On the HCN â HNC Energy Difference - The Journal of Physical

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On the HCN – HNC Energy Difference Thanh Lam Nguyen, Joshua H. Baraban, Branko Ruscic, and John F. Stanton J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b08406 • Publication Date (Web): 08 Oct 2015 Downloaded from http://pubs.acs.org on October 23, 2015

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The Journal of Physical Chemistry

On the HCN – HNC Energy Difference Thanh L. Nguyen,a Joshua H. Baraban,a Branko Ruscic,*,b,c and John F. Stanton*,a

a

Institute for Theoretical Chemistry, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712

b

Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439

c

Computation Institute, The University of Chicago, Chicago, Illinois 60637

Corresponding Authors: *e-mail: [email protected], [email protected].

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

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Abstract The value for the HCN → HNC 0 K isomerization energy has been investigated by combining state-of-the art electronic structure methods with the Active Thermochemical Tables (ATcT) approach. The directly computed energy difference between HCN and HNC at the HEAT-456QP level of theory is 5236 ± 50 cm−1. This is substantially lower (by ~470 cm−1 or ~1.3 kcal/mol) than the recently proposed high-level MRCI value of 5705 ± 20 cm−1 of Barber et al. (Mon. Not. Roy. Astron. Soc. 2014, 437, 1828-1835). The discrepancy was analyzed by the Active Thermochemical Tables (ATcT) approach, using several distinct steps, which (a) independently corroborated the current single-reference HEAT-456QP result, (b) independently found that the recent multireference-based value is highly unlikely to be correct within its originally stated uncertainty, and (c) produced a recommended value of 5212 ± 30 cm−1 for the HCN → HNC isomerization energy at 0 K, based on all currently available knowledge. The ATcT standard enthalpies of formation at 0 K and 298 K for HCN, HNC, and their cations and anions are also presented.


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Introduction The interconversion of hydrocyanic and hydroisocyanic acids (HCN and HNC, respectively) is arguably one of the simplest isomerization processes in all of chemistry. The former isomer is more stable thermodynamically, and overwhelmingly the dominant form found on Earth. However, the isomeric ratio in deep space is not under thermodynamic control, and the abundance of the less stable form (HNC) is comparable to that of HCN (and in fact exceeds that of HCN along certain lines of sight1). The HCN/HNC interconversion has been extensively studied both experimentally and theoretically, and the rather small size of the system is such that very high levels of theory (including methods like the parametric two-electron reduced density matrix (2-RDM) theory2 and high-level multireference configuration interaction,3 as well as more commonly-used approaches such as single-reference coupled-cluster theory4,5,6) can be applied to study its electronic structure and potential energy surface. The purpose of this note is to document a new and accurate estimate for the 0 K isomerization energy of HCN, by combining the results of high-accuracy quantum chemistry with the Active Thermochemical Tables (ATcT) approach.7,8 Motivation is provided by a recent work which indicated that a fairly significant upward revision of the estimated isomerization energy – supported by very high-level multireference configuration interaction calculations – leads to an improved partition function at high energies.9 The magnitude of this revision from a previously calculated value3 of 5185.637 cm−1 (which was given an uncertainty of ± 50 cm−1 by the authors) is substantial: the new value is 5705 cm−1 (with a stated uncertainty of ± 20 cm−1), and perhaps surprising given that both values were obtained from highlevel calculations, the former using single-reference coupled-cluster computations, and the latter based on an unspecified multireference configuration interaction level of theory. Given our interest and experience in the field of high-accuracy thermochemistry, as well as in HCN and related systems such as acetylene, it seemed worthwhile to reinvestigate the situation. Computational Method The HEAT protocol,10,11,12 as well as the related W4 and focal point approaches developed by Martin13 and Allen,14,15 respectively, have been shown to easily reach the goal of chemical accuracy (± 1 kcal mol−1 or roughly 350 cm−1) and in fact achieve what has been termed “sub-chemical” accuracy (± 1 kJ mol−1 or roughly 80 cm−1), where uncertainties are reckoned16 as 95% confidence intervals (2σ). The HEAT approach, which includes no empirical corrections apart from that associated with basis set extrapolation, is intended to determine the ground state energy of atoms and molecules within the adiabatic approximation as accurately as possible. In HEAT, the energy is approximated by the additive 3 ACS Paragon Plus Environment


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decomposition

= + Δ

() + Δ() + Δ + Δ + Δ + Δ + Δ ,

where the various terms are discussed in detail in Refs. 10-12. Briefly, the Hartree-Fock and correlation energies, obtained through the coupled-cluster singles, doubles and perturbative triples model, CCSD(T),17 are based on all-electron, large basis set calculations that are extrapolated to the basis set limit, while residual electron correlation effects (deficiencies in the perturbative treatment of triple excitations, T-(T), and correlation effects of quadruple and higher-order excitations, HLC) are treated with smaller basis set approximations. The electronic energy is extended by scalar relativistic effects11 and the so-called diagonal Born-Oppenheimer correction, which is the expectation value of the nuclear kinetic energy operator over the clamped-nuclei electronic wavefunction. An additional correction for first-order spin-orbit effects is formally in the definition of Etotal, but it vanishes here for both HCN and HNC. Finally, the energy is corrected for zero-point vibrational motion. Various flavors of HEAT differ in the basis sets used to determine the extrapolated energies and the treatment used to evaluate EHLC; that chosen for application here, HEAT-456QP,12 makes use of the aug-cc-pCVXZ basis sets, X = Q, 5 and 618,19 for the former, and calculates EHLC with the CCSDTQP model.20 In a set of benchmark calculations involving twenty small molecules and atoms, the HEAT-456QP approximation exhibited a root meansquare error of 0.42 kJ mol−1 (ca. 35 cm−1) for atomization energies,12 giving a 95% confidence limit of 70 cm−1. For the problem at hand, where deficiencies in the theoretical treatment might be expected to cancel owing to the very similar electronic structures of the two isomers, it would seem very likely that the HEAT-456QP energy is within 50 cm−1 of the exact ground state energy difference. ATcT Approach Pertinent details of the Active Thermochemical Tables approach have been given in earlier papers.7,8,21-25 Succinctly, while traditional thermochemistry uses a sequential approach to establish the enthalpies of formation of targeted chemical species (A begets B, B begets C), ATcT obtains the desired thermochemical parameters by constructing, statistically analyzing, and solving a thermochemical network (TN). The TN contains the available thermochemically-relevant measurements for the chemical species of interest, such as reaction enthalpies, constants of equilibria, bond dissociation enthalpies, adiabatic ionization energies and electron affinities, etc. that were either experimentally determined (actual measurements) or obtained from state-of-the-art electronic structure methods (virtual measurements). Each measurement included in the TN is assigned an initial (a.k.a. prior) uncertainty that reflects the best estimate of its perceived 95 % confidence interval. The TN effectively presents an


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intricate set of constraints that need to be simultaneously satisfied by the final enthalpies of formation, providing that the measurements included are internally consistent. Ergo, ATcT performs an iterative statistical analysis that evaluates every measurement for consistency with the remaining knowledge content of the TN by exploiting all available thermochemical cycles in the TN. The goal is to identify those measurements that have overly optimistic uncertainties, which would, if their initial uncertainties were left uncorrected, skew the resulting thermochemistry. Once internal consistency has been achieved across the whole TN, ATcT solves the resulting set of adjusted constraints and obtains the enthalpies of formation for all species simultaneously, exploiting optimally the cumulative knowledge stored in the TN. Computational Results, ATcT Analysis, and Discussion The results of the HEAT-456QP calculation, decomposed according to the various terms in Eq. 1, are listed in Table 1. The HEAT-456QP value for the isomerization energy, 5236 ± 50 cm−1, while indeed higher than the “old” value3 of 5185.64 cm−1 is substantially lower than the “new” value9 of 5705 cm−1 obtained with extremely high-level multireference calculations. The magnitude of the discrepancy – some 450 cm−1 – is roughly an order of magnitude greater than the error assumed in our humble singlereference calculations, and further analysis is warranted. To address the question raised by the discrepancy between the HEAT-456QP calculations and the highquality multireference calculations of Tennyson and co-workers,9 we turn to the Active Thermochemical Table approach for further analysis. The analysis presented here is based on the current version of ATcT TN (1.122), which contains over 19,000 determinations spanning 1180 chemical species and is described in more detail elsewhere.25 In preparation for the current study, the TN sections relevant to determining the thermochemistry of HCN, HNC, and their energy difference (the latter centered around experimental measurements on the neutral species by Wenthold26 and by Pau and Hehre27, and charge exchange experiments by Hansel et al.,28 together with several computational results discussed below; see also Table 2) were re-scrutinized for completeness and soundness of the underlying determinations. One of the preliminary checks consisted of the variance decomposition analyses of the provenance24 of the ATcT value for ∆rH°(HCN → HNC) from earlier versions of the TN. These indicated that since the introduction of the computational result by van Mourik et al.,3 the resulting ATcT energy difference was highly dominated by the latter computational result, having a contribution larger than 82 %, with the charge exchange experiment28 being the next highest contributor at less than 2 %. The result of van Mourik et al.3 was inserted in the TN several versions ago, taking the ± 50 cm−1 uncertainty (as suggested 5 ACS Paragon Plus Environment


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by these authors) at face value. Top-heavy provenances occur when a single determination is disproportionally accurate in comparison to the remaining knowledge content of the TN. However, if the primary contribution approaches (or even exceeds) 80 %, this generally indicates one of three possible underlying weaknesses. Occasionally, the top contributor is truly a solitary determination in the TN, in which case it would be best to acquire additional corroborating measurements (such as, for example, occurred with the bond dissociation energy of N224,29). In other cases, this typically indicates either that the related TN section is underdeveloped due to missing determinations that have not been (yet) included, or that the uncertainty of the leading contributor is inappropriately tight to the point that it unduly overshadows the remaining knowledge content of the TN (or possibly a combination of both). A more careful examination of the origin of the ± 50 cm−1 uncertainty proposed by van Mourik et al.,3 suggested that – contrary to their “conservative error bar” designation – such uncertainty is inherently optimistic in view of the fact that their recommended energy difference, obtained from the fitted potential energy surface and amounting to 5282 cm−1 without zpe correction, differs by 60 cm−1 from their ‘best’ directly calculated value, 5222 cm−1 without zpe correction. This, together with the fact that their electronic structure protocol did not include correlation corrections beyond the T - (T) term, prompted us to relax in ver. 1.122 of the TN the estimated prior uncertainty of this determination to ± 100 cm−1. In addition, the TN was further expanded by including several literature determinations that were not present in prior versions, such as the HCN – HNC energy difference obtained by Dawes et al.30 from their automatically generated IMLS (interpolative moving least squares method) potential energy surfaces (based on both coupled-cluster and multireference configuration interaction approaches), the W4 result of Karton et al.,31 the 2-RDM result of DePrince and Mazziotti,2 the results of Klopper et al.32,33 obtained by using explicitly correlated methods, as well as the earlier results by Lee et al.4,34 The resulting value ∆rH°0(HCN → HNC) = 5194 ± 40 cm−1 represents a ‘baseline’ ATcT result for the purpose of this analysis, since ver. 1.122 of the TN does not contain either the result of Barber et al.9 or the present HEAT-456QP result. The provenance of the baseline ATcT value, obtained by variance decomposition analysis, is moderately distributed (16 determinations contribute to the top 90 % of the provenance), and the top four contributors consist of the HCN – HNC energy differences obtained by Karton et al.31 (19.5 %), Dawes et al.30 (14.9 %), and van Mourik et al.3 (14.9 %), and the total atomization energy of HNC by Karton et al.31 (13.3 %). The next step in the ATcT analysis consists of adding the ‘new’ higher value for the HCN – HNC energy differences obtained by Barber et al.9 to the TN. Barber et al. provide a surprisingly tight uncertainty of ± 20 cm−1, but give scant details of the computational protocol used (it is, in fact, unclear if the uncertainty 6 ACS Paragon Plus Environment

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is intended to convey a 95% confidence interval, or just one standard deviation); this lack of information leaves no choice but to take their tight uncertainty at face value as the assigned prior, and rely on the ATcT analysis to provide the necessary arbitration. The addition of the determination of Barber et al. was the only change performed at this point, producing ver. 1.122a of the TN. Interestingly, the resulting ATcT value, ∆rH°0(HCN → HNC) = 5197 ± 40 cm−1, was hardly affected at all by this addition. The provenance of the value also stayed essentially unchanged, with the same top four contributors as in ver. 1.122: the HCN – HNC energy difference obtained by Karton et al.31 (19.4 %), Dawes et al.30 (14.8 %), and van Mourik et al.3 (14.8 %), and the total atomization energy of HNC by Karton et al.31 (13.2 %). The freshly introduced value by Barber et al.9 contributes negligibly to the final result (0.6 %). In fact, the ATcT iterative statistical analysis that precedes the computation of the final value finds that their HCN – HNC energy difference of 5705 cm−1 is quite unlikely to be correct within its nominal uncertainty of ± 20 cm−1, and – in order to maintain internal consistency with the remaining knowledge content of the TN – it finds it necessary to augment the assigned prior by a whopping factor of almost 26, to ± 515 cm−1. At this point we should take note of the fact that the ATcT results from versions 1.122 and 1.122a of the TN, 5194 ± 40 cm−1 and 5197 ± 40 cm−1, respectively, fully and independently corroborate the current HEAT-456QP result of 5236 ± 50 cm−1, with the difference of 42 cm−1 or 39 cm−1 comfortably contained within the combined uncertainties. The final step of the ATcT approach is then to make use of all available knowledge, and incorporate both the result of Barber et al.9 and the current HEAT-456QP result. This produces TN ver. 1.122b, which yields a further improved ATcT value for the HCN – HNC energy difference of 5212 ± 30 cm−1. Similar to ver. 1.112a of the TN, the ATcT statistical analysis of ver. 1.122b of the TN finds the value given by Barber et al.9 unlikely to be correct within its prior uncertainty of ± 20 cm−1, and iteratively augments the uncertainty to nearly ± 500 cm−1. The variance decomposition analysis indicates that the added HEAT value has emerged as the top contributor (37.2 %), immediately followed by the previous 4 top contributors: the HCN – HNC energy difference obtained by Karton et al.31 (12.2 %), Dawes et al.30 (9.3 %), and van Mourik et al.3 (9.3 %), and the total atomization energy of HNC by Karton et al.31 (8.3 %). The final ATcT value ∆rH°0(HCN → HNC) = 5212 ± 30 cm−1 becomes the current recommendation for this thermochemical quantity. This value is slightly higher (by 18 cm−1), and slightly more accurate (± 30 cm−1 vs. ± 40 cm−1) than that obtained from the baseline version 1.122 of the TN. The ATcT value is marginally higher (by 26 cm−1) than the value of van Mourik et al.,3 and slightly lower than the HEAT-456QP value (by 24 cm−1), though in both cases the differences are well contained within the uncertainty of the ATcT 7 ACS Paragon Plus Environment


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value, and even more so within the combined uncertainties. However, the current ATcT value is markedly lower (by 493 cm−1) than the recently proposed value of Barber et al.9 that was based on multireference configuration interaction, and essentially rules out the latter result as a likely possibility, based on the current knowledge. ATcT values for the standard enthalpies of formation of HCN, HNC, and their ions While the aim of this study is to provide the best available HCN - HNC energy difference, for the sake of completeness we also report the related ATcT enthalpies of formation for HCN, HNC, and their ions (Table 3). The current ATcT values for the enthalpies of formation of hydrocyanic acid and hydroisocyanic acids are ∆fH°0(HCN) = 129.66 ± 0.10 kJ/mol and ∆fH°0(HNC) = 192.00 ± 0.38 kJ/mol, and are significantly more accurate than the often quoted values found in Gurvich et al.35 (132.4 ± 4 kJ/mol at 0 K for HCN, 194 ± 9 kJ/mol at 0 K for HNC) or the JANAF Tables36 (135.5 ± 8.4 kJ/mol at 0 K for HCN, no value for HNC). As pointed out previously in the literature (see, for example, Bieri and Jonsson37), compared to the neutrals the stability of HCN+ and HNC+ cations is reversed: ∆fH°0(HNC+) = 1352.85 ± 1.14 kJ/mol and ∆fH°0(HCN+) = 1442.53 ± 0.20 kJ/mol. The corresponding adiabatic ionization energies fully reflect this fact: IE(HCN) = 13.607 ± 0.002 eV (in perfect agreement with one38 of the available photoelectron determinations) and IE(HNC) = 12.032 ± 0.012 eV (in fair agreement with the available estimate of 12.5 ± 0.2 eV obtained from charge-exchange reactions37). HCN- and HNC- are dipole bound negative ions, corresponding to extremely low adiabatic electron affinities EA(HCN) = 0.00157 ± 0.00005 eV (in excellent agreement with the spectroscopic study of Ard et al.39 and related theoretical studies40,41,42,43,44) and EA(HNC) = 0.0046 ± 0.0002 eV (in good agreement with theoretical studies41,42,43,44). Conclusion In this work, we have shown evidence that the previous estimate for the 0 K isomerization energy of HCN to HNC by van Mourik et al.3 is somewhat on the low side, as was recently suggested by Barber et al.,9 albeit only by a marginal amount. However, a careful analysis based on very high-level ab initio calculations coupled with the ATcT approach, indicates that the correction predicted by the very highlevel multireference configuration interaction calculations of Ref. 9 is too high by more than 450 cm−1, and perhaps as much as nearly 500 cm−1, a difference that far exceeds the ‘chemical accuracy’ threshold of 1 kcal/mol (350 cm−1). That is, the (single-reference) HEAT approach significantly outperforms multireference configuration interaction in this example. Perhaps the behavior exhibited here should serve as a warning to those that might choose to use multireference methods for problems that are 8 ACS Paragon Plus Environment

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decidedly single-reference in character. One should never lose sight of the fact that use of the former does not in any way always imply that superior results will be obtained, due to factors such as the lack of size-extensivity and what could be considered to be rather arbitrary methods for choosing extended active spaces. For problems like the isomerization of HCN, where very high-level correlation effects are small (see Table I), and significant cancellation of errors in the treatment of electron correlation can be anticipated by the very similar electronic structures of the species involved, a well-defined singlereference method like coupled-cluster theory (which is the method upon which all modern protocols for high-accuracy computational thermochemistry are based) is the preferred option. The

On the HCN â HNC Energy Difference - The Journal of Physical

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