Standard formation enthalpies of gas phase molecular complexes derived by taking into account the heat capacity difference of the gas phase dissociation processes: Experimental tensimetry data revisited

Journal Pre-proof Standard formation enthalpies of gas phase molecular complexes derived by taking into account the heat capacity difference of the gas phase dissociation processes: Experimental tensimetry data revisited E.I. Davydova, Yu.V. Kondrat’ev, A.S. Lisovenko, A.V. Pomogaeva, T.N. Sevastianova, A.Y. Timoshkin

PII:

S0040-6031(19)30970-0

DOI:

https://doi.org/10.1016/j.tca.2020.178571

Reference:

TCA 178571

To appear in:

Thermochimica Acta

Received Date:

31 October 2019

Revised Date:

22 February 2020

Accepted Date:

24 February 2020

Please cite this article as: Davydova EI, Kondrat’ev YV, Lisovenko AS, Pomogaeva AV, Sevastianova TN, Timoshkin AY, Standard formation enthalpies of gas phase molecular complexes derived by taking into account the heat capacity difference of the gas phase dissociation processes: Experimental tensimetry data revisited, Thermochimica Acta (2020), doi: https://doi.org/10.1016/j.tca.2020.178571

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Standard formation enthalpies of gas phase molecular complexes derived by taking into account the heat capacity difference of the gas phase dissociation processes: experimental tensimetry data revisited. E.I. Davydova, Yu.V. Kondrat’ev, A.S. Lisovenko, A.V. Pomogaeva, T.N. Sevastianova, A.Y. Timoshkin*

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Institute of Chemistry, Saint Petersburg State University, Universitetskaya emb. 7/9, 199034 St. Petersburg, Russia. Correspondence e-mail: [email protected]

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Highlights

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 Accounting for dispersion interactions is essential for the thermodynamics of gaseous donor-acceptor complexes.  Assessment methods for the heat capacity of gaseous complexes are evaluated.  Values of standard formation enthalpies for 26 gaseous molecular complexes are recommended

Abstract.

High temperature tensimetry data on homogeneous gas phase dissociation of donor-acceptor complexes of group 13-15 metal halides have been analyzed.

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Thermodynamic characteristics and heat capacities have been computed by DFT methods. Standard dissociation enthalpies and standard formation enthalpies of

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gaseous donor-acceptor complexes have been obtained by combination of experimental and computational data with accounting for the heat capacity

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change.

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Keywords: molecular complexes; gaseous metal halides; thermodynamics; heat

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capacity; tensimetry; DFT

1. Introduction

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Reliable gas phase thermochemical data are of great importance as a benchmark values for the testing of performance of quantum chemical methods and for the construction of solvent-independent acidity and basicity scales. Experimental tensimetry measurements of the vapor pressure - temperature dependence of molecular complexes AD in the unsaturated vapor provide equilibrium constants and their dependence on the temperature. On this basis, it is possible to derive the thermodynamic characteristics of processes of homogeneous gas phase dissociation of the complexes AD into acceptor (A) and donor (D) components (equation 1). AD(g) = A(g) + D(g) 2

(1)

Results of the experimental studies of inorganic and coordination compounds using the static tensimetric method are summarized in reviews [1,2]. As a rule, values of ΔdissH°T and ΔdissS°T, derived from tensimetry measurements, are assigned to the average temperature T of the measurement interval. However, for the reference data, such as thermodynamic databases (NIST [3] and TKV [4]), thermodynamic characteristics at standard temperature 298.15 K are more relevant. The conversion of experimental high temperature ΔdissH°T and ΔdissS°T values to the standard temperature is possible by taking into account the change of the heat capacity in the gaseous process ΔdissCpT. This requires data on the heat capacities of all participants in the reaction as well as their temperature dependence. In the case of relatively simple donor D (NH3,

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POCl3, pyridine) and acceptor A (main group element halides) molecules, these data are available in the literature or can be obtained experimentally. In the case of donor-acceptor complexes AD, the situation is complicated: polar complexes have lower volatility compared to components and vaporize at higher temperatures. For many complexes, the process of irreversible thermal destruction takes place at elevated temperatures, which makes

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experimental studies of heat capacities of gaseous complexes problematic. An alternative approach is to estimate the change in the heat capacity of the reaction. There are two ways to

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approach this task: calculation of the ΔdissCpT changes using assessment methods for the heat capacity estimations [5,6] or computation of heat capacity values using modern quantum

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chemical methods.

The current paper is aimed to compare the performance of different approaches in the obtaining of the standard ΔdissH°298 values from high temperature values for homogeneous gas

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phase dissociation processes of group 13-15 halide complexes, reported by static tensimetry method [1]. We choose the homogeneous gas phase dissociation processes reported in review [1] (Table S1) to evaluate a) the validity of chosen computational approach; b) the influence of

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the ΔdissCpT on the reported thermodynamic characteristics. On the basis of our analysis, values

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of standard formation enthalpies for 26 gas phase complexes are recommended.

2. Computational details.

All computations have been carried out using Gaussian 16 program package [7] on the HighPerformance Computing cluster of St. Petersburg State University. The geometries of the compounds have been fully optimized using three DFT methods: (i) hybrid three-parameter exchange functional of Becke [8] with the gradient corrected correlation functional of Lee, Yang, and Parr [9] (B3LYP); (ii) dispersion corrected DFT method (B3LYP-D3) [10]; (iii) 3

M06-2X method including high-nonlocality functional with double the amount of nonlocal exchange (2X) [11]. All electron def2-TZVP basic set [12] (with quasi-relativistic effective core potentials (ECP) for In, Ta, Hf, Sb, Sn, Nb, and Zr [13]) was used throughout. All structures correspond to minima on the respective potential energy surfaces (PES) as verified by subsequent vibrational analysis.

3. Results and discussion. 3.1. Evaluation of the performance of quantum chemical methods. Usually, when comparing performance of different computational methods, computed

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standard ΔH°298 and ΔS°298 values for the process of interest are compared with respective experimental values derived from thermochemical databases [3,4]. However, it should be noted, that values, derived from high temperature tensimetry experiments, are seldom corrected to the standard temperature, since the heat capacities of gaseous complexes are usually

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unknown. When such correction has been made, it is often based on the estimated heat capacity data (vide infra). From this point of view, it is desirable to compare experimental and computational ΔH°T and ΔS°T values at experimental temperature T.

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In addition, it should be noted, that tensimetry study does not provide the direct measurement of the gas phase dissociation enthalpies and entropies of the complex. The actual

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parameter, measured in the tensimetry experiment at a given temperature T, is the total vapor pressure, from which equilibrium partial pressures of the donor-acceptor complex PAD, Lewis acid PA and Lewis base PD are derived and the equilibrium constant KdissT for dissociation

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process (eq. 1) is calculated as KdissT=PAPD/PAD. Thus, from the tensimetry experiment, the standard Gibbs energy values ΔdissG°T at specific temperature T can be directly derived as ΔdissG°T = -RTlnKdissT. In contrast, values of ΔdissH°T and ΔdissS°T are indirectly derived from

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equilibrium constant – temperature dependence (equation 2 [14]) by performing tensimetry measurements at several temperatures and are usually attributed to the mean temperature T of

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the studied temperature range. Since studied temperature interval is usually narrow, the obtained values of ΔdissH°T and ΔdissS°T are determined with large uncertainty. lnKdissT = -ΔdissH°T/T + ΔdissS°T/R

(2)

Therefore, in order to compare performance of computational methods to reproduce high temperature tensimetry results, comparison of experimental and computational values of Gibbs energies of the complex dissociation ΔdissG°T appears to be a better choice than comparison of values of the dissociation enthalpies ΔdissH°T.

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Comparison of the performance of chosen computational methods for the homogeneous gas phase dissociation processes is presented in Table 1. Values at B3LYP/def2-TZVP level of theory are underestimated compared to the experimental data. Moreover, for weakly bound donor-acceptor complexes 14,16,21-26 (Table 1) geometry optimization at B3LYP/def2-TZVP level of theory results in only van der Waals bound fragments, which indicates instability of such complexes. In contrast, geometry optimization using M06-2X and B3LYP-D3 functionals, which include dispersion interaction term, leads to molecular complexes, featuring donor-acceptor bond. This indicates a crucial importance of taking into account the dispersion interaction. For the complexes with N-containing donors, ΔdissG°T are usually positive, which

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implies that equilibrium dissociation constant KdissT is less than 1 and partial pressure of AD is significant. For these strongly bound complexes, values at M06-2X/def2-TZVP level of theory are generally overestimated. For complexes 1-10, root mean square deviations (RMSD) of computed ΔdissG°T from experimental values are 6.8, 18.9, and 20.2 kJ mol-1 for B3LYPD3/def2-TZVP, M06-2X/def2-TZVP and B3LYP/def2-TZVP levels of theory, respectively.

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The best overall agreement with experiment is also observed for the values computed at B3LYP-D3/def2-TZVP level of theory (Table 1). Therefore, we choose B3LYP-D3/def2-

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TZVP level of theory for the subsequent computational studies. This level of theory also provides molar heat capacity Cp values for donor and acceptor species which are in excellent

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agreement with literature values (Table 2S, Supporting information). This good agreement allows us to assume that heat capacity values obtained for the donor-acceptor complexes will

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be also reliable.

3.2. Evaluation of the assessment methods for the heat capacity difference in the gas phase dissociation reaction of molecular complexes.

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The simplest way to estimate the heat capacity for the gas phase molecule is to use ideal gas approximation. For the nonlinear N-atomic molecule in the gas phase at high temperatures

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heat capacity can be estimated [15] as Cp = (3N-2)R

(3),

where R is the universal gas constant. From (3), for the process (1) of dissociation of gaseous complex into gaseous components the ΔdissСр equals -2R or -16.6 J·mol-1 K-1. However, approximation (3) represents only an upper limit to Cp, which is reached only at very high temperatures (for example, for SO2 molecule at 1800 K [15]). For lower temperatures, the heat capacities of gases are smaller than (3N-2)R since contribution of each vibrational degree of freedom at low temperatures is less than R. 5

Therefore, empirical estimations of ΔdissCp are often used instead. For example, for the homogeneous gas phase dissociation of ammonia complexes (compounds 1-6 in Table 1), Suvorov assumed ΔdissCp to be equal -8.4 J mol-1 K-1 [16]. Another approach is to estimate the unknown heat capacity of the molecular complex Cp(AD), and, combining it with literature heat capacities for components, obtain the heat capacity change in the reaction ΔdissCp. The Cp(AD) can be estimated in two different ways: a) using the equation (3), b) using the additivity scheme [6,17,18] as a sum of heat capacities of components without taking into account of changes in vibrations associated with the formation of a donor-acceptor

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bond. DFT computed values and estimated values of the Cp of the complexes AlCl3·NH3 and AlCl3·POCl3 are presented in Table 2, together with Cp values for their dissociation products. There is a good agreement between DFT calculated and experimental Cp values for ammonia, AlCl3 and POCl3. The comparison shows that none of the assessment approaches provides

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reasonable results for ΔdissCp. In case of approach (a) estimated value of ΔdissCp is positive, which will lead to a decrease in ΔdissHo298 of the process compared to ΔdissHoT. In approach (b)

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ΔdissCp = 0 and the temperature contribution of the heat capacity is 0.

Analysis of the different assessment approaches for the estimation of heat capacity

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difference indicates that data obtained are contradictory. Another drawback of the assessment approaches is that the estimated value of ΔdissCp is temperature independent. Therefore, we conclude that assessment methods are unsuitable for the estimation of ΔdissCp.

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Instead of the assessment methods, the following approach is proposed for the computation of ΔdissCpT at a given temperature T.

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3.3 Computation of ΔdissCpT using temperature dependence of heat capacity. The temperature dependence of the heat capacity of gas phase compound can be

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described by the Maier&Kelley equation: СpT = a + bT – cT-2

(4)

The coefficients a, b, c in the equation 4 are available [19] for all donor and acceptor compounds studied in the present work (Table 3S). Most values were obtained from calculations of the heat capacity of the gas in the model of a rigid rotator-harmonic oscillator. As the authors [19] indicate, in the temperature range 298–2000 K, the error in the used approach is about 1%. B3LYP-D3/def2-TZVP level of theory provides Cp values for donor and acceptor species which are in excellent agreement with literature values. The RMSD of the 6

DFT computed values against the values obtained by the processing of the experimental data is 0.7 J mol-1 K-1 at B3LYP-D3/def2-TZVP level of theory. For temperatures other than standard temperature, values for donor and acceptor compounds CpT(D) and CpT(A), obtained by quantum chemical computations and via the experimental data processing according to [19] are given in Table 4S. The choice of specific temperatures is due to the values of the temperature in the experimental tensimetry studies (see Table 1S for temperature ranges). Changes in heat capacity for the dissociation reactions, computed at B3LYP-D3/def2TZVP level of theory, are summarized in Table 3. At elevated (700 and 1000 K) temperatures,

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values of ∆dissCpT are approaching the estimated values of -2R (-16.6 J mol-1 K-1) derived from the estimation of the heat capacities of gaseous compounds on the basis of equation (3). However, for complexes with ammonia, the ∆dissCpT converge to -2R at much larger temperature, than for complexes with POCl3 (see Figure 1S,f in the supplementary information). This observation supports our conclusion that estimated by assessment methods

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∆dissCp are not reliable.

The coefficients of the Maier&Kelley equation obtained by fitting of DFT calculated

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Cp(AD) values to the equation (4) for studied complexes AD are given in the supporting information (Table 5S). Using data provided in Tables 3S and 5S, CpT values for all studied

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compounds and ∆dissCpT can be computed at any chosen temperature T.

3.4. Recount of the gas phase reaction enthalpy to the standard temperature.

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Now, with the established procedure to calculate ∆dissCpT, we may proceed to the recount of high temperature experimental ∆dissH°T values to the standard temperature 298.15 K. Table 4 summarizes four different ways for the recount. First of all, values ∆dissH°T-

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∆dissH°298 can be obtained by quantum chemical computations. Second, taking DFT computed values of heat capacity changes either at standard temperature ∆dissCp298 or at experimental

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temperature ∆dissCpT the Kirchhoff equation can be used: ∆dissH°T - ∆dissH°298 = ∆dissCp298·(T-298.15)

(5)

∆dissH°T - ∆dissH°298 = ∆dissCpT·(T-298.15)

(6)

At last, using fitting parameters provided in Tables 3S and 5S, the equation (7) can be used: 𝑇

∆diss H°T − ∆diss H°298 = ∫298 ∆diss 𝐶𝑝 (T)dT

(7)

Data in Table 4 indicate that the use of equations (6) and (7) provides similar results, which are in better agreement with ∆dissH°T-∆dissH°298 values than values derived according to the 7

equation (5). The use of ∆dissCp298 values at standard temperature underestimates the value of temperature correction. In the following, the correction to the standard temperature was made using the equation (7), taking into account temperature dependence of ∆dissCpT.

3.5 Standard dissociation enthalpies and standard formation enthalpies of gaseous molecular complexes. Before recounting the enthalpy values for the dissociation process (1) ∆dissH°T to the standard temperature, it should be noted, that these ∆dissH°T values can be derived from the experimental tensimetry data in two ways. The first way is to measure equilibrium constants

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KdissT at different temperatures and derive dissociation enthalpy value from the lnKdissT – 1/T dependence (equation 2). This approach was used in experimental works reviewed in [1] and the data obtained by such a treatment (so called by the II law) are summarized in Table 7S. However, this approach has several drawbacks. First, experimentally derived values of KdissT are sensitive to the accuracy of determination of equilibrium vapor pressures. If the partial

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pressure of the complex PAD is small (dissociation process is almost completely finished) or the partial pressure of one of the dissociation products, PA or PD, is small (dissociation of the

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complex is just started or it is suppressed by the large excess of the second dissociation product) the values of KdissT, derived from vapor pressure measurements, may have large experimental

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errors. The change of the vapor pressure of the dissociation products of ±1 torr may lead to the error in KdissT of more than one order of magnitude if one (or more) partial pressures are about 1 torr. Second, measurements of KdissT are usually performed in the narrow temperature

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range, which increases uncertainty in ∆dissH°T value, derived by the II law. For example, for the complex GaCl3·pyz·GaCl3 the inaccuracy of ±0.2 mg in weighing of the sample results in an error in the dissociation enthalpy of of ±6-8 kJ mol-1, obtained by the II law [20].

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Therefore, in the present report we used alterative approach to derive dissociation enthalpies ∆dissH°T from the experimental tensimetry values. At a given temperature, from the

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experimental value of the KdissT the Gibbs energy change can be derived as ΔdissG°T = RTlnKdissT. On the other hand, using equation ∆dissG°T = ∆dissH°T - T∆dissS°T, we obtain ∆dissH°T = -RTlnKdissT + T∆dissS°T

(8)

Thus, using the experimental value of the equilibrium constant KdissT at temperature T

and computational value for the gas phase reaction entropy ∆dissS°T, the reaction enthalpy ∆dissH°T can be calculated by equation (8) at any experimental temperature. This approach is called calculation by the III law. For the complexes, for which original experimental

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equilibrium constants were available, we computed dissociation enthalpies by the III law (Table 8S) and recounted them to the standard temperature using equation (7). Comparison of the obtained standard dissociation enthalpies ∆dissH°298 is presented in Table 5. For complexes 1, 5, 11, 12, 14, 15, 21 values obtained by II and III law are within experimental errors, which indicates consistency of the experimental and computational data. For several complexes the difference in standard reaction enthalpies calculated by II and III law is rather large, for example it approaches 40 kJ mol-1 in case of complex 4. Note that values of standard gas phase dissociation enthalpies of aluminum and gallium halides with ammonia derived by the III law are monotonically decrease in order AlCl3>AlBr3>GaCl3>GaBr3 in qualitative agreement with trend found in early computational

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study [21]. In contrast, values of ΔdissH°298 of these complexes derived by the II law are equal within experimental errors (Table 5). In our opinion, values derived by III law are more reliable, and therefore we used these values to calculate standard formation enthalpies for the studied gaseous complexes AD using available thermodynamic data for gaseous donor and acceptor

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compounds [3,4]. Recommended values of the standard formation enthalpies of 26 gaseous

at B3LYP-D3/def2-TZVP level of theory.

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4. Conclusions.

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molecular complexes are summarized in Table 6, together with standard entropies, computed

Performance of three computational DFT approaches to describe thermodynamics of gas phase dissociation of molecular complexes AD has been tested with respect to the values

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derived from high temperature gas phase tensimetry data. For the strongly bound complexes, B3LYP-D3/def2-TZVP level of theory provides better agreement with experimental ΔdissG°T values with RSMD of 7 kJ mol-1, which indicates importance of the accounting for the

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dispersion interactions for the thermodynamics of molecular complexes. Analysis of the assessment methods for the estimation of heat capacity of molecular complexes reveals that

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estimation approaches are not satisfactory. It is recommended to use CpT(AD) values obtained from quantum chemical computations. Dissociation enthalpies of gaseous complexes AD ΔdissHºT were derived from the

experimental equilibrium constants KdissT using values of ΔdissSºT computed at B3LYPD3/def2-TZVP level of theory. These values were recounted to standard temperature 298.15 K using temperature - dependent ΔdissCpT values. Using obtained ΔdissHº298 and literature standard formation enthalpies of components, new values of standard formation enthalpies for 26 gaseous molecular complexes are recommended. 9

E.I. Davydova Data curation, methodology, treatment of experimental tensimetry data Yu.V. Kondrat’ev heat capacity assessment methods A.S. Lisovenko Methodology, quantum chemical computations A.V. Pomogaeva Methodology, quantum chemical computations T.N. Sevastianova Data curation, tensimetry methodology A.Y. Timoshkin Conceptualization, Supervision, Writing - original draft and revised version

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Authors declare no conflict of interests. Acknowledgements

This work was supported by RSF grant 18-13-00196. We thank Scientific park SPSU, Resource

References

E.I. Davydova, T.N. Sevastianova, A.V. Suvorov, A.Y. Timoshkin, Molecular complexes

re

[1]

-p

Center Computer Center for the computational time.

formed by halides of group 4,5,13–15 elements and the thermodynamic characteristics of

lP

their vaporization and dissociation found by the static tensimetric method, Coord. Chem. Rev. 254 (2010) 2031–2077, http://dx.doi.org/10.1016/j.ccr.2010.04.001. [2]

E.I. Davydova, D.A. Doinikov, I.V. Kazakov, I.S. Krasnova, T.N. Sevast’yanova, A.V.

na

Suvorov, A.Y. Timoshkin, Study of Inorganic and Coordination Compounds by the Static Tensimetric Method from Mendeleev to the Present Day, Russ. J. Gen. Chem. 89

[3]

ur

(2019) 1069-1084, https://doi.org/10.1134/S1070363219060021. NIST Standard Reference Database Number 69, Eds. P. J. Linstrom, W. G. Mallard.

Jo

Internet: https://webbook.nist.gov/chemistry. [4]

Database Thermal Constants of Substances (Termicheskie Konstanty Vezschestv), Eds. V.S.

Iorish,

V.S.

Jungman.

Internet:

http://www.chem.msu.su/cgi-

bin/tkv.pl?show=welcome.html

[5]

I.B. Rabinovich, V.P. Nistratov, V.I. Telnoy, M.S. Sheiman, Thermodynamics of Organometallic Compounds, Nizhny Novgorod, Nizhny Novgorod University Press, 1996. 227 p.

10

[6]

V.A. Kireev, Methods of Practical Calculations in the Thermodynamics of Chemical Reactions (Metody Prakticheskikh Raschetov v Termodinamike Khimicheskikh Reaktsii), Moscow, Khimiya, 1970, 519 p.

[7]

M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, G.A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A.V. Marenich, J. Bloino, B.G. Janesko, R. Gomperts, B. Mennucci, H.P. Hratchian, J.V. Ortiz, A.F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V.G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M.

ro of

Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M.J. Bearpark, J.J. Heyd, E.N. Brothers, K.N. Kudin, V.N. Staroverov, T.A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A.P. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, J.M. Millam, M. Klene, C. Adamo, R. Cammi, J.W. Ochterski, R.L. Martin, K. Morokuma, O. Farkas, J.B.

[8]

-p

Foresman, D.J. Fox, Gaussian 16, Revision A.03, Gaussian, Inc., Wallingford, CT, 2016. A.D. Becke, A new mixing of Hartree-Fock and local-density-functional theories, J.

[9]

re

Chem. Phys. 98 (1993) 1372-1377, https://dx.doi.org/10.1063/1.464304. C. Lee, W. Yang, R.G. Parr, Development of the Colle-Salvetti correlation-energy

lP

formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785-789, https://dx.doi.org /10.1103/PhysRevB.37.785. [10] S. Grimme, S. Ehrlich, L. Goerigk, Effect of the damping function in dispersion

na

corrected density functional theory, J. Comput. Chem. 32 (2011) 1456-1465, https://dx.doi.org/10.1002/jcc.21759. [11] Y. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group

ur

thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class

Jo

functionals and 12 other functionals, Theor. Chem. Acc. 120 (2008) 215-241, https://dx.doi.org/10.1007/s00214-007-0310-x.

[12] F. Weigend, R. Ahlrichs, Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy, Phys. Chem. Chem. Phys. 7 (2005) 3297-3305, https://dx.doi.org/10.1039/b508541a. [13] T. Leininger, A. Nicklass, W. Kuechle, H. Stoll, M. Dolg, A. Bergner, The accuracy of the pseudopotential approximation: non-frozen-core effects for spectroscopic constants

11

of alkali fluorides XF (X = K, Rb, Cs), Chem. Phys. Lett. 255 (1996) 274-280, https://dx.doi.org/10.1016/0009-2614(96)00382-X. [14] P. Atkins, Julio de Paula, Physical Chemistry. Oxford University Press. 8th Ed. 2006. 1065 p. [15] P. Richet, The Physical Basis of Thermodynamics: With Applications to Chemistry, 2001, Springer Science+Business Media, New York, p. 70. [16] A.V. Suvorov, Chemistry of the Inorganic Molecular Complexes in the Gas Phase, Doctor of Science Thesis, Leningrad, 1977. [17] Kh.M. Kadiev, A.M. Gyul'maliev, N.A. Kubrin, An additive method for calculating the

https://dx.doi.org/ 10.1134/S0965544116090073.

ro of

thermodynamic functions of heavy feedstock, Petroleum Chemistry 56 (2016) 805-811,

[18] O.V. Dorofeeva, Development and application of methods for calculating the thermodynamic properties of gaseous compounds, Doctor of Science Thesis, Moscow, 2008.

-p

[19] A.G. Morachevskii, I.B. Sladkov, Physicochemical Properties of Molecular Inorganic Compounds: Experimental Data and Calculation Methods (Fiziko-Khimicheskie

re

Svoistva Molekulyarnykh Neorganicheskikh Soedinenii: Eksperimenlal'nye Dannye i Metody Rascheta), St. Petersburg, Khimiya, 1996, 312 p.

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[20] A.Y. Timoshkin, E.A. Berezovskaya, A.V. Suvorov, A.D. Misharev, Thermodynamic Characteristics of Gaseous GaCl3pyz and GaCl3pyzGaCl3 Complexes, Russ. J. Gen. Chem. 75 (2005) 1173-1179, https://doi.org/10.1007/s11176-005-0391-y.

na

[21] A.Y. Timoshkin, A.V. Suvorov, H.F. Bettinger, H.F. Schaefer, Role of the Terminal Atoms in the Donor−Acceptor Complexes MX3−D (M = Al, Ga, In; X = F, Cl, Br, I; D = YH3, YX3, X-; Y = N, P, As), J. Am. Chem. Soc. 121 (1999) 5687-5699,

Jo

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https://doi.org/10.1021/ja983408t

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Table 1. Comparison of experimental (tensimetry) and computed at different levels of theory Gibbs energies ΔdissG°T (kJ mol-1) for the gas phase dissociation processes (eq. 1) at high temperatures. № Complex (AD)

Tensimetry

M06-2X/def2B3LYPTZVP D3/def2-TZVP 1 AlCl3·NH3 739 48.3 66.6 53.1 2 AlBr3·NH3 744 38.5 61.7 48.8 3 GaCl3·NH3 723 31.7 50.7 33.6 4 GaBr3·NH3 729 22.1 49.3 36.3 5 InCl3·NH3 763 22.6 39.2 22.0 6 InBr3·NH3 781 13.6 28.2 13.2 7 AlI3·Py 709 52.5 62.7 49.5 8 GaI3·Py 675 27.5 44.0 28.2 9 GaCl3·pyz 625 40.7 50.2 35.5 10 GaCl3·pyz·GaCl3 667 3.9 21.1 -2.4 11 AlCl3·POCl3 725 26.2 30.0 17.3 12 GaCl3·POCl3 668 2.3 7.4 -8.4 13 FeCl3·POCl3 697 39.8 -3.7 -18.9 14 GeBr4·POCl3 480 -12.9 -41.7 -39.0 15 TiBr4·POCl3 552 -13.2 -40.3 -46.2 16 ZrCl4·POCl3 666 -6.6 -17.6 -26.2 17 HfCl4·POCl3 693 -13.9 -18.1 -36.1 18 SbCl5·POCl3 462 -6.5 -4.1 -15.3 19 NbCl5·POCl3 611 -7.8 -16.3 -25.1 20 TaCl5·POCl3 609 -8.0 -13.1 -25.1 21 SnBr4·POBr3 510 -17.8 -31.5 -42.3 22 ZrBr4·POBr3 648 -0.8 -11.3 -21.3 23 FeCl3·PCl5 799 -27.7 -41.4 -27.0 24 AlBr3·PBr3 516 -1.9 -46.3 -38.2 25 GaCl3·SbCl3 506 -1.3 -41.6 -33.4 26 AlBr3·SbBr3 573 -2.0 -63.5 -54.3 RMSD 28.0 26.6 *Optimization of the complex did not converge.

B3LYP/def2TZVP 39.6 33.7 22.7 8.2 10.9 -3.3 25.3 -0.5 14.9 -22.4 9.8 -15.8 -65.4 -* -26.5 -* -37.0 -47.3 -56.8 -57.9 -* -* -* -* -* -* 35.4

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Table 2. Heat capacities (J mol-1 K-1) of acceptor CpT(A), donor CpT(D), and complex CpT(AD) molecules and heat capacity change in the complex dissociation reaction ΔdissCpT, estimated by approaches (a) and (b) (see text for details) and computed at B3LYP-D3/def2-TZVP level of theory. ΔdissCpT +24.5(a) 0 (b) -3.9 +45.9(a) 0 (b) -13.2 +60.9(a) 0 (b) -13.7 +86.8(a) 0 (b) -16.3

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Method Estimation B3LYP-D3/def2-TZVP Estimation B3LYP-D3/def2-TZVP Estimation

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T CpT(A) CpT(D) CpT(AD) 298.15 72.0±1.3 35.6±0.1 83.1(a) 107.6(b) 298.15 71.6 35.1 110.6 739 80.9 48.1 83.1(a) 129.0(b) 739 80.7 47.9 141.8 AlCl3·POCl3(g) 298.15 72.0±1.3 84.5±0.4 95.6(a) 156.5(b) 298.15 71. 6 85.0 170.2 724 80.8 101. 6 95.6(a) 182.4(b) 724 80.6 101. 5 198.4

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B3LYP-D3/def2-TZVP Estimation B3LYP-D3/def2-TZVP

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Table 3. Heat capacity change ∆dissCpT, J mol-1 K-1, calculated at B3LYP-D3/def2-TZVP level of theory for the dissociation reactions at different temperatures. № Reaction 298.15 K 500 K 700 K 1000 K 1 AlCl3·NH3 = AlCl3 + NH3 -3.9 -10.1 -12.8 -14.7 2 AlBr3·NH3 = AlBr3 + NH3 -3.7 -9.9 -12.7 -14.7 3 GaCl3·NH3 = GaCl3 + NH3 -5.2 -10.9 -13.3 -15.0 4 GaBr3·NH3 = GaBr3 + NH3 -5.0 -10.7 -13.2 -14.9 5 InCl3·NH3 = InCl3 + NH3 -7.0 -11.9 -13.9 -15.3 6 InBr3·NH3 = InBr3 + NH3 -6.9 -11.9 -14.0 -15.3 7 AlI3·Py = AlI3 + Py -13.3 -14.5 -15.0 -15.5 8 GaI3·Py = GaI3 + Py -13.9 -14.8 -15.2 -15.6 9 GaCl3·pyz = GaCl3 + pyz -14.1 -15.1 -15.5 -15.8 10 GaCl3·pyz·GaCl3 = GaCl3·pyz + GaCl3 -14.3 -15.2 -15.6 -16.0 11 AlCl3·POCl3 = AlCl3 +POCl3 -13.5 -15.7 -16.3 -16.5 12 GaCl3·POCl3 = GaCl3 +POCl3 -14.6 -16.1 -16.5 -16.6 -15.1 -16.3 -16.6 -16.7 13 FeCl3·POCl3 = FeCl3 + POCl3 -16.4 -16.6 -16.6 -16.6 14 GeBr4·POCl3 = GeBr4 + POCl3 -15.8 -16.5 -16.6 -16.7 15 TiBr4·POCl3 = TiBr4 + POCl3 -15.2 -16.2 -16.5 -16.6 16 ZrCl4·POCl3 = ZrCl4 + POCl3 -15.1 -16.2 -16.5 -16.6 17 HfCl4·POCl3 = HfCl4 + POCl3 -15.0 -16.2 -16.6 -16.7 18 SbCl5·POCl3 = SbCl5 + POCl3 -15.2 -16.3 -16.5 -16.6 19 NbCl5·POCl3 = NbCl5 + POCl3 -14.9 -16.1 -16.5 -16.6 20 TaCl5·POCl3 = TaCl5 + POCl3 -16.2 -16.5 -16.6 -16.6 21 SnBr4·POBr3 = SnBr4 + POBr3 -15.5 -16.0 -16.4 -16.6 22 ZrBr4·POBr3 = ZrBr4 + POBr3 -17.8 -19.6 -20.2 -20.5 23 FeCl3·PCl5 = ½Fe2Cl6 + PCl3 + Cl2 -6.7 -7.6 -7.9 -8.1 24 AlBr3·PBr3 = ½Al2Br6 + PBr3 GaCl ·SbCl = GaCl + SbCl -16.5 -16.6 -16.6 -16.6 25 3 3 3 3 -8.3 -8.2 -8.3 -8.3 26 AlBr3·SbBr3 = ½Al2Br6 + SbBr3

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Table 4. Temperature correction ∆dissH°T-∆dissH°298 (in kJ mol-1) to the enthalpy of gas phase dissociation reactions at B3LYP-D3/def2-TZVP level of theory and using approaches (5),(6),(7), see text for details. Reaction T, K ∆dissH°T-∆dissH°298 (5) (6) (7) AlCl3·NH3 = AlCl3 + NH3 739 -4.33 -5.45 -1.72 -5.81 AlBr3·NH3 = AlBr3 + NH3 744 -4.32 -5.57 -1.64 -5.86 GaCl3·NH3 = GaCl3 + NH3 728 -4.54 -5.50 -2.24 -5.82 GaBr3·NH3 = GaBr3 + NH3 729 -4.47 -5.50 -2.14 -5.80 InCl3·NH3 = InCl3 + NH3 763 -5.49 -6.17 -3.24 -6.66 InBr3·NH3 = InBr3 + NH3 759 -5.43 -6.24 -3.20 -6.60 AlI3·Py = AlI3 + Py 709 -5.90 -6.33 -5.45 -6.18 GaI3·Py = GaI3 + Py 675 -5.53 -5.70 -5.26 -5.72 GaCl3·pyz = GaCl3 + pyz 625 -4.85 -5.24 -4.60 -5.00 GaCl3·pyz·GaCl3 = GaCl3·pyz + GaCl3 667 -5.47 -5.70 -5.28 -5.70 AlCl3·POCl3 = AlCl3 +POCl3 724 -6.60 -6.31 -5.77 -6.95 GaCl3·POCl3 = GaCl3 +POCl3 668 -5.87 -5.98 -5.40 -6.08 FeCl3·POCl3 = FeCl3 + POCl3 691 -6.33 -5.92 -6.51 -5.65 GeBr4·POCl3 = GeBr4 + POCl3 486 -3.10 -3.08 -3.11 -3.65 TiBr4·POCl3 = TiBr4 + POCl3 551 -4.12 -4.01 -4.18 -4.62 ZrCl4·POCl3 = ZrCl4 + POCl3 670 -5.98 -5.65 -6.14 -5.66 HfCl4·POCl3 = HfCl4 + POCl3 693 -6.34 -5.96 -6.51 -5.85 SbCl5·POCl3 = SbCl5 + POCl3 462 -2.56 -2.45 -2.64 -2.55 NbCl5·POCl3 = NbCl5 + POCl3 609 -4.98 -4.73 -5.11 -5.08 TaCl5·POCl3 = TaCl5 + POCl3 609 -4.94 -4.65 -5.10 -4.92 SnBr4·POBr3 = SnBr4 + POBr3 512 -3.51 -3.46 -3.54 -3.74 ZrBr4·POBr3 = ZrBr4 + POBr3 648 -5.69 -5.42 -5.80 -5.36 FeCl3·PCl5 = ½Fe2Cl6 + PCl3 + Cl2 824 -10.33 -9.38 -10.70 -11.05 AlBr3·PBr3 = ½Al2Br6 + PBr3 516 -1.58 -1.46 -1.66 -1.69 GaCl3·SbCl3 = GaCl3 + SbCl3 506 -3.44 -3.44 -3.45 -3.48 AlBr3·SbBr3 = ½Al2Br6 + SbBr3 573 -2.27 -2.28 -2.27 -2.28

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Table 5. Standard gas phase dissociation enthalpies ΔdissH°298, kJ mol-1 for the gaseous complexes derived from experimental values by II law and by III law. III law 147.0±0.9 138.4±0.4 122.7±1.0 103.6±0.9 115.2±1.8 108.2±2.7

119.9±1.1 93.1±6.7 140.4±1.8 44.0±1.1 64.5±0.9 86.8±1.6 91.3±0.9 67.7±5.5 82.0±3.1 95.9±2.1 55.2±1.1

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II law 142.7± 3.8 149.5± 4.6 139.8± 0.8 142.7±0.8 118.3± 5.4 120.4± 6.3 162.3± 7 129.7± 5 129.4± 2.8 104.1± 3.3 125.1± 3.3 96.0± 1.3 124.9± 2.5 46.8± 6.3 61.1± 2.1 108.2± 4.2 97.1± 3.8 52.6 a 70.0± 3.8 75.9± 4 57.3± 6.3 91.4 a 187.1± 59 38.5± 6.3 67.5± 3 36.6± 6.3

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№ Process 1 AlCl3·NH3 = AlCl3 + NH3 2 AlBr3·NH3 = AlBr3 + NH3 3 GaCl3·NH3 = GaCl3 + NH3 4 GaBr3·NH3 = GaBr3 + NH3 5 InCl3·NH3 = InCl3 + NH3 6 InBr3·NH3 = InBr3 + NH3 7 AlI3·Py = AlI3 + Py 8 GaI3·Py = GaI3 + Py 9 GaCl3·pyz = GaCl3 + pyz 10 GaCl3·pyz·GaCl3 = GaCl3·pyz + pyz 11 AlCl3·POCl3 = AlCl3 +POCl 12 GaCl3·POCl3 = GaCl3 +POCl3 13 FeCl3·POCl3 = FeCl3 + POCl3 14 GeBr4·POCl3 = GeBr4 + POCl3 15 TiBr4·POCl3 = TiBr4 + POCl3 16 ZrCl4·POCl3 = ZrCl4 + POCl3 17 HfCl4·POCl3 = HfCl4 + POCl3 18 SbCl5·POCl3 = SbCl5 + POCl3 19 NbCl5·POCl3 = NbCl5 + POCl3 20 TaCl5·POCl3 = TaCl5 + POCl3 21 SnBr4·POBr3 = SnBr4 + POBr3 22 ZrBr4·POBr3 = ZrBr4 + POBr3 23 FeCl3·PCl5 = ½Fe2Cl6 + PCl3 + Cl2 24 AlBr3·PBr3 = ½Al2Br6 + PBr3 25 GaCl3·SbCl3 = GaCl3 + SbCl3 26 AlBr3·SbBr3 = ½Al2Br6 + SbBr3 a) Estimated value.

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117.8±7.3

Table 6. Recommended values for the standard formation enthalpies ΔfH°298, kJ mol-1 derived from the experimental tensimetry data, and standard entropies S°298 J mol-1 K-1 (B3LYPD3/def2-TZVP level of theory) for the gaseous donor-acceptor complexes AD.

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Compound ΔfH°298 S°298 AlCl3·NH3 (g) -778.5±3.7 372.7 AlCl3·POCl3 (g) -1263.9±5.7 503.8 AlBr3·NH3 (g) -594.6±3.2 405.9 a AlBr3·PBr3 (g) -641.5±9.8 551.9 AlBr3·SbBr3 (g) -688.1±10.3a 622.4 a AlI3·Py (g) -174.6±16.9 508.2 FeCl3·POCl3 (g) -951.9±8.1 541.3 FeCl3·PCl5 (g) -724.7±10.7 621.1 GaCl3·NH3 (g) -613.2±5.5 390.9 GaCl3·POCl3 (g) -1097.3±7.3 518.7 GaCl3·pyz (g) -433.1±8.5a 466.2 GaCl3·pyz·GaCl3 (g) -981.3±9.0 648.3 a GaCl3·SbCl3 (g) -823.8±8.4 588.0 GaBr3·NH3 (g) -443.9±2.5 445.0 a GaI3·Py (g) -78.4±10.7 529.1 GeBr4·POCl3 (g) -902.6±5.7 619.7 HfCl4·POCl3 (g) -1531.8±5.4 574.0 InCl3·NH3 (g) -537.8±11.2 411.5 InBr3·NH3 (g) -422.6±12.7 445.8 NbCl5·POCl3 (g) -1434.8±7.5 581.2 SbCl5·POCl3 (g) -1016.3±10.1 585.3 SnBr4·POBr3 (g) -794.1±8.5 666.0 TaCl5·POCl3 (g) -1418.3±6.0 585.9 TiBr4·POCl3 (g) -1176.3±6.8 598.6 ZrCl4·POCl3 (g) -1516.0±5.2 567.6 b ZrBr4·POBr3 (g) -1127±14 649.4 a) Using dissociation enthalpies derived by the II law. b) Estimated value.

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