17
(268.01) 244
a
De with respect to the adiabatic products. RCCSD(T)/A5ζ results. c C-RCCSD(T)/AC5ζ results. d RCCSD(T)-DK/A5ζ -DK results. e Reference 45. f Reference 18. b
B. BO+
We have studied all molecular states arising from B+ (1 S) + O(3 P) → BO+ (3 − , 3 ), B+ (1 S) + O(1 D) → BO+ (1 + , 1 , 1 ), B+ (1 S) + O(1 S) → BO+ (1 + ), B+ (3 P) + O(3 P) → BO+1,3,5 ( + , − [2], [2], ), B(2 P) + O+ (4 S) → BO+3,5 ( − , ), and B+ (3 P) + O(1 D) → BO+3 ( + [2], − , [3], [2], ), lying at 1.949(1.963)[1.958], 4.154(4.178)[4.180],
4.691(4.669)[4.631], 5.534(5.186)[5.320], and 6.650(6.579)[6.589] eV higher than the ground state channel at the MRCI(+Q)[exp]43 level. The first four electronic states of the neutral BO species are the X2 + , A2 (Te = 68.7 kcal/mol), B2 + (Te = 122.3 kcal/mol), and 44 + (Te = 130.2 kcal/mol). The ground state of BO+ , correlating adiabatically to the first excited dissociation channel, B+ (1 S) + O(1 D, M = 0), results primarily from the X2 + (BO) state by removal of a ∼2sB nature σ electron.
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124308-7
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
Its equilibrium configurations are surprisingly enough of multi reference character: |X1 + ∼ = 0.813σ 2 4σ 2 1πx2 1πy2 + 0.323σ 2 4σ 1 5σ¯ 1 1πx2 1πy2 + 0.313σ 2 4σ 2 1πx2 1π¯ y1 2πy1 + 1π¯ x1 2πx1 1πy2 .
FIG. 2. Potential energy curves of all 37 BO+ states at the MRCI/A5ζ level of theory.
The “0.81” component reflects clearly a triply bonded σ , π x , π y system, where the removed electron comes from the rear side (5σ ) of the B atom (see the discussion on the X2 + BO state). In the “0.32” component the charged species resulted when an electron was ejected from the σ bond (4σ ), while the “0.31” component mirrors the 44 + state42 of the neutral species. The bonding situation is a real hybrid of three different constituent parts pictorially represented by the following vbL schemes (see Scheme 3). It is quite revealing to contrast its MRCI(+Q) molecular constants with those of the X2 + BO state; re (BO+ ) = 1.208(1.208) Å vs re (BO) = 1.210(1.209) Å and ωe (BO+ ) = 1807.5(1806.7) cm−1 vs ωe (BO) = 1874.0(1868.6) cm−1 . This similarity reflects the “0.81” component of the X1 + state identical in bonding nature with the X2 + of the neutral BO, their difference is the non-bonding 5σ electron residing in the rear side of the B atom. The limited experimental data,45 re = 1.2052 Å and ωe = 1787 cm−1 , are in harmony with our calculated values (cf. Table II). The ionization energy (IE) is
TABLE III. Energies E(Eh ), bond distances re (Å), dissociation energies De (kcal/mol), harmonic frequencies ωe (cm−1 ), anharmonic corrections ωe xe (cm−1 ), rotation-vibration coupling constants ae (cm−1 ), centrifugal distortion constants D¯ e (cm−1 ), and energy gaps Te (kcal/mol) of eleven 11 B16 O− states at the MRCI(+Q)/A5ζ level of theory; experimental results in square brackets. State
−E
re
De a
ωe
ω e xe
α e × 102
D¯ e × 106
X1 +
99.968225 (100.001693) 100.001431b 100.115685c 100.060224d
1.2521 (1.2428) 1.2400b 1.2365c 1.2399d [1.236±0.010]e 1.1996 (1.2113) (1.2034) 1.2159 (1.2167) 1.3200 (1.3098) 1.3517 (1.3657) 1.3510 (1.3541) 1.4627 (1.4354) 1.4686 (1.4409) (1.4824) (1.4850)
220.86 (217.47) 217.84b 219.20c 217.74d [216.54±3.46]e 143.57 (142.78) (141.31) 146.38 (139.48) 36.83 (76.38) 78.98 (70.63) 79.97 (71.11) 75.66 (67.92) 75.54 (67.89) (67.96) (62.96)
1687.72 (1716.61) 1709.75b 1720.04c 1709.19d [1665±30]e
10.11 (12.31) 10.75b 10.65c 10.75d
1.47 (1.67) 1.68b 1.71c 1.69d
6.92 (4.41) 8.93b 4.67c 9.43d
(1866.55)
(32.21)
(2.76)
(9.12)
1854.54 (1821.99)
10.23 (9.88)
1.56 (1.56)
5.96 (5.82)
(1791.25) 1288.03
(35.21) 13.42
(2.00) 1.62
(4.47) 5.08
1322.44 (1308.47) 874.76 (849.62) 880.53 (855.07)
19.03 (18.60) 12.23 (9.36) 12.29 (8.73)
1.88 (2.07) 1.87 (2.37) 1.72 (2.18)
5.68 (8.77) 11.4 (11.6) 8.65 (9.58)
23 31 43 + 51 + 61 73 81 91 103 113
99.842743 (99.881336) (99.879527) 99.849243 (99.876823) 99.674964 (99.776849) 99.740056 (99.766892) 99.741046 (99.766261) 99.735749 (99.762055) 99.735535 (99.761976) (99.761912) (99.753907)
Te 0.0 (0.0) 0.0b 0.0c 0.0d 78.74 (75.53) (76.66) 74.66 (78.36) (141.09) 143.18 (147.34) 142.56 (147.74) 145.88 (150.38) 146.02 (150.42) (150.46) (155.49)
a
De with respect to the adiabatic products. RCCSD(T)/A5ζ results. C-RCCSD(T)/AC5ζ results. d RCCSD(T)-DK/A5ζ -DK results. e Reference 33, the binding energy reported is a D0 0 value. b c
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124308-8
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
SCHEME 1.
SCHEME 2.
FIG. 3. Potential energy curves of all 12 BO− states at the MRCI+Q/A5ζ level of theory along with the MRCI/A5ζ PECs of the X2 + and A2 BO states.
found to be IE = 12.94(13.04)[13.01, 13.03, 13.00] eV at the MRCI(+Q)[CCSD(T), C-CCSD(T), DK-CCSD(T)] levels of theory while the latest experimental value of 12.849 eV18 is indeed very close to our calculated values. The first (23 ) and second (A1 ) excited states (see Fig. 2) are of identical bonding character, their energy difference is only E = 10 mEh , but they are related to different dissociation channels, i.e., the 23 dissociates to the ground state fragments while the A1 to the first excited one. Both result from the A2 BO state (see Fig. 1) by removing one electron from the σ frame (5σ orbital of primarily 2sB character). All their equilibrium features like CFs, Mulliken analysis, and molecular constants point to their similarity: |23 ∼ = 0.933σ 2 4σ 2 5σ 1 1πx1 1πy2 ,
SCHEME 3.
SCHEME 4.
|A1 ∼ = 0.943σ 2 4σ 2 5σ 1 1π¯ x1 1πy2 , 2s 0.89 2pz0.51 2px0.09 2py0.24 /B 2s 1.93 2pz1.57 2px0.90 2py1.71 /O , qB = 1.24, (similar for both states) re (2, A) = 1.309, 1.309 Å and ωe (2, A) = 1462.4, 1487.5 cm−1 . The above can be synopsized pictorially below (see Scheme 4).
SCHEME 5.
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124308-9
I. Magoulas and A. Kalemos
J. Chem. Phys. 141, 124308 (2014)
The difference between the 2 and A states is the spin coupling of the 5σ 1 1π x 1 electrons. We should note the complete disagreement between the only experimental value of Te (A– X) = 6.18 kcal/mol18 and our MRCI(+Q) calculated values of 19.42(20.67) kcal/mol (cf. Table II). We strongly believe that the former value is in error.
ACKNOWLEDGMENTS
C. BO−
A.K. thanks Dr. Hélène Lefebvre-Brion for reading and commenting on the manuscript.
We have constructed PECs for all states converging to B(2s2 2p1 ; 2 P) + O− (2s2 2p5 ; 2 P) → 1,3 ( + [2], − , [2], ). The ground state of the anion is of 1 + symmetry and inherently of closed shell character. Its equilibrium CFs and Mulliken atomic distributions |X1 + ∼ = 0.93|3σ 2 4σ 2 5σ 2 1πx2 1πy2 and 2s 1.38 2pz0.75 2px0.34 2py0.34 /B 2s 1.89 2pz1.63 2px1.61 2py1.61 /O both point to the following vbL scheme (see Scheme 5). It has a spectacularly high binding energy of De = 218(219) kcal/mol at the RCCSD(T)/A5ζ [CRCCSD(T)/AC5ζ ] level of theory in excellent agreement with the experimental value of D0 0 = 216.54 ± 3.46 kcal/ mol33 or De = D0 0 + ωe /2 = 218.92 ± 3.46 kcal/mol. It is indeed very close to the binding energy of the isoelectronic system N2 (D0 0 = 225.06 kcal/mol).45 The C-RCCSD(T)/AC5ζ re = 1.2365 Å, ωe = 1720 cm−1 , and EA = 2.502 eV values have practically converged to the experimental ones,33 i.e., re = 1.236 ± 0.010 Å, ωe = 1665 ± 30 cm−1 , and EA = 2.508 ± 0.08 eV. The MRCI EA value of 2.17 eV is rather low mainly due to size nonextensivity errors. The +Q Davidson correction changes it by +0.204 eV but it is still far from the experimental value. IV. CONCLUSIONS
We present for the first time high level ab initio MRCI(+Q), RCCSD(T), and C-RCCSD(T) results for a plethora of BO0,+,− states. We have constructed PECs for 38 (BO), 37 (BO+ ), and 12 (BO− ) states, and reported their molecular constants. We have analyzed and discussed the most salient features of their electronic structure and compared our theoretical findings to all existing experimental data. The ground states of BO0,+,− are of 2 + (De = 193.4 kcal/mol, re = 1.2095 Å, ωe = 1874 cm−1 ), 1 + (De = 127.5 kcal/ mol, re = 1.2077 Å, ωe = 1808 cm−1 ), and 1 + (De = 220.9 kcal/mol, re = 1.2521 Å, ωe = 1688 cm−1 ) symmetry, respectively, with first excited states the A2 (BO: De = 123.0 kcal/mol, re = 1.3517 Å, ωe = 1281 cm−1 ) and 23 (BO+ : De = 69.15 kcal/mol, re = 1.3086 Å, ωe = 1462 cm−1 ). The proximity of the low lying BO+ states is the root cause of the observed perturbations through spin orbit coupling. Perturbations are also observed in the neutral BO system (a band system) between the highly excited vibrational states of the X state with the low ones of the A state.
We believe that we offer the most concise and trusted road map to the experimentalists interested in the presently studied systems and especially in their highly perturbed spectra (see Ref. 15).
1 W.
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