Thermochemistry of organometallic compounds: Structure-property relationships in alkylferrocenes

Journal Pre-proofs Research paper Thermochemistry of organometallic compounds: structure-property relationships in alkylferrocenes Sergey P. Verevkin, Vladimir N. Emel´yanenko, Kseniya V. Zherikova, Ludmila N. Zelenina, Dzmitry H. Zaitsau, Andrey A. Pimerzin PII: DOI: Reference:

S0009-2614(19)30892-9 https://doi.org/10.1016/j.cplett.2019.136911 CPLETT 136911

To appear in:

Chemical Physics Letters

Received Date: Revised Date: Accepted Date:

6 October 2019 28 October 2019 29 October 2019

Please cite this article as: S.P. Verevkin, V.N. Emel´yanenko, K.V. Zherikova, L.N. Zelenina, D.H. Zaitsau, A.A. Pimerzin, Thermochemistry of organometallic compounds: structure-property relationships in alkylferrocenes, Chemical Physics Letters (2019), doi: https://doi.org/10.1016/j.cplett.2019.136911

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© 2019 Published by Elsevier B.V.

Chem. Phys. Lett., 2019

Thermochemistry

of

organometallic

compounds:

structure-property

relationships in alkylferrocenes Sergey P. Verevkin,a,b,* Vladimir N. Emel´yanenko,b Kseniya V. Zherikova,c Ludmila N. Zelenina,c Dzmitry H. Zaitsau,a Andrey A. Pimerzinb a Department

of Physical Chemistry and Department of „Science and Technology of Life, Light and Matter“, University of Rostock, 18059, Rostock, Germany b Chemical Technological Department, Samara State Technical University, Samara 443100, Russia cNikolaev Institute of Inorganic Chemistry of Siberian Branch of Russian Academy of Sciences, 630090 Novosibirsk, Russia

ABSTRACT

The standard molar enthalpies of vaporization of ethylferrocene n-butylferrocene, and 1,1`dimethylferrocene have been determined from the temperature dependence of vapor pressures measured by the transpiration method. Vapor pressures and vaporization enthalpy of the nbutylferrocene were also measured by the static method. The internal consistency of thermodynamic data on vaporization and formation enthalpies of alkyl-substituted ferrocenes has been proved by using structure-property analysis and quantum-chemical calculations. The simple procedures were developed for calculation enthalpies of vaporization and enthalpies of formation of alkyl substituted ferrocenes based on the reliable data for alkylsubstituted benzenes. Parameters of these procedures are expected to be transferable for prediction of thermodynamic properties of organometallic compounds.

Keywords: ferrocene derivatives; vapor pressure; enthalpy of vaporization; enthalpy of formation; quantum-chemical calculations

a To

whom correspondence should be addressed, e-mail: [email protected] (S.P.

Verevkin). Phone: +49-381-498-6508. FAX: +49-381-498-6502

2

1.

Introduction An increased need for energy storage technologies, because of the deployment of

intermittent renewable energy sources, has generated a broad interest in hydrogen as a form of chemical energy storage, which may be used in internal combustion engines or fuel cells. Liquid organic hydrogen carriers (LOHCs) can be considered as one of the most attractive hydrogen storage media since they can be safely transported and distributed using the existing liquid fuel infrastructure [1]. Effective catalytic hydrogenation and dehydrogenation reactions are extremely important in LOHC technologies. The substitution of expensive and potentially toxic noble-metal catalysts by cheap, abundant, environmentally benign, and less toxic iron is highly desirable and in line with green chemistry guidelines [2,3]. Iron complexes serve as efficient catalysts for hydrogenation and dehydrogenation of aromatic compounds under remarkably mild conditions [2]. In addition, the light-driven iron-based catalytic system for hydrogen generation from formic acid was reported recently [3]. Organometallic complexes of noble metals have already been shown to act as homogeneous catalysts for reversible dehydrogenation [4]. However, due to limited availability and high cost of noble metals, and sometimes sensitivity and toxicity of their complexes, there is an increasing interest to substitute such catalysts by earth-abundant metals. Ferrocenes are expected to be one of the most promising complexes in homogeneous catalysis with respect to their availability, low toxicity, and price [5–8]. However, applications of ferrocenes are not restricted with catalysis. Ferrocenes are also used as antiknock agents in the petroleum industry, in synthetic chemistry (ligand scaffolds, pharmaceuticals), as reversible electrodes for cyclic voltammetric measurements (internal redox standards), and reference material for calibration of vapor pressure measuring equipment [9]. Substituted ferrocenes are used as precursors for manufacturing magnetoelectric and magnetic materials by metal-organic chemical vapor deposition [10–13]. Such a broad niche of the ferrocenes applications is due to their physical and chemical properties: a high thermal stability and vapor pressure unusually high for the organometallic compound, low toxicity, good solubility in organic solvents and, most importantly, a high chemical reactivity. Admittedly, substitution on cyclopentadienyl ring leads to a significant changing of physical-chemical properties of the complexes. For example, melting points of the unsubstituted metallocenes are above 433 K (447 K in case of ferrocene [14]), while the introduction of methyl into cyclopentadienyl rings lowers that more than 100 K (312 K in case of methylferrocene [15]), and most of the ethyl-substituted metal cyclopentadienyls are already liquids (274 K in case of ethylferrocene [16]). Moreover, the methyl- or ethylcyclopentadienyl

3

metal compounds exhibit significantly higher vapor pressures in comparison to the unsubstituted metallocenes. From this viewpoint, the substituted derivatives of ferrocene, can be considered as suitable model compounds to study structure-property relationships arising by variation of substitution of the cyclopentadienyl ligand. Nowadays, structure-property relationships in organic compounds are well established and they can be predicted by empirical methods successfully [17]. In contrast, experimental thermochemical data on organometallic are rare and they are very often of questionable quality. Combination of experimental thermochemical methods with quantum chemical calculations becomes a valuable tool for validation of available experimental data [18-19]. In focus of the current study are thermodynamic properties of alkylferrocenes. This paper extends our previous studies on the ferrocene derivatives [20–22] and deals with evaluation of thermochemical properties of a series of alkyl substituted ferrocenes based on the complementary measurements of saturated vapor pressures of ethylferrocene, n-butylferrocene, and 1,1´-dimethylferrocene combined with high-level quantum-chemical calculations.

2. Experimental 2.1 Materials Samples of ethyl- and n-butylferrocenes were of commercial origin (see Table S1). They were additionally purified by a fractional distillation. The commercial sample of 1,1´dimethylferrocene was purified by a fractional sublimation in vacuum. The degree of purity was determined using a gas chromatograph equipped with a flame ionization detector. A capillary column HP-5 (stationary phase crosslinked 5% PH ME silicone) was used with a column length of 30 m, an inside diameter of 0.32 mm, and a film thickness of 0.25 m. The standard temperature program of the GC was T = 333 K for 180 s followed by a heating rate of 0.167 K·s-1 to T = 523 K. No impurities (greater than mass fraction 0.001) could be detected in the samples used for the vapor pressure measurements. 2.2 Vapor pressure measurements 2.2.1 Transpiration method Vapor pressures and enthalpies of vaporization/sublimation of alkylferrocenes were determined using the method of transpiration in a saturated N2-stream [23–26]. A U-shaped tubular saturator was filled with approximately 0.5 g of the sample, which was mixed with glass beads

4

in order to avoid a pressure drop along the tube, as well as to provide sufficient surface for the vapor-liquid equilibration. At a series of constant temperatures (± 0.1 K), a nitrogen stream was passed through the saturator and the transported amount of material was collected in a cold trap (kept at 273 K). The volume of the carrier gas VN2 was determined by the digital flow rate sensor from integration with a microcontroller. We used the Honeywell S&C HAFBLF0200C2AX5 digital flow rate sensor with uncertainty at the level of 2.5 %. The flow rate of the nitrogen stream was also controlled by using a soap bubble flow meter and optimized in order to reach the saturation equilibrium of the transporting gas at each temperature under study. The volume of the carrier gas VN2 was read from the calibrated digital flow rate sensor. In our apparatus, the contribution due to diffusion was negligible at a flow rate up to 0.45 dm3·h-1. The upper limit for our apparatus where the speed of nitrogen could already disturb the equilibration was at a flow rate of 9.0 dm3·h-1. Thus, we carried out the experiments in the flow rate interval of (1 to 8) dm3·h-1, which has ensured that the transporting gas was in saturated equilibrium with the coexisting liquid phase in the saturation tube. The saturation vapor pressure psat at each temperature Ti was calculated from the amount of the material collected in the cold trap within a definite period of time. The amount of the transported material was determined by the GC analysis using an external standard (hydrocarbon n-CnH2n+2). Assuming validity of the Dalton`s law applied to the nitrogen stream saturated with the substance i, values of psat were calculated with equation: psat = mi·R·Ta / V·Mi ;

V= VN2 + Vi; (VN2 » Vi)

(1)

where R = 8.3144598 J·K-1·mol-1 is the ideal gas constant; mi is the mass of the transported compound, Mi is the molar mass of the compound, and Vi is its volume contribution to the gaseous phase. VN2 is the volume of the carrier gas and Ta is the temperature of the devices used for measurement of the gas flow. Experimental vapor pressures at different temperatures are given in Table 1. 2.2.2 Static method Static method with a pyrex membrane-gauge manometer [27] was applied for the vapor pressure measurements on n-butylferrocene in temperature range (408 ≤ T/K ≤ 474) and pressure range (678 ≤ p/Pa ≤ 9003). The main characteristics of the experimental set-up and the experimental procedure were described in detail elsewhere [28–30]. The sensitivity of the differential membrane gauge-manometer used was 5 Pa. The standard uncertainties (u) in pressure and temperature values were 25 Pa and 0.5 K respectively. Measurements were

5

performed in two series with a significantly different sample masses (0.0220 and 0.0401 g) as well as with the different volumes of the manometer inner chamber (0.03976 and 0.03342 dm3). The sample was loaded into the inner chamber of the membrane-gauge manometer and after evacuation it was sealed. The sample was heated and the pressure was recorded after reaching the equilibrium at a desired temperature. In order to ensure equilibrium conditions and the absence of decomposition, the pressures were measured at the increasing and decreasing temperature sequences. However, results obtained at the same temperatures from the upwards and backwards runs were indistinguishable proving the achievement of equilibrium within 15– 20 min. Experimental vapor pressures at different temperatures are given in Table 2.

2.3 Computational details. Quantum chemical calculations of alkylferrocenes were performed with the ORCA 4.0.1 package [31]. Energies of molecules involved in this study were calculated by using the B3LYP/def2-TZVP [32,33] method with D3 dispersion correction [34] and Becky-Jonson damping [35]. The same method and basis were applied for computation of the gas phase vibrational spectra required for calculation of the Zero Point Vibration Energy (ZPVE) and the thermal correction ∆𝑇0𝐻om by using statistical thermodynamics methods.

3. Results and discussion 3.1. Vapor pressures and vaporization enthalpies of alkylferrocenes Temperature dependences of vapor pressures psat measured for alkylferrocenes (see Table 1) were fitted with Eq. (2) [23]: 𝑅ln (𝑝𝑠𝑎𝑡/𝑝𝑟𝑒𝑓) = 𝑎 +

𝑏 𝑇

()

+ ∆gl𝐶o𝑝,𝑚𝑙𝑛

𝑇

𝑇0

(2),

where a and b are adjustable parameters. ∆gl𝐶op,m-value is the difference between molar heat capacities of the gaseous and the condensed phase, respectively. T0 appearing in Eq. (2) is an arbitrarily chosen reference temperature (which has been chosen to be T0 = 298.15 K in this work), 𝑝𝑟𝑒𝑓 = 1 Pa, and R is the molar gas constant. Values of ∆gl𝐶op,min Eq. (2) were calculated (see Table S2) according to the empirical procedure developed by Chickos and Acree [36] based on the isobaric molar heat capacities 𝐶op,m estimated by the group-additivity procedure [37] modified for metalorganic compounds in our recent work [22].

6

Table 1 Results from transpiration method: vapor pressures psat, standard molar vaporization/sublimation enthalpies and standard molar vaporization/sublimation entropies T/ Ka

m/ mgb

∆gl,cr𝐻om(T)/ kJmol-1 ethylferrocene: ∆gl𝐻om(298.15 K) = (65.20.6) kJ.mol-1 𝑇 312.85 90814.2 86.0 𝑅ln (𝑝𝑠𝑎𝑡/𝑝𝑟𝑒𝑓) = ― ― ln 𝑅𝑇 𝑅 298.15K 𝑅

V(N2)c / dm3

292.6 295.4 298.4 302.3 305.1 308.0 309.3 312.2 314.3 316.3 317.3 320.1 325.1 322.5 329.0 335.3 332.8 338.3 341.4 345.4 351.0 352.1 348.7 355.1

0.92 1.60 1.42 1.54 1.03 2.00 1.13 1.60 1.71 0.97 1.52 1.26 1.65 3.36 2.28 2.78 6.09 3.11 3.74 4.24 3.26 5.91 4.96 4.46

303.2 307.8 312.6 318.1 323.0 328.2 333.1 338.2 343.1 348.3 353.3 358.3 363.4

0.54 0.70 1.46 0.69 0.76 1.40 0.62 1.37 1.79 1.36 1.36 1.15 1.48

Ta/ Kd

Flow/ dm3·h-1

psat / Pae

u(psat)/ Paf

∆gl,cr𝑆om(T)/ JK-1mol-1

6.56 297.2 7.15 1.63 0.05 65.65 8.58 295.7 7.15 2.15 0.06 65.41 6.08 295.2 7.15 2.68 0.07 65.16 4.73 294.7 7.28 3.74 0.10 64.82 2.38 298.2 7.15 5.02 0.15 64.58 3.64 294.7 7.28 6.30 0.18 64.33 1.91 298.2 7.15 6.89 0.20 64.22 2.06 294.7 7.28 8.88 0.25 63.97 1.91 298.2 7.15 10.39 0.28 63.79 0.962 299.2 3.21 11.78 0.32 63.62 1.34 299.2 3.21 13.21 0.36 63.53 0.909 299.2 3.21 16.10 0.43 63.29 0.855 299.2 3.21 22.36 0.58 62.86 2.00 294.2 7.28 19.17 0.50 63.08 0.909 299.2 3.21 29.17 0.75 62.52 0.705 295.2 2.65 45.19 1.15 61.98 1.80 294.2 7.22 38.56 0.99 62.19 0.639 295.2 2.65 55.81 1.42 61.72 0.617 295.2 2.65 69.45 1.76 61.45 0.555 295.2 2.56 87.60 2.22 61.11 0.292 295.2 1.17 128.0 3.2 60.63 0.507 295.2 2.65 133.7 3.4 60.54 0.529 295.2 2.65 107.6 2.7 60.83 0.321 295.2 1.17 159.3 4.0 60.28 n-butylferrocene: ∆gl𝐻om(298.15 K) = (73.91.0) kJ.mol-1 𝑇 343.01 104513.0 102.6 𝑅ln (𝑝𝑠𝑎𝑡/𝑝𝑟𝑒𝑓) = ― ― 𝑙𝑛 𝑅𝑇 𝑅 298.15K 𝑅 8.55 6.76 9.02 2.79 2.07 2.52 0.719 1.08 0.970 0.539 0.384 0.240 0.224

295.2 295.2 295.2 295.2 295.2 295.2 295.2 295.2 294.7 294.7 295.2 295.2 295.2

5.40 5.41 5.41 5.40 5.40 5.41 2.16 2.16 2.16 2.16 0.96 0.96 0.96

0.64 1.05 1.64 2.51 3.73 5.64 8.80 12.86 18.70 25.62 35.90 48.70 67.02

0.02 0.03 0.05 0.07 0.10 0.17 0.25 0.35 0.49 0.67 0.92 1.24 1.70

73.41 72.94 72.44 71.88 71.37 70.84 70.34 69.82 69.32 68.78 68.27 67.76 67.23

132.8 132.1 130.9 129.7 129.3 128.5 128.0 127.4 126.7 125.9 126.0 125.1 123.5 124.4 122.4 120.8 121.5 120.2 119.5 118.4 117.4 116.9 117.6 116.2

142.7 141.7 140.1 137.9 136.2 134.5 133.5 132.0 130.7 128.8 127.3 125.7 124.2

7

1,1´-dimethylferroceneg: ∆gcr𝐻om(298.15 K) = (78.23.1) kJ.mol-1 𝑇 313.85 90163.8 40.3 ― ― 𝑙𝑛 𝑅ln (𝑝𝑠𝑎𝑡/𝑝𝑟𝑒𝑓) = 𝑅𝑇 𝑅 298.15K 𝑅 289.4 292.4 295.2 298.0 300.9 303.2

0.56 4.20 294.2 3.11 1.53 0.04 78.50 0.70 3.78 294.2 3.11 2.11 0.06 78.38 0.66 2.64 294.2 3.11 2.87 0.08 78.27 0.82 2.44 294.2 3.11 3.85 0.10 78.15 0.79 1.76 295.2 3.11 5.15 0.15 78.04 1.32 2.23 295.7 3.11 6.83 0.20 77.95 g o . 1,1´-dimethylferrocene: ∆l 𝐻m(298.15 K) = (62.80.9) kJ mol-1 311.10 88697.7 86.8 𝑇 𝑅ln (𝑝𝑠𝑎𝑡/𝑝𝑟𝑒𝑓) = ― ― 𝑙𝑛 𝑅 𝑅𝑇 𝑅 298.15K

179.1 178.6 178.2 177.7 177.3 177.4

311.9 1.66 1.29 296.2 1.80 14.79 0.39 61.71 125.1 314.0 1.41 0.900 296.2 1.80 18.08 0.48 61.45 124.1 317.0 1.67 0.840 296.2 1.80 22.90 0.60 61.18 123.3 320.5 1.82 0.720 296.2 1.80 29.05 0.75 60.88 122.3 323.7 1.88 0.600 296.2 1.80 36.16 0.93 60.60 121.4 326.8 1.88 0.476 296.2 1.24 45.38 1.16 60.34 120.7 329.8 1.77 0.372 296.2 1.24 54.65 1.39 60.07 119.7 333.2 2.45 0.414 296.2 1.24 68.11 1.73 59.78 118.8 337.2 2.41 0.310 296.2 1.24 89.26 2.26 59.43 117.9 340.8 3.04 0.310 296.2 1.24 112.8 2.8 59.12 117.1 342.8 2.96 0.274 295.2 1.03 123.7 3.1 58.95 116.3 347.9 3.78 0.257 295.2 1.03 168.6 4.2 58.50 115.1 352.0 5.65 0.292 295.2 1.03 222.2 5.6 58.14 114.4 355.1 5.81 0.257 295.2 1.03 259.1 6.5 57.88 113.5 a Saturation temperature (u(T) = 0.1 K). b Mass of transferred sample condensed at T = 273 K. c Volume of nitrogen (u(V) = 0.005 dm3) used to transfer m (u(m) = 0.0001 g) of the sample. d T is the temperature of the measurement of the gas flow. e Vapor pressure at temperature T, a calculated from the m and the residual vapor pressure at the condensation temperature calculated by an iteration procedure. f Uncertainties were calculated with u(p/Pa) = 0.005 +0.025(p/Pa) for pressures below 5 Pa and with u(p/Pa) = 0.025 + 0.025(p/Pa) for pressure from 5 to 3000 Pa. Uncertainty of the vaporization enthalpy U(∆gl𝐻om) is the expanded uncertainty (0.95 level of confidence) calculated according to procedure described elsewhere [25,26]. g Measured over the solid sample. Vaporization enthalpies at temperatures T were derived from the temperature dependence of vapor pressures by using Eq. (3): ∆gl𝐻om(𝑇) = ―𝑏 + ∆gl𝐶op,m × 𝑇

(3)

Entropies of sublimation at temperatures T were also derived from the temperature dependence of vapor pressures by using Eq. (4): ∆gl𝑆om(𝑇) =

∆gl𝐻om

(

)

𝑇 + 𝑅ln 𝑝sat 𝑝o

(4)

8

Experimental vapor pressures measured by the transpiration method, coefficients a and b of Eq. (2), as well as values of ∆gl𝐻om(T) and ∆gl𝑆om (T) are given in Table 1 (primary data) and final results are collected in Table 3. However, Eqs. (2-4) are also valid for the treatment of vapor pressure temperature dependence measured over the solid sample, giving the standard molar enthalpy of sublimation ∆gcr𝐻om(T) and the standard molar sublimation entropy ∆gcr𝑆om(T). In this case in Eqs. (2-4) we used the value ∆gcr𝐶op,m instead of the ∆gl𝐶op,m. Table 2 Results from the static method: vapor pressures psat, standard molar vaporization enthalpy and standard molar vaporization entropy of n-butylferrocene. ∆gl𝐻om(T)/ ∆gl𝑆om(T) kJmol-1 JK-1mol-1 n-butylferrocene: ∆gl𝐻om(298.15 K) = (78.82.5) kJ.mol-1 𝑇 354.15 109384.1 102.6 ― ― ln 𝑅ln (𝑝𝑠𝑎𝑡/𝑝0) = 𝑅𝑇 𝑅 298.15K 𝑅 408.1 678 67.51 123.9 412.8 797 67.03 122.2 413.5 881 66.96 122.6 421.4 1175 66.15 120.0 422.4 1268 66.05 120.0 423.4 1337 65.94 119.9 428.3 1628 65.44 118.6 432.4 1853 65.02 117.2 433.4 2097 64.92 117.7 436.2 2336 64.63 116.9 442.2 2969 64.01 115.5 443.5 3154 63.88 115.3 448.0 3568 63.42 113.8 451.2 4064 63.09 113.2 452.3 4226 62.98 112.9 454.0 4650 62.80 112.8 461.5 6140 62.03 111.2 463.7 6653 61.81 110.8 466.7 7055 61.50 109.7 472.4 8602 60.92 108.6 473.7 9003 60.78 108.3 a Saturation temperature (u(T) = 0.5 K). b Measured with the standard uncertainty of u(p ) = 25 sat Pa T/ Ka

psat / Pab

Procedure for calculation of the combined uncertainties of vaporization/sublimation enthalpies includes uncertainties from the transpiration experimental conditions, uncertainties

9

in vapor pressure, and uncertainties in the temperature adjustment to T = 298.15 K as described elsewhere [25,26]. Experimental vapor pressure of ethylferrocene and n-butylferrocene were previously measured by using Knudsen-effusion technique by Karyakin et al. [16]. However, their vapor pressures are significantly lower in comparison to the results from this study for both alkylferrocenes (see Figs. S1 and S2). Such a disagreement could be probably explained due to an effect of the failure of isotropy of a gas in an effusion cell [38], which is important for studies of liquid samples by the traditional Knudsen method, but it was not taken into account by Karyakin et al. [16]. A compilation of the available vaporization/sublimation enthalpies of alkylferrocenes is presented in Table 3. For the sake of a proper comparison, we have uniformly treated the original experimental vapor pressures of alkylferrocenes available in the literature by using Eqs. (2) and (3) and calculated ∆gl𝐻om(298.15 K) or ∆gcr𝐻om(298.15 K) (see Table 3). In spite of the significant deviation of vapor pressures reported by Karyakin et al. [16] for ethylferrocene and n-butylferrocene (see Figs. S1 and S2), the enthalpies of vaporization derived for both compounds are in fair agreement with the results obtained in this work (see Table 3). Taking into account the general agreement of data sets for ethyl- and n-butylferrocene, measured by different methods, we calculated the weighted average value ∆gl𝐻om(298.15 K) for each alkylferrocene (see Table 3) by using the experimental uncertainties as the weighting factor. These mean values are given in bold and they have been recommended for further thermochemical calculations. Table 3 Vaporization/sublimation enthalpies of alkylsubstituted ferrocenes (in kJmol-1). ∆gl𝐻om/Tav ∆gl𝐻om/298.15 Kb Compounds Ma T-range ferrocene (liq) 1-methylferrocene (liq)

SP

1-ethylferrocene (liq)

K T

Ref

60.9±1.9

[22]

61.3±1.0

this work

297.5-319.8 292.6-355.1

64.9±3.7 63.1±0.2

65.7±7.6 65.2±0.6 65.2±0.6c 65.5±1.0

[16] this work average this work

A 1-n-propylferrocene (liq)

T A

298.4-358,1

66.7±0.2

69.2±0.7 69.4±1.0

[21]

1-n-butylferrocene (liq)

K S T

314.6-333.6 408.1-473.7 303.2-363.4

74.4±2.9 64.2±1.5 70.5±0.4

77.0±6.0 78.8±2.5 73.9±1.0 74.6±0.9 c 74.0±1.0

[16] this work this work average this work

308.0-362.5

67.4±0.3

71.0±0.9

[21]

A 1-iso-butylferrocene (liq)

T

10

A

71.2±1.0

this work

1-benzylferrozene (liq)

T A

350.7-377.1

83.3±0.6

90.4±1.7 93.1±1.0

[20] this work

1,1´-dimethylferrocene (cr)

C K T

298.15 276.7-283.6 289.4-303.2

87.0±1.9 78.2±1.1

(84.7±0.2) d 84.5±5.4 d 78.2±3.1 d 79.8±1.0 e 79.8±0.9 c

[39] [39] this work this work average

1,1´-dimethylferrocene (liq)

T A

311.9-355.1

59.9±0.3

62.8±0.9 61.7±2.4

this work this work

1,1´-diethylferrocene (liq)

K A

299.2-325.8 298.15

79.0±1.0

(80.5±2.1) 70.1±2.4

[40] this work

1,1´-di-n-butylferrocene (liq)

S A

384.2-505.4 298.15

68.0±0.8

87.9±2.6 87.1±2.4

[41] this work

1,1´-di-tert-butylferrocene (liq)

S A

417.0-533.5 298.15

52.1±0.3

74.6±2.5 77.7±2.4

[42] this work

a

Methods: K = Knudsen effusion method; SP = structure-property correlations (see text); C = calorimetry; T = transpiration method; S = static method; A = additivity (see text). b Uncertainty of the vaporization enthalpy U(∆g𝐻o ) is the expanded uncertainty (0.95 level of l m confidence) calculated according to procedure described elsewhere [25,26]. c Average values were calculated using the uncertainty as a weighing factor. Recommended values are given in bold. d The sublimation enthalpy ∆gcr𝐻om was measured over the solid sample. e Calculated as the sum: ∆gcr𝐻om(298.15 K) = ∆gl𝐻om(298.15 K) + ∆lcr𝐻om(298.15 K), see text. As it can be seen in Table 3, for the 1,1´-dimethylferrocene the sublimation enthalpy, ∆gcr 𝐻om(298 K) = (78.2 ± 3.1) kJ mol-1, obtained in this work in the temperature range of 289.4 – 303.2 K by the transpiration method is somewhat lower (see Fig. S3) in comparison to the results reported by Lousada et al. [39], which were measured by the Knudsen, as well as by the calorimetric method. In order to ascertain the sublimation data for 1,1´-dimethylferrocene, an additional measurement is required. For this purpose, we have deliberately measured vapor pressures for 1,1´-dimethylferrocene above the melting point (Tfus = 311.6 K) in the range 311.9 – 355.1 K and the vaporization enthalpy ∆gl𝐻om(298.15 K) = (62.8 ± 0.9) kJ mol-1 has been derived. A plot in Fig. S3 shows that the new and old results on vapor pressures seem to be in agreement, but the temperature ranges are significantly different in order to make any proper conclusion. In order to obtain more confidence with the sublimation enthalpy of 1,1´dimethylferrocene, we calculated the (298 K)-value from vaporization enthalpy ∆gl𝐻om(298.15 K) = (62.8 ± 0.9) kJ mol-1, measured in this work (see Table 3) combined with the enthalpy of fusion, ∆lcr𝐻om(Tfus) = (17.7 ± 0.1) kJ mol-1, available for 1,1´-dimethylferrocene in the literature [39]. The latter value has been adjusted to the reference temperature T = 298.15 K (details see in ESI) ∆lcr𝐻om(298.15 K) = (17.0 ± 0.4) kJ mol-1 and used to calculate the sublimation enthalpy:

11

∆gcr𝐻om(298.15 K) = ∆gl𝐻om(298.15 K) + ∆lcr𝐻om(298.15 K) = 62.8 + 17.0 = (79.8±1.0) kJ mol-1, which in very good agreement with the ∆gcr𝐻om(298.15 K) = (78.2 ± 3.1) kJ mol-1, directly measured by the transpiration in the temperature range of 289.4 – 303.2 K. Such a good agreement provides the confidence on the transpiration results and we would recommend for 1,1´-dimethylferrocene the value ∆gcr𝐻om(298.15 K) = (79.8 ± 1.0) kJ mol-1, measured by the transpiration in this work for further thermochemical calculations. 3.2 Structure-property relationships in vaporization enthalpies of alkylferrocenes. 3.2.1 Correlation of vaporization enthalpies of alkylferrocenes and alkylbenzenes Admittedly,

structure-property

relationships

are

well-established

tools

for

understanding of energetics at the molecular level, validation and prediction of thermochemical properties. In order to check an internal consistency of the experimental vaporization enthalpies ∆gl𝐻om(298.15 K) of alkyl-substituted ferrocenes evaluated in Table 3 it has been reasonable to perform the structure-property correlation with ∆gl𝐻om(298.15 K)-values of a similarly shaped alkyl-benzenes: ethylbenzene, n-propylbenzene, and n-butylbenzene, iso-butylbenzene, and diphenylmethane, where experimental data are of implacable quality (see Table S3). It has turned out, that vaporization enthalpies of alkylferrocenes excellently correlate with those of alkylbenzenes (see the input data for five data pairs in Table S4) and the straight line (see Fig. S4) with the correlation coefficient 0.998 (see Eq. 5) has confirmed the reliability of the experimental results on alkylferrocenes evaluated in this work: ∆gl𝐻om(298.15 K, alkylferrocene)/(kJ.mol-1) = = 0.98×∆gl𝐻om(298.15 K, alkylbenzene) + 24.0

(R2 = 0.998)

(5)

Such a good correlation between thermochemical properties of alkyl-substituted ferrocenes and benzenes provides a valuable tool for a reliable assessment of the unknown properties of substituted ferrocenes by using the structure-property relationships according to Eq. (5), provided that ∆gl𝐻om(298.15 K)-values for alkyl-substituted benzenes are available [43]. 3.2.2 Quick assessment of vaporization enthalpies of ferrocene derivatives by a group-additivity It is well known, that standard molar sublimation enthalpies, ∆gcr𝐻om, are hardly possible to predict by using any group-additivity methods. The main reason is that the value of the

12

sublimation enthalpy encompasses the enthalpy of vaporization, ∆gl𝐻om, and the enthalpy of fusion, ∆lcr𝐻om as two independent contributions: ∆gcr𝐻om = ∆gl𝐻om + ∆lcr𝐻om

(6)

As a consequence, any prediction of sublimation enthalpies suffers from a large ambiguity [44]. In contrast, vaporization enthalpies definitely obey the additive rules [45] and an incremental approach developed in our recent work [25] for prediction of ∆gl𝐻om(298.15 K)-values of the substituted aromatic compounds can be reasonably applied for alkylferrocenes. The procedure is based on a starting basic molecule having a well-established data on vaporization enthalpy. For example, using the experimental ∆gl𝐻om(298.15 K)-values of methylbenzene and benzene (see Table S3), we can derive the increment H(H→CH3) = 38.1 – 33.9 = (4.20.3) kJ.mol-1 for substitution of H atom on the benzene ring by the CH3-group. The structure-property correlation established in 3.2.1 according to Eq. (5) is a clear evidence that the increments for the substitution of H atom on the benzene and on the ferrocene moiety are transferrable. In the current study, we used Eq. (5) to calculate the theoretical vaporization enthalpy of methylsubstituted ferrocene ∆gl𝐻om(298.15 K) = (61.31.0) kJ.mol-1. Using this value and the contribution H(H→CH3) = (4.2  0.3) kJ.mol-1, the contribution to the vaporization enthalpy for the ferrocene moiety H([C5H5-Fe-C5H4]) = 61.3 – 4.2 = (57.11.0) kJ.mol-1 was derived. The compilation of increments H(H→R) for substitution of H atom on the benzene ring by different substituents (supposed to be equal to those for substitution of H atom on the ferrocene ring) is given in Table 4 and these increment have been used for calculation of theoretical vaporization enthalpies of alkylferrocenes. For example, using this starting value ∆gl𝐻om(298.15 K) = (57.11.0) kJ.mol-1 for ferrocene moiety ([C5H5-Fe-C5H4]) and the increment H(H→nC4H9) from Table 4, the theoretical value of vaporization enthalpy for the n-butyl-ferrocene ∆gl 𝐻om(298.15 K) = (74.01.0) kJ.mol-1 was calculated, which is in excellent agreement with the experimental value ∆gl𝐻om(298.15 K) = (74.60.9) kJ.mol-1 (see Table 3). In the similar way, by using increments H(H→R), the theoretical values of vaporization enthalpies for other Rsubstituted ferrocenes can be calculated (see Table 3 for the values indicated with method A) and they are mostly in very close agreement with the experimental results. The similar procedure has been developed for calculation of the di-alkylsubstituted ferrocene derivatives. In order to predict vaporization enthalpy of di-substituted ferrocenes, the starting ferrocene moiety ([C5H4-Fe-C5H4]) is required. The contribution for this moiety has been calculated as follows: the difference between vaporization enthalpy of the ferrocene

13

([C5H5-Fe-C5H5]) with ∆gl𝐻om(298.15 K) = (60.91.9) kJ.mol-1 (see Table 3) and monosubstituted moiety ([C5H5-Fe-C5H4]) with the value ∆gl𝐻om(298.15 K) = (57.11.0) kJ.mol-1 (see above) provide the increment  = (57.1 – 60.9) = -(3.82.1) kJ.mol-1 for the substitution vacancy on the second ferrocene ring. Table 4 Parameters for calculation vaporization enthalpies ∆gl𝐻om(298.15 K) and enthalpies of formation of alkylferrocenes (in kJ.mol-1) ∆gl𝐻om(298.15 K) ∆f𝐻om(g) ∆f𝐻om(liq) Increments ([C5H5-Fe-C5H4]) a 57.1 ([C5H4-Fe-C5H4]) b 53.3 4.2 H(H→ CH3) 8.4 H(H→ C2H5) 12.3 H(H→ n-C3H7) 16.9 H(H→ n-C4H9) 14.1 H(H→ i-C4H9) 36.0 H(H→ Ph-CH2) a Contribution for mono-substituted ferrocene b Contribution for 1,1´-di-substituted ferrocene

225 220 -36.0 -61.3 -87.3 -112.2 -118.8 48.1

168 167 -32.2 -52.7 -74.7 -95.7 -104.1 82.4

Thus, the starting di-substituted moiety ([C5H4-Fe-C5H4]) should have the contribution to the vaporization enthalpy (57.1 – 3.8) = (53.32.4) kJ.mol-1. Using the latter contribution together with the increments H(H→R) from Table 4, the theoretical values of vaporization enthalpies for di-R-substituted ferrocenes have been calculated (see Table 3). As a rule, the uncertainty of the basic structural element (in this case [C5H5-Fe-C5H4] and [C5H4-Fe-C5H4], see table 4) are taken into account by the group-additivity calculations. Conventionally the uncertainties of increments H(H→R) are neglected. It should be mentioned, that the quality of the experimental results on the di-substituted ferrocenes (see Table 3) is mostly questionable (except for the 1,1´-di-methylferrocene) due to insufficiently characterized purity of the samples [40–42]. Nevertheless, the predicted by the group-additivity procedure theoretical ∆gl𝐻om-values of di-substituted ferrocenes, which are listed in Table 3 (and indicated as method A), are in reasonable agreement with the available experiment, except for 1,1´-diethylferrocene, where the estimate seems to be more reliable then the available experimental value. Thus, the simple and straightforward incremental procedure suggested in this work is useful for a quick appraisal of the reliability of experimental vaporization enthalpies of alkyl-ferrocenes. We also suggest that together with the groupadditivity procedure, the structure-property correlation according to Eq. (5) can be used for the

14

reliable assessment of ∆gl𝐻om(298.15 K) of the broad range of the linear and branched alkylferrocenes which are similarly in the shape to alkylbenzenes evaluated in our previous study [43]. 3.2.3 Indirect assessment of sublimation enthalpies of ferrocene derivatives In spite of troubles with prediction of sublimation enthalpies described in section 3.2.2, an indirect assessment of ∆gcr𝐻om-values of ferrocene derivatives can be achieved with help of the group-additivity procedure developed for the vaporization enthalpies in 3.2.2 combined with enthalpies of fusion according to Eq. (6). Fusion enthalpies can be reliably measured by the DSC or calculated according to the Walden’s rule [46]: ∆lcr𝐻om/Tfus = Walden-constant

(7)

As a matter of fact, for the broad scope of organic molecules the empirical Walden-constant = 0.054 kJ.K-1.mol-1 was suggested irrespective to the structure of the molecule of interest. However, this rule has not been tested for metalorganic compounds yet. In this work we calculated the Walden-constant using the experimental fusion enthalpies ∆lcr𝐻om and Tfus for substituted ferrocenes (see Table S5). We have derived the Walden-constant = 0.059±0.012 kJ.K-1.mol-1 (uncertainty was calculated as the standard deviation of the mean) for alkylsubstituted ferrocenes. This value (within the boundaries of experimental uncertainties) is essentially the same as the original value suggested by Walden. As a consequence, having reliable experimental data on Tfus for ferrocene derivatives, their enthalpies of fusion can be quickly assessed with the Walden-constant at the level 0.06 kJ.K-1.mol-1. Thus, the combination of the incremental group-additivity procedure for vaporization enthalpy with the estimation of the fusion enthalpy can serve for the reasonable assessment of the level of sublimation enthalpies of the ferrocene derivatives. 3.3 Standard molar enthalpies of formation of ferrocene and ferrocene derivatives Standard molar enthalpies of formation, ∆f𝐻om, in the gas, liquid, or crystal state are valuable thermodynamic properties required for calculation of energetic balances of chemical reactions according to the Hess`s Law. Unfortunately, even for ferrocene itself the available data on ∆f𝐻om (cr) spread from 141 kJ·mol-1 to 179 kJ·mol-1 (see Table S6). The evaluation of the combustion energy of ferrocene with help of additional measurements have been performed few times [47–

15

49] and in this work we follow the recommended by Domracheva et al. [40] value ∆f𝐻om(cr) = (157±6) kJ·mol-1. Using the experimental sublimation enthalpy of ferrocene 72.8±0.6 kJ·mol-1 evaluated in our recent work [22], the gas phase enthalpy of formation of ferrocene was calculated to be ∆f𝐻om(g) = (230±6) kJ·mol-1 (see Table 5, column 5). Only few liquid-phase enthalpies of formation of alkylferrocenes with ethyl- and nbutyl-substituent were reported from the combustion calorimetry (see Table 5, column 3). Using vaporization enthalpies of the alkylsubstituted ferrocenes evaluated in Table 3, the gas phase formation enthalpies of these compounds were calculated (see Table 5, column 5). Table 5 Thermochemical data for alkyl substituted ferrocenes at T = 298.15 K (in kJ·mol-1)a ∆f𝐻om(g) ∆f𝐻om(g) ∆f𝐻om(g) exp DFT Eq.(8) 1 2 3 4 5 6 7 d ferrocene cr 157±6 [40] 72.8±0.6 [20] 230±6 231 229 methylferrocene liq (132±6)e 61.3±1.0 193 194 e,f ethylferrocene liq (107±6) 65.2±0.6 172 173 n-propylferrocene liq (79±6)e 69.2±0.7 148 149 n-butylferrocene liq 54±6 [16] 74.6±0.9 128±6 129 127 benzylferrocene liq (227±6)e 90.4±1.7 317d 316 a All uncertainties in this table are expressed as twice the standard deviation. b From Table 3. c From Table 7 d Results from Dorofeeva et al. [50] calculated at B3LYP/6-311+G(3df,2p)//B3LYP/631G(d,p) level of theory. e Values given in brackets were calculated as the difference between column 6 and 4 from this table. f For comparison, the available experimental value for ethylferrocene ∆ 𝐻o (l) = 127±8 kJ·mol-1 f m (see text). Compound

state ∆f𝐻om(l or cr)

∆gl,cr𝐻om b

Few ∆f𝐻om(g)-values were calculated by Dorofeeva et al. [50] using the DFT method (see Table 5). Thus, the very restricted data set available on enthalpies of formation of alkylferrocenes suffers from the large uncertainties of ±(6÷15) kJ·mol-1 [16, 50], as well as from the total ambiguity of the available enthalpy of formation data. For example, the experimental value ∆f𝐻om(l) = 127±8 kJ·mol-1 available for ethylferrocene [16] is significantly different from the DFT-based estimate ∆f𝐻om(l) = 107±6 kJ·mol-1 (see Table 5, column 2). The inconsistent data set on formation enthalpies on alkylferrocenes available in the literature requires validation with the help of quantum-chemical methods as well as by using structureproperty correlations.

16

3.4 Gas state standard molar enthalpies of formation from quantum-chemical calculations It has been already shown, that the DFT methods could serve as a valuable tool for validation of the experimental data on ∆f𝐻om(g) of ferrocene derivatives [50]. Indeed, an agreement between the experimental and theoretical results could provide a desired validation for both results and support the reliability of the thermochemical data for the ferrocene derivatives. The first step in quantum-chemical calculations is the geometry optimisation of stable conformers of the compound under study. Admittedly, the conformational studies of flexible molecules are important for a correct calculation of ∆f𝐻om(g). From our experience, only few most stable conformers usually contribute to the theoretical enthalpy of formation, provided that differences in their energies do not exceed 1-3 kJ·mol-1 [51]. This assumption is quite successful if we are working with the enthalpies of formation of compounds at 298.15 K. Obviously, with increasing temperature, the situation may change significantly. In order to quantify this temperature dependence, we performed calculations of deviations in the enthalpy of formation ∆f𝐻om(g) of a compound for different temperatures, if two arbitrary conformers gradually differing in energy (Table 6, column 1) represent it. The results given in this table clearly illustrate that from the point of view of the conformational composition and its influence on the formation enthalpy accuracy of a compound, different groups of conformers are significant for all temperatures. For example, the maximum deviation [∆f𝐻om(g)] in the enthalpy of formation of a compound at 298.15 K was observed for a conformer that differs from the most stable one by 3 kJ·mol-1 (see Table 6, column 1 and column 2). The amount of this conformer in the equilibrium mixture was estimated to be at the level of 23%, which leads to a correction in ∆f𝐻om(g) equal to 0.68 kJ·mol-1(Table 6,column 2). By the increase of the temperature up to 600 K, the maximum correction of 1.38 kJ·mol-1 in ∆f𝐻om(g) was observed for conformer that differ from the most stable one already by 7.0 kJ·mol-1 (see Table 6 column 3). The amount of such a less stable conformer in the mixture is 19.7%. Apparently, the further temperature increase up to 1000 K makes it necessary to account for even less stable conformers, which can differ by 10 kJ·mol-1 or more. The correction to ∆f𝐻om(g) of the compound represented by such a pair of conformers is 2.3 kJ·mol-1 (see Table 6, column 4) and the concentration of the least stable of them is 14.1%. We used the B3LYP/6-31+G(d,p) for initial search for stable conformers by constructing the functions of the potential energy of a substituted ferrocene molecule when the corresponding dihedral angle changes with a step of 10 degrees. Conformational analysis of

17

alkylsubstituted ferrocenes has revealed a vanishing small (less than 1 kJ·mol-1) differences in energies of possible stable conformers. Since the main task of this work was to obtain reliable data on ∆f𝐻om(g) at 298.15 К, we took into account only the most stable conformers. The expected error in the enthalpies of formation of alkylferrocenes from the use of such an approximation should not exceed 0.7 kJ·mol-1, which is much less than the expected error in calculating the enthalpies H298 by suitable quantum chemical methods. Table 6 Temperature dependence of the difference [∆f𝐻om(g)] between the enthalpy of formation ∆f𝐻om (g) of a mixture of two arbitrary conformers and the enthalpy of formation of the most stable conformer (in kJ·mol-1). [∆f𝐻om(g)] a 298 K 600 K 1000 K 20.0 0.006 0.35 1.65 15.0 0.035 0.71 2.12 10.0 0.17 1.18 2.31 7.0 0.39 1.38 2.11 5.0 0.59 1.34 1.77 4.0 0.66 1.20 1.53 3.0 0.68 1.06 1.23 2.0 0.62 0.80 0.88 1.0 0.40 0.45 0.47 0.5 0.22 0.23 0.24 a The difference  in the enthalpies of formation ∆ 𝐻o (g) of two conformers, in kJ·mol-1 f m Table 7 Enthalpies of isodesmic reactions, ∆r𝐻𝑜m(g), used for calculation of enthalpies of formation ∆f 𝐻om(g) alkylferrocenes (in kJ·mol-1). Compound/Reaction ∆f𝐻om(g)/(g)a Methylferrocene ∆f𝐻om(g)=193.1 ± 0.1 Ferrocene + C3H8 = Methylferrocene + C2H6 ∆r𝐻om(g)=-15.9 Ferrocene + C5H12 = Methylferrocene + C4H10 ∆r𝐻om(g)=-16.0 Ferrocene + C4H10 = Methylferrocene + C3H8 ∆r𝐻om(g)=-15.8 Ethylferrocene ∆f𝐻om(g)=172.2 ± 0.3 Ferrocene + C4H10 = Ethylferrocene + C2H6 ∆r𝐻om(g)=-15.8 Ferrocene + C5H12 = Ethylferrocene + C3H8 ∆r𝐻om(g)=-15.9 Ferrocene + C6H14 = Ethylferrocene + C4H10 ∆r𝐻om(g)=-16.2 n-Propylferrocene ∆f𝐻om(g)=147.8 ± 0.3 Ferrocene + C5H12 = n-Propylferrocene + C2H6 ∆r𝐻om(g)=-19.4 Ferrocene + C6H14 = n-Propylferrocene + C3H8 ∆r𝐻om(g)=-19.7 Ferrocene + 2C4H10 = n-Propylferrocene + C2H6 + C3H8 ∆r𝐻om(g)=-19.3 n-Butylferrocene ∆f𝐻om(g)=129.2 ± 0.7 Ferrocene + C6H14 = n-Butylferrocene + C2H6 ∆r𝐻om(g)=-17.3 Ferrocene + 2C4H10= n-Butylferrocene + 2C2H6 ∆r𝐻om(g)=-16.8 Ferrocene + 2C5H12 = n-Butylferrocene + 2C3H8 ∆r𝐻om(g)=-17.1

18 a

Details on calculations are given in Table S7. Uncertainties correspond to the twice standard deviation of the mean and do not account for the uncertainty of the experimental enthalpies of formation of the reaction participants and the uncertainty of the computation method. For the most stable conformers of the alkylsubstituted ferrocenes the enthalpies H298 have been estimated at the B3LYP/def2-TZVP level of theory and they were converted to enthalpies of formation ∆f𝐻om(g, 298.15 K) with help of the isodesmic reactions by using the ferrocene as the reference molecule (see Table 7). Using enthalpies of isodesmic reactions, ∆r 𝐻𝑜m(g), calculated from enthalpies H298 of ferrocene derivatives together with the enthalpies of formation, ∆f𝐻om(g), of ethane, n-propane, and n-butane (all data from Pedley et al. [52]), theoretical enthalpies of formation of alkylsubstituted ferrocenes have been calculated (see Table 5, column 6). Theoretical enthalpy of formation of n-butylferrocene calculated via isodesmic reactions value ∆f𝐻om(g) = 129.2±0.7 kJ·mol-1 is in very good agreement with the experimental value ∆f𝐻om(g) = 128±6 kJ·mol-1 derived in Table 5, proving the necessary confidence to the thermochemical data for the ferrocene derivatives evaluated in this work. 3.5 Structure-property correlations of enthalpies of formation The DFT calculation performed in section 3.4 have established the internal consistency of the gas-phase enthalpies of formation of alkylferrocenes collected in Table 5. An additional validation has been performed with the help of the structure-property correlations as follows. Indeed, the general structure-property correlation according to Eq. (5) observed for vaporization enthalpies of alkylbenzenes and alkylferrocenes can also be applied for correlation of formation enthalpies ∆f𝐻om(g, 298.15 K) of alkylferrocenes (see Table 5, column 6) with those of the alkylbenzenes, where reliable experimental data are available from the literature (see Table S3). From the plotting of ∆f𝐻om(g, 298.15 K) of alkylferrocenes (R-Fe) against ∆f𝐻om(g, 298.15 K) of alkylbenzenes (R-C6H5) a following linear trend (for six data pairs, see Fig. S5) was observed: ∆f𝐻om(g, 298.15 K, R-Fe)/(kJ·mol-1) = = 141.0 + 1.1×∆f𝐻om(g, 298.15 K, R-C6H5) with (R2 = 0.9995)

(8).

The very high correlation coefficient R2 is an apparent evidence of the mutual consistency of both data sets involved in the correlation according to Eq. (8). As can be seen from Table 5, enthalpies of formation of alkylferrocenes estimated by Eq. (8) are in agreement within ± 1-2 kJmol-1 with the system of theoretical ∆f𝐻om(g, 298.15 K)-values obtained from the DFT method, as well as with the experimental values for ferrocene and n-butyl-ferrocene (see table 5, columns 5-7). For this reason we suppose that Eq. (8) can be used for a quick, but reliable

19

assessment of ∆f𝐻om(g, 298.15 K) of the broad range of the alkylferrocenes based on the available [52] thermochemical properties of the similarly shaped alkylbenzenes. The liquid phase formation enthalpies are also of importance for industrial applications. From the plotting of ∆f𝐻om(liq, 298.15 K) of alkylferrocenes, R-Fe, (see Table 5, column 2) against ∆f𝐻om(liq, 298.15 K) of alkylbenzenes, R-C6H5, (for five data pairs, see Table S3) a following linear trend (see Fig. S6) was observed: ∆f𝐻om(liq, 298.15 K, R-Fe)/(kJ·mol-1) = = 120.7 + 1.1×∆f𝐻om(liq, 298.15 K, R-C6H5) with (R2 = 0.9995)

(9).

Also in this case the very high correlation coefficient R2 can be considered as an evidence of the mutual consistency of both data sets involved in the correlation according to Eq. (9). Enthalpies of formation of alkylferrocenes estimated by Eq. (9) are in agreement within ± 1-2 kJmol-1 with the empirical ∆f𝐻om(liq, 298.15 K)-values (see table S8). Consequently, we could recommend Eq. (9) for assessment of ∆f𝐻om(liq, 298.15 K) of the broad range of alkylferrocenes based on the reliable thermochemical properties of the similarly shaped alkylbenzenes [52]. Another way for prediction of ∆fHom(g or liq, 298.15 K)-values of alkylferrocenes is using of the group-additivity procedure similar to those suggested in Section 3.2.1 for assessment of vaporization enthalpies. In order to derive the group contribution for the gasphase and the liquid phase ferrocene moieties [C5H5-Fe-C5H4] and [C5H4-Fe-C5H4], we used enthalpies of formation ∆f𝐻om(g or liq) compiled in Table 5. Details on the calculation procedure are given in Supporting Information. The numerical values for ferrocene moieties are given in Table 4, columns 3 and 4. These values together with group-contributions for the alkyl chain could be used for calculation of ∆f𝐻om(g or liq) of alkylferrocenes of different structures. 4. Conclusions In this paper we carefully collected experimental vapor pressure and vaporization enthalpy data for the series of alkylsubstituted ferrocenes. We proved the internal consistency of our experimental data on vaporization and formation enthalpies by using structure-property analysis and quantum-chemical calculations. The simple group-contribution procedure was developed for calculation enthalpies of vaporization and enthalpies of formation of alkylsubstituted ferrocenes based on the reliable data for alkylsubstituted benzenes. Parameters of these procedures are expected to be transferable for prediction of thermodynamic properties of other organometallic compounds. Acknowledgements

20

Authors gratefully acknowledge financial support from the Government of Russian Federation (decree №220 of 9 April 2010), agreement №14.Z50.31.0038. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:

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Graphical abstract

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Highlights

Vapor pressures of alkylferrocenes were measured by transpiration and static methods Vaporization enthalpies were derived and compared with the literature Experimental data were evaluated and validated with help of empirical methods Enthalpies of formation were validated by quantum chemistry Group-contribution method developed for prediction thermochemical properties

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: