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A fully {it ab initio} potential curve of near-spectroscopic quality for the OH^- anion imp

A fully ab initio potential curve of near-spectroscopic quality for OH? ion: importance of connected quadruple excitations and

arXiv:physics/0003039v1 [physics.chem-ph] 16 Mar 2000

scalar relativistic e?ects
Jan M.L. Martin*
Department of Organic Chemistry, Kimmelman Building, Room 262, Weizmann Institute of Science, IL-76100 Rehovot, Israel. E-mail: comartin@wicc.weizmann.ac.il . (Special issue of Spectrochimica Acta A: Received March 6, 2000; In ?nal form March 16, 2000)

A benchmark study has been carried out on the ground-state potential curve of the hydroxyl anion, OH? , including detailed calibration of both the 1particle and n-particle basis sets. The CCSD(T) basis set limit overestimates ωe by about 10 cm?1 , which is only remedied by inclusion of connected quadruple excitations in the coupled cluster expansion — or, equivalently, the inclusion of the 2π orbitals in the active space of a multireference calculation. Upon inclusion of scalar relativistic e?ects (-3 cm?1 on ωe ), a potential curve of spectroscopic quality (sub-cm?1 accuracy) is obtained. Our best computed EA(OH), 1.828 eV, agrees to three decimal places with the best available experimental value. Our best computed dissociation energies, D0 (OH? )=4.7796 eV and D0 (OH)=4.4124 eV, suggest that the experimental D0 (OH)=4.392 eV may possibly be about 0.02 eV too low.


Molecular anions play an important role in the chemistry of the interstellar medium [1], of carbon stars [2], and the Earth’s ionosphere [3]. As pointed out in Ref. [4], the presence of


anions in the interstellar medium may have profound consequences for our understanding of the interstellar processing of the biogenic elements (see e.g. Ref. [5] and references therein). Yet as judged from the number of entries in the compilations of Huber and Herzberg [6] (for diatomics) and of Jacox [7] (for polyatomics), high- or even medium-resolution spectroscopic data for anions are relatively scarce compared to the amount of data available for neutral or even cationic species: in the 1992 review of Hirota [8] on spectroscopy of ions, only 13 molecular anions were listed in Table VII, compared to 4 1/2 pages worth of entries for cations. (Early reviews of anion spectroscopy are found in Refs. [9,10], while ab initio studies of structure and spectroscopy of anions were reviewed fairly recently by Botschwina and coworkers [11].) Some of the reasons for this paucity are discussed in the introductions to Refs. [12,4]. One such species is the hydroxyl anion, OH? . By means of velocity modulation spectroscopy [13], high-resolution fundamentals were obtained [14,15] for three isotopomers, namely

OH? ,


OD? , and


OH? ; in addition, some pure rotational transitions have been

observed [16]. Lineberger and coworkers [17] earlier obtained some rotational data in the course of an electron photodetachment study, and obtained precise electron a?nities (EAs) of 14741.03(17) and 14723.92(30) cm?1 , respectively, for OH and OD. Very recently, the same group re-measured [18] EA(OH) and obtained essentially the same value but with a higher precision, 14741.02(3) cm?1 . The spectroscopic constants of OH? were previously the subject of ab initio studies, notably by Werner et al. [19] using multireference con?guration interaction (MRCI) methods, and recently by Lee and Dateo (LD) [12] using coupled cluster theory with basis sets as large as [7s6p5d4f 3g2h/6s5p4d3f 2g]. The LD paper is particularly relevant here. The CCSD(T) (coupled cluster with all single and double substitutions [20] and a quasiperturbative treatment for triple excitations [21]) method, in combination with basis sets of at least spdf g quality and including an account for inner-shell correlation, can routinely predict vibrational band origins of small polyatomic molecules with a mean absolute error on the order of a few cm?1 (e.g. for 2

C2 H2 [22], SO2 [23]). Yet while LD found very good agreement between their computed CCSD(T)/[6s5p4d3f2g/5s4p3d2f] spectroscopic constants and available experimental data, consideration of further basis set expansion and of inner-shell correlation e?ects leads to a predicted fundamental ν at the CCSD(T) basis set limit of 3566.2±1 cm?1 , about 11 cm?1 higher than the experimental results [14] of 3555.6057(22) cm?1 , where the uncertainty in parentheses represents two standard deviations. In a recent benchmark study [24] on the ground-state potential curves of the ?rst-row diatomic hydrides using both CCSD(T) and FCI (full con?guration interaction) methods, the author found that CCSD(T) has a systematic tendency to overestimate harmonic frequencies of A–H stretching frequencies by on the order of 6 cm?1 . Even so, the discrepancy seen by LD is a bit out of the ordinary, and the question arises as to what level of theory is required to obtain ‘the right result for the right reason’ in this case. In the present work, we shall show that the discrepancy between the CCSD(T) basis set limit and Nature is mostly due to two factors: (a) neglect of the e?ect of connected quadruple excitations, and (b) neglect of scalar relativistic e?ects. When these are properly accounted for, the available vibrational transitions can be reproduced to within a fraction of a cm?1 from the computed potential curve. In the context of the present Special Issue, this will also serve as an illustrative example of the type of accuracy that can be achieved for small systems with the present state of the art. Predicted band origins for higher vibrational levels (and ‘hot bands’) may assist future experimental work on this system. Finally, as by-products of our analysis, we will show that the electron a?nity of OH can be reproduced to very high accuracy, and tentatively propose a slight upward revision of the dissociation energy of neutral hydroxyl radical, OH.


The coupled cluster, multireference averaged coupled pair functional (ACPF) [25], and full CI calculations were carried out using MOLPRO 98.1 [26] running on DEC/Compaq Alpha workstations in our laboratory, and on the SGI Origin 2000 of the Faculty of Chemistry. 3

Full CCSDT (coupled cluster theory with all connected single, double and triple excitations [27]) and CCSD(TQ) (CCSD with quasiperturbative corrections for triple and quadruple excitations [28]) calculations were carried out using ACES II [29] on a DEC Alpha workstation. Correlation consistent basis sets due to Dunning and coworkers [30,31] were used throughout. Since the system under consideration is anionic, the regular cc-pVnZ (correlation consistent polarized valence n-tuple zeta, or VnZ for short) basis sets will be inadequate. We have considered both the aug-cc-pVnZ (augmented correlation consistent, or AVnZ for short) basis sets [32] in which one low-exponent function of each angular momentum is added to both the oxygen and hydrogen basis sets, as well as the aug′ -cc-pVnZ basis sets [33] in which the addition is not made to the hydrogen basis set. In addition we consider both uncontracted versions of the same basis sets (denoted by the su?x ”uc”) and the aug-cc-pCVnZ basis sets [34] (ACVnZ) which include added core-valence correlation functions. The largest basis sets considered in this work, aug-cc-pV6Z and aug-cc-pCV5Z, are of [8s7p6d5f4g3h2i/7s6p5d4f3g2h] and [11s10p8d6f4g2h/6s5p4d3f2g] quality, respectively. The multireference ACPF calculations were carried out from a CASSCF (complete active space SCF) reference wave function with an active space consisting of the valence (2σ)(3σ)(1π)(4σ) orbitals as well as the (2π) Rydberg orbitals: this is denoted CAS(8/7)ACPF (i,e, 8 electrons in 7 orbitals). While the inclusion of the (2π) orbitals is essential (see below), the inclusion of the (5σ) Rydberg orbital (i.e., CAS(8/8)-ACPF) was considered and found to a?ect computed properties negligibly. In addition, some exploratory CAS-AQCC (averaged quadratic coupled cluster [35]) calculations were also carried out. Scalar relativistic e?ects were computed as expectation values of the one-electron Darwin and mass-velocity operators [36,37] for the ACPF wave functions. The energy was evaluated at 21 points around re , with a spacing of 0.01 ?. (All energies A were converged to 10?12 hartree, or wherever possible to 10?13 hartree.) A polynomial in (r ? re )/re of degree 8 or 9 (the latter if an F-test revealed an acceptable statistical signi?cance for the nonic term) was ?tted to the energies. Using the procedure detailed in Ref. [24], the Dunham series [38] thus obtained was transformed by derivative matching into 4

a variable-beta Morse (VBM) potential [39] Vc = De 1 ? exp[?z(1 + b1 z + b2 z 2 + . . . + b6 z 6 )]


in which z ≡ β(r ? re )/re , De is the (computed or observed) dissociation energy, and β is an adjustable parameter related to that in the Morse function. Analysis of this function was then carried out in two di?erent manners: (a) analytic di?erentiation with respect to (r ? re )/re up to the 12th derivative followed by a 12th-order Dunham analysis using an adaptation of the ACET program of Ogilvie [40]; and (b) numerical integration of the onedimensional Schr¨dinger equation using the algorithm of Balint-Kurti et al. [41], on a grid of o 512 points over the interval 0.5a0 —5a0 . As expected, di?erences between vibrational energies obtained using both methods are negligible up to the seventh vibrational quantum, and still no larger than 0.4 cm?1 for the tenth vibrational quantum.

III. RESULTS AND DISCUSSION A. n-particle calibration

The largest basis set in which we were able to obtain a full CI potential curve was ccpVDZ+sp(O), which means the standard cc-pVDZ basis set with the di?use s and p function from aug-cc-pVDZ added to oxygen. A comparison of computed properties for OH? with di?erent electron correlation methods is given in Table I, while their errors in the total energy relative to full CI are plotted in Figure 1. It is immediately seen that CCSD(T) exaggerates the curvature of the potential surface, overestimating ωe by 10 cm?1 . In addition, it underestimates the bond length by about 0.0006 ?. These are slightly more pronounced variations on trends previously seen [24] for A the OH radical. The problem does not reside in CCSD(T)’s quasiperturbative treatment of triple excitations: performing a full CCSDT calculation instead lowers ωe by only 1.7 cm?1 and lengthens the bond by less than 0.0001 ?. Quasiperturbative inclusion of connected quadruple excitaA tions, however, using the CCSD(TQ) method, lowers ωe by 8.5 cm?1 relative to CCSD(T), 5

and slightly lengthens the bond, by 0.00025 ?. (Essentially the same result was obtained by A means of the CCSD+TQ* method [42], which di?ers from CCSD(TQ) in a small sixth-order term E6T T .) No CCSDT(Q) code was available to the author: approximating the CCSDT(Q) energy by the expression E[CCSDT (Q)] ≈ E[CCSDT ]+E[CCSD(T Q)]?E[CC5SD(T )] = E[CCSDT ] + E5QQ + E5QT , we obtain a potential curve in fairly good agreement with full CI. What is the source of the importance of connected quadruple excitations in this case? Analysis of the FCI wave function reveals prominent contributions to the wave function from (1π)4 (2π)0 → (1π)2 (2π)2 double excitations; while the (2π) orbitals are LUMO+2 and LUMO+3 rather than LUMO, a large portion of them sits in the same spatial region as the occupied (1π) orbitals. In any proper multireference treatment, the aforementioned excitations would be in the zero-order wave function: obviously, the space of all double excitations therefrom would also entail quadruple excitations with respect to the HartreeFock reference, including a connected component. Since the basis set sizes for which we can hope to perform CCSDT(Q) or similar calculations on this system are quite limited, we considered multireference methods, speci?cally ACPF from a [(2σ)(3σ)(4σ)(1π)(2π)]8 reference space (denoted ACPF(8/7) further on). As might be expected, the computed properties are in very close agreement with FCI, except for ωe being 1.5 cm?1 too high. AQCC(8/7) does not appear to represent a further improvement, and adding the (5σ) orbital to the ACPF reference space (i.e. ACPF(8/8)) a?ects properties only marginally.

B. 1-particle basis set calibration

All relevant results are collected in Table II. Basis set convergence in this system was previously studied in some detail by LD at the CCSD(T) level. Among other things, they noted that ωe still changes by 4 cm?1 upon expanding the basis set from aug-cc-pVQZ to augcc-pV5Z. They suggested that ωe then should be converged to about 1 cm?1 ; this statement


is corroborated by the CCSD(T)/aug-cc-pV6Z results. Since the negative charge resides almost exclusively on the oxygen, the temptation exists to use aug′ -cc-pVnZ basis sets, i.e. to apply aug-cc-pVnZ only to the oxygen atom but use a regular cc-pVnZ basis set on hydrogen. For n=T, this results in fact in a di?erence of 10 cm?1 on ωe , but the gap narrows as n increases. Yet extrapolation suggests convergence of the computed fundamental to a value about 1 cm?1 higher than the aug-cc-pVnZ curve. For the AVnZ and A’VnZ basis sets (n=T,Q), the CAS(8/7)-ACPF approach systematically lowers harmonic frequencies by about 8 cm?1 compared to CCSD(T); for the fundamental the di?erence is even slightly larger (9.5 cm?1 ). Interestingly, this di?erence decreases for n=5. It was noted previously [24] that the higher anharmonicity constants exhibit rather greater basis set dependence than one might reasonably have expected, and that this sensitivity is greatly reduced if uncontracted basis sets are employed (which have greater radial ?exibility). The same phenomenon is seen here. In agreement with previous observations by LD, inner-shell correlation reduces the bond lengthen slightly, and increases ωe by 5–6 cm?1 . This occurs both at the CCSD(T) and the CAS(8/7)-ACPF levels.

C. Additional corrections and best estimate

At our highest level of theory so far, namely CAS(8/7)-ACPF(all)/ACV5Z, ν is predicted to be 3559.3 cm?1 , still several cm?1 higher than experiment. The e?ects of further basis set improvement can be gauged from the di?erence between CCSD(T)/AV6Z and CCSD(T)/AV5Z results: one notices an increase of +1.0 cm?1 in ωe and a decrease of 0.00006 ? in re . We also performed some calculations with a doubly augmented cc-pV5Z basis set A (i.e. d-AV5Z), and found the results to be essentially indistinguishable from those with the singly augmented basis set. Residual imperfections in the electron correlation method can be gauged from the CAS(8/7)-ACPF ? FCI di?erence with our smallest basis set, and appear to consist principally of a contraction of re by 0.00004 ? and a decrease in ωe by 1.5 cm?1 . A 7

Adding the two sets of di?erences to obtain a ‘best nonrelativistic’ set of spectroscopic constants, we obtain ν=3558.6 cm?1 , still 3 cm?1 above experiment. In both cases, changes in the anharmonicity constants from the best directly computed results are essentially nil. Scalar relativistic corrections were computed at the CAS(8/7)-ACPF level with and without the (1s)-like electrons correlated, and with a variety of basis sets. All re-

sults are fairly consistent with those obtained at the highest level considered, CAS(8/7)ACPF(all)/ACVQZ, namely an expansion of re by about 0.0001 ? and — most importantly A for our purposes — a decrease of ωe by about 3 cm?1 . E?ects on the anharmonicity constants are essentially nonexistent. Upon adding these corrections to our best nonrelativistic spectroscopic constants, we obtain our ?nal best estimates. These lead to ν=3555.44 cm?1 for

OH? , in excellent

agreement with the experimental result [14] 3555.6057(22) cm?1 . The discrepancy between computed (3544.30 cm?1 ) and observed [14] (3544.4551(28) cm?1 ) values for similar. For
16 18

OH? is quite

OD? , we obtain ν=2625.31 cm?1 , which agrees to better than 0.1 cm?1 with

the experimental value [15] 2625.332(3) cm?1 . Our computed bond length is slightly shorter than the observed one [14] for OH? , but within the error bar of that for OD? [15]. If we assume an inverse mass dependence for the experimental diabatic bond distance and extrapolate to in?nite mass, we obtain an experimentally derived Born-Oppenheimer bond distance of 0.96416(16) cm?1 , in perfect agreement with our calculations. While until recently it was generally assumed that scalar relativistic corrections are not important for ?rst-and second-row systems, it has now been shown repeatedly (e.g. [43–45]) that for kJ/mol accuracy on computed bonding energies, scalar relativistic corrections are indispensable. Very recently, Csaszar et al. [46] considered the e?ect of scalar relativistic corrections on the ab initio water surface, and found corrections on the same order of magnitude as seen for the hydroxyl anion here. Finally, Bauschlicher [47] compared ?rst-order Darwin and mass-velocity corrections to energetics (for single-reference ACPF wave functions) with more rigorous relativistic methods (speci?cally, Douglas-Kroll [48]), and found that for ?rst-and second-row systems, the two approaches yield essentially identical results, 8

lending additional credence to the results of both Csaszar et al. and from the present work. (The same author found [49] more signi?cant deviations for third-row main group systems.) Is the relativistic e?ect seen here in OH? unique to it, or does it occur in the neutral ?rstrow diatomic hydrides as well? Some results obtained for BH, CH, NH, OH, and HF in their respective ground states, and using the same method as for OH? , are collected in Table III. In general, ωe is slightly lowered, and re very slightly stretched — these tendencies becoming more pronounced as one moves from left to right in the Periodic Table. The e?ect for OH? appears to be stronger than for the isoelectronic neutral hydride HF, and de?nitely compared to neutral OH. The excellent agreement (±1 cm?1 on vibrational quanta) previously seen [24] for the ?rst-row diatomic hydrides between experiment and CCSD(T)/ACV5Z potential curves with an FCI correction is at least in part due to a cancellation between the e?ects of further basis set extension on the one hand, and scalar relativistic e?ects (neglected in Ref. [24]) on the other hand. The shape of the relativistic contribution to the potential curve is easily understood qualitatively: on average, electrons are somewhat further away from the nucleus in a molecule than in the separated atoms (hence the scalar relativistic contribution to the total energy will be slightly smaller in absolute value at re than in the dissociation limit): as one approaches the united atom limit, however, the contribution will obviously increase again. The ?nal result is a slight reduction in both the dissociation energy and on ωe . In order to assist future experimental studies on OH? and its isomers, predicted vibrational quanta G(n) ?G(n?1) are given in Table V for various isotopic species, together with some key spectroscopic constants. The VBM parameters of the potential are given in Table IV. The VBM expansion generally converges quite rapidly [39] and, as found previously for OH, parameters b5 and b6 are found to be statistically not signi?cant and were omitted. The VBM expansion requires the insertion of a dissociation energy: we have opted, rather than an experimental value, to use our best calculated value (see next paragraph). Agreement between computed and observed fundamental frequencies speaks for itself, as does that between computed and observed rotational constants. At ?rst sight agreement 9

for the rotation-vibration coupling constants αe is somewhat disappointing. However, for

OH? and


OH? , the experimentally derived ‘αe ’ actually corresponds to B1 ? B0 , i.e. to

αe ? 2γe + . . .. If we compare the observed B1 ? B0 with the computed αe ? 2γe instead, excellent agreement is found. In the case of

OD? , the experimentally derived αe given is

actually extrapolated from neutral 16 OD: again, agreement between computed and observed B1 ? B0 is rather more satisfying. We also note that our calculations validate the conclusion by Lee and Dateo that the experimentally derived ωe and ωe xe for

OH should be revised upward.

D. Dissociation energies of OH and OH? ; electron a?nity of OH

This was obtained in the following manner, which is a variant on W2 theory [44]: (a) the CASSCF(8/7) dissociation energy using ACVTZ, ACVQZ, and ACV5Z basis sets was extrapolated geometrically using the geometric formula A + B/C n ?rst proposed by Feller [50]; (b) the dynamical correlation component (de?ned at CAS(8/7)-ACPF(all) ? CASSCF(8/7)) of the dissociation energy was extrapolated to in?nite maximum angular momentum in the basis set, l → ∞ from the ACVQZ (l=4) and ACV5Z (l=5) results using the formula [51] A + B/l3 ; (c) the scalar relativistic contribution obtained at the CAS(8/7)-ACPF level was added to the total, as was the spin-orbit splitting [52] for O? (2 P ). Our ?nal result, D0 =4.7796 eV, is about 0.02 eV higher than the experimental one [6]; interestingly enough, the same is true for the OH radical (computed D0 =4.4124 eV, observed 4.392 eV). In combination with either the experimental electron a?nity of oxygen atom, EA(O)=1.461122(3) eV [53] or the best computed EA(O)=1.46075 eV [54], this leads to electron a?nities of OH, EA(OH)=1.8283 eV and 1.8280 eV, respectively, which agree to three decimal places with the experimental value [18] 1.827611(4) eV. We note that the experimental De (OH? ) is derived from De (OH)+EA(OH)?EA(O), and that a previous calibration study on the atomization energies of the ?rst-row hydrides [55] suggested that the experimental De (OH) may be too low. While a systematic error in the electronic structure treatment that cancels almost exactly between OH and OH? cannot entirely be ruled out, the excellent agreement 10

obtained for the electron a?nity does lend support to the computed De values.


We have been able to obtain a fully ab initio radial function of spectroscopic quality for the hydroxyl anion. In order to obtain accurate results for this system, inclusion of connected quadruple excitations (in a coupled cluster expansion) is imperative, as is an account for scalar relativistic e?ects. Basis set expansion e?ects beyond spdf gh take a distant third place in importance. While consideration of connected quadruple excitation e?ects and of basis set expansion e?ects beyond spdf gh would at present be prohibitively expensive for studies of larger anions, no such impediment would appear to exist for inclusion of the scalar relativistic e?ects (at least for one-electron Darwin and mass-velocity terms). Our best computed EA(OH), 1.828 eV, agrees to three decimal places with the best available experimental value. Our best computed dissociation energies, D0 (OH? )=4.7796 eV and D0 (OH)=4.4124 eV, suggest that the experimental D0 (OH)=4.392 eV (from which the experimental D0 (OH? ) was derived by a thermodynamic cycle) may possibly be about 0.02 eV too low. One of the purposes of the paper by Lee and Dateo [12] was to point out to the scienti?c community, and in particular the experimental community, that state-of-the art ab initio methods now have the capability to predict the spectroscopic constants of molecular anions with su?cient reliability to permit assignment of a congested spectrum from an uncontrolled environment — such as an astronomical observation — on the basis of the theoretical calculations alone. The present work would appear to support this assertion beyond any doubt.


JM is the incumbent of the Helen and Milton A. Kimmelman Career Development Chair. Research at the Weizmann Institute was supported by the Minerva Foundation, Munich, Germany, and by the Tashtiyot program of the Ministry of Science (Israel). 11

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TABLE I. Computed total energy (hartree), bond distance (?), harmonic frequency (cm?1 ) A and anharmonicity constants (cm?1 ) of of the electron correlation method Ee FCI CCSD CCSD(T) CC5SD(T) CCSDT CCSD(TQ) CCSD+TQ* approx. CCSDT(Q) approx. CCSDT+Q* CAS(8/7)-ACPF CAS(8/7)-AQCC CAS(8/8)-ACPF CAS(8/8)-AQCC -75.623457 -75.616478 -75.622380 -75.621379 -75.622656 -75.621660 -75.621473 -75.622937 -75.622750 -75.623089 -75.622147 -75.623084 -75.622669 re 0.97503 0.97209 0.97442 0.97428 0.97449 0.97467 0.97463 0.97488 0.97484 0.97499 0.97500 0.97501 0.97493 ωe 3701.7 3747.1 3711.6 3709.5 3709.9 3703.1 3702.8 3703.5 3703.2 3703.2 3702.9 3703.0 3704.2 ω e xe 96.65 95.28 96.45 97.74 96.37 98.17 98.48 96.78 97.10 96.60 96.54 96.66 96.59 ωe ye 0.454 0.537 0.401 0.367 0.465 0.352 0.337 0.452 0.438 0.455 0.456 0.444 0.443 ωe ze -0.024 -0.010 -0.031 -0.025 -0.023 -0.024 -0.023 -0.022 -0.020 -0.023 -0.029 -0.024 -0.024
16 OH?

using the cc-pVDZ+sp(O) basis set as a function


TABLE II. Computed bond distance, harmonic frequency, anharmonicity constants, and Dunham correction to harmonic frequency for 16 OH? as a function of basis set and electron correlation ? method. All data in cm?1 except re (A)
Corr. method basis set 1s corr? re 0.96776 0.96517 0.96528 0.96476 0.96741 0.96486 0.96456 0.96809 0.96551 0.96488 0.96781 0.96520 0.96472 0.96476 0.96466 0.96734 0.96522 0.96473 0.96789 0.96558 0.96501 0.96768 0.96525 0.96472 0.96725 0.96468 0.96410 0.96688 0.96435 0.96378 0.96478 0.00010 0.96417 ωe 3725.01 3742.24 3739.00 3745.58 3733.55 3750.37 3751.56 3716.44 3737.30 3744.47 3723.56 3745.61 3749.39 3749.31 3750.41 3724.84 3744.72 3749.21 3713.45 3735.72 3740.66 3718.89 3744.90 3749.22 3714.74 3741.86 3746.51 3725.04 3751.76 3756.27 3738.69 -3.17 3742.87 ωe x e 92.738 93.610 93.564 93.856 91.987 92.948 93.183 92.083 93.868 93.816 91.345 93.159 93.193 93.079 93.237 92.600 93.044 93.243 91.642 93.894 94.081 91.145 93.038 93.225 92.017 94.110 94.317 91.122 93.151 93.347 94.098 -0.012 94.404 ωe y e 0.3623 0.3855 0.3881 0.4968 0.3284 0.3474 0.4643 0.2144 0.4277 0.5236 0.1745 0.3900 0.4966 0.4900 0.4839 0.4875 0.4081 0.4435 0.2137 0.4219 0.4691 0.1639 0.3867 0.4361 0.1855 0.4205 0.4682 0.1509 0.3929 0.4427 0.4193 -0.0012 0.4527 ωe z e -0.0566 -0.0068 -0.0066 -0.0192 -0.0524 -0.0121 -0.0227 -0.0133 -0.0034 -0.0157 -0.0188 -0.0107 -0.0291 -0.0283 -0.0214 -0.0734 -0.0219 -0.0103 0.0000 -0.0130 -0.0005 -0.0044 -0.0191 -0.0101 -0.0035 -0.0129 0.0009 -0.0022 -0.0202 -0.0088 -0.0102 0.0027 0.0100 Y10 ? ωe -0.37 -0.24 -0.24 -0.14 -0.40 -0.27 -0.17 -0.42 -0.19 -0.13 -0.46 -0.22 -0.15 -0.16 -0.14 -0.39 -0.27 -0.16 -0.41 -0.23 -0.14 -0.45 -0.26 -0.17 -0.43 -0.23 -0.14 -0.46 -0.26 -0.17 -0.24 -0.01 -0.14 ν 3540.07 3556.00 3552.86 3559.24 3549.99 3565.28 3566.42 3532.49 3550.75 3558.33 3540.88 3560.29 3564.32 3564.45 3565.26 3540.46 3559.58 3563.95 3530.45 3549.01 3553.87 3536.66 3559.73 3563.96 3530.86 3554.71 3559.26 3542.81 3566.37 3570.80 3551.57 -3.14 3555.44 CAS(8/7)-ACPF aug’-cc-pVTZ no CAS(8/7)-ACPF aug’-cc-pVQZ no CAS(8/7)-ACPF aug’-cc-pVQZ no+REL CAS(8/7)-ACPF aug’-cc-pV5Z no CCSD(T) CCSD(T) CCSD(T) aug’-cc-pVTZ no aug’-cc-pVQZ no aug’-cc-pV5Z no no no no no no no no no no no no no no no no no no yes yes yes yes yes yes yes+REL




CAS(8/7)-ACPF ACVQZ all ?REL best calc.

The su?x “+REL” indicates inclusion of scalar relativistic (Darwin and mass-velocity) effects obtained as expectation values for the wave function indicated.


TABLE III. E?ect of scalar relativistic contributions on the bond lengths (?) and harmonic A frequencies (cm?1 ) of the AH (A=B–F) diatomics. All calculations were carried out at the

CAS(2σ3σ4σ1π)-ACPF/ACVQZ level with all electrons correlated ?re BH CH NH OH HF OH? -0.00001 +0.00001 +0.00003 +0.00004 +0.00005 +0.00010 ?ωe -0.57 -1.08 -1.77 -2.35 -2.80 -3.14

E?ects on the anharmonicity constants are negligible.
TABLE IV. Parameters for the VBM representation, eq. (1), obtained from our best potential. A De , re are in cm?1 and ?, respectively; the remaining parameters are dimensionless De re β b1 b2 b3 b4 40398.7079 0.964172 2.128977 -0.047181 0.022371 -0.0070906 0.0018429


TABLE V. Spectroscopic constants and band origins (in cm?1 ) of di?erent isotopomers of the hydroxyl anion obtained from our best potential
16 OH? 16 OD? 18 OH? 18 OD?

calc Y00 Y10 ≈ ωe ?Y20 ≈ ωe xe Y30 ≈ ωe ye Y01 ≈ Be ?Y11 ≈ αe Y21 ≈ γe αe -2γe ?Y02 ≈ De Y12 ≈ βe ZPVE G(1)-G(0) G(2)-G(1) G(3)-G(2) G(4)-G(3) G(5)-G(4) G(6)-G(5) G(7)-G(6) 2.38 3742.72 94.298 0.4686 19.126021 0.779874 0.003913 0.772048 0.001998 0.000032 1850.23 3555.63 3371.17 3189.42 3010.39 2834.11 2660.70 2490.31


calc 1.26


calc 2.36


calc 1.25 2707.77 49.357 0.1774

3738.44(99)c 91.42(49)c

2724.79 49.979 0.1808

2723.5(10) 49.72(50) 0.38(15) 10.13599(30) 0.3043(5)

3730.35 93.676 0.4639 18.999788 0.772165 0.003861 18.99518(49) 0.76409(16)

19.12087(37) 0.77167(13)

10.136936 0.300914 0.001099

10.010698 0.295310 0.001072

0.77167(13) 0.001995(6) 0.000032(2)

0.298716 0.000561 0.000006 1351.19

0.2984(3) 0.000559(2)d 0.000008(2)

0.764443 0.001972 0.000031 1844.18

0.76409(16) 0.000031(2) 0.000031(2)

0.293166 0.000547 0.000006 1342.81


2625.42 2527.06 2429.75 2333.49 2238.28 2144.12 2051.03


3544.49 3361.24 3180.66 3002.78 2827.63 2655.31 2485.97


2609.63 2512.49 2416.38 2321.29 2227.23 2134.21 2042.24

The Dunham constants Ymn include higher-order corrections to the mechanical spectroscopic constants (like ωe , ωe xe ) as obtained from the potential function. (a) Ref. [14]. Uncertainties in parentheses correspond to two standard deviations. (b) Ref. [15]. Uncertainties in parentheses correspond to three standard deviations. (c) LD proposed ωe =3741.0(14) and ωe xe =93.81(93) cm?1 , obtained by mass scaling of the

OD? results, as more reliable.

(d) From observed D0 and D1 in Ref. [15].


FIG. 1. Deviation from the FCI potential curve of OH? for di?erent electron correlation methods



CCSD(T) E-E[FCI] (hartree) 0.0015 CCSDT CCSD+TQ CCSD+TQ* CC5SD(T) CAS(8/8)-ACPF CAS(8/8)-AQCC 0.001 approx. CCSDT+Q* approx. CCSDT+Q


0 0.87 0.92 0.97 r[O-H] (?) 1.02 1.07




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