Accurate Computational Thermodynamics Using Anharmonic Density

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Article Cite This: ACS Omega 2019, 4, 8786−8794

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Accurate Computational Thermodynamics Using Anharmonic Density Functional Theory Calculations: The Case Study of B−H Species Robert Maillard, Daniel Sethio,† Hans Hagemann, and Latévi M. Lawson Daku* Department of Physical Chemistry, University of Geneva, Quai Ernest Ansermet 30, 1211 Geneva, Switzerland

Downloaded by 79.133.107.99 at 00:36:38:767 on May 25, 2019 from https://pubs.acs.org/doi/10.1021/acsomega.9b00218.

S Supporting Information *

ABSTRACT: The thermal decomposition of boron−hydrogen compounds is complex and multistep and involves the formation of various intermediates. An accurate description of the thermodynamics of the reactants, products, and intermediates is required for an in-depth understanding of their reactivity. In this respect, we have proceeded to the accurate determination of the key thermodynamic functions (ΔH(T), S(T), and CP(T)) of 44 isolated B−H molecular species involved in the decomposition of B−H solids, with the inclusion of anharmonic effects. An excellent agreement is observed with available experimental data. We report the analytic expressions of these functions obtained by fitting them with NASA functions in the 200−900 K temperature range. Because the vibrational spectra of these species are their fingerprints, we also report the predicted IR and Raman spectra. The calculated anharmonic spectra show an excellent agreement with experiments and allow for a clear-cut identification of fundamentals, combinations, and overtones.

1. INTRODUCTION Boron hydrogen compounds have been attracting a considerable interest over the years since the pioneering works of Schlesinger et al. (Nobel prize 1979) and Muetterties (Nobel prize 1976) (see, for instance, refs1,2). Since about 20 years, they have been studied as potential hydrogen storage materials3,4 with high gravimetric and volumetric hydrogen content, leading to a wealth of new compounds with BH4− which have been prepared and characterized.5 Higher boranes such as B12H2− 12 and their derivatives can be used for neutron therapy applications, and more recently, as solid ionic conductors for all-solid-state batteries.6−8 However, reversible and rapid hydrogen release and absorption reactions of materials such as Mg(BH4)2 is not easily achieved and a detailed understanding of the different reactions taking place during hydrogenation and dehydrogenation is still lacking. In the course of a detailed extensive study of hydrogen storage in these materials,9−11 it appeared useful to obtain accurate thermochemical data of these compounds to probe possible reaction pathways. For a series of neutral gaseous boron−hydrogen species such as B2H6, B4H10, B5H9, ..., thermodynamical data have been collected and reviewed by Yu and Bauer.12 More recently, solid-phase equilibria using CALPHAD methods have been applied to systems like Mg(BH4)2 and solid solutions of alkali borohydrides.13,14 In this paper, we present an entirely theoretical approach using anharmonic density functional theory (DFT) calculations © 2019 American Chemical Society

to obtain thermochemical data of the 44 different gaseous boron hydrogen species (charged and neutral) shown in Table 1. This approach is validated by detailed comparisons with available experimental structural and spectroscopic data for the reference compounds BH3, B2H6, B4H10, and B5H9. These calculations allow us to obtain the temperature-dependent heat capacity, entropy, and enthalpy data, which are parameterized with the NASA functions15,16 in the 200−900 K temperature range, and to study theoretically possible reaction pathways including intermediates which so far have only been poorly characterized. The excellent agreement with available experimental data indicates that our theoretical approach may also find general applications for other families of compounds and provide thermochemical predictions with a good accuracy when experimental data are lacking or difficult to obtain.

2. COMPUTATIONAL DETAILS All calculations were performed with the Gaussian16 program package17 using the procedure reported in ref 18 for the accurate prediction of the vibrational species of boron−hydrogen species. The dispersion-corrected B3LYP-D2 functional19−22 was thus employed in combination with the correlation-consistent Received: January 24, 2019 Accepted: April 30, 2019 Published: May 22, 2019 8786

DOI: 10.1021/acsomega.9b00218 ACS Omega 2019, 4, 8786−8794

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with ΔH(T) = H(T) − H(0 K). Data analyses were carried out using the Igor program27 and Perl and Python scripts. Molecular visualization was done using GaussView28 and a trial version of Chemcraft.29 For BH3, B2H6, and B4H10, the calculations have also been performed using the cc-pVQZ basis sets: passing from the ccpVTZ to the cc-pVQZ basis set led to negligible changes in the calculated structures and in the calculated harmonic and anharmonic vibrational frequencies and spectra. This indicates that the reported results do not suffer from noticeable basis set truncation effects.

Table 1. Structures and Chemical Formulae of the 44 Investigated B−H Species

3. RESULTS AND DISCUSSION 3.1. Predicted Structures, Rotational Constants, and Anharmonic Frequencies. 3.1.1. Structures and Rotational Constants. The structures and ground-state rotational constants of some boranes have been accurately determined using (i) rotational−vibrational spectroscopy: BH3,30,31 Table 2. Calculated Structural Parameters and GroundState Rotational Constants (A0, B0, C0) of 11BH3 (D3h)a r(B−H) (Å) A0 = B0 (cm−1) C0 (cm−1)

calc.

exp.b

1.189 7.8622 3.8726

1.185c 7.8741 3.8788

a

Available experimental data are also shown. bRovibrational spectroscopy, ref 30. cRovibrational spectroscopy, note that the often quoted B−H bond length of 1.190 Å corresponds to the B−H bond length in the ground vibrational state determined from the B0 constant (see ref 30).

Table 3. Calculated Structural Parameters and GroundState Rotational Constants (A0, B0, C0) of 11B2H6 (D2h)a

cc-pVTZ basis set23 to determine the geometries of the 44 molecules using an “ultra-fine” integration grid and “tight” convergence criteria for the forces and displacements. Subsequent vibrational frequency analyses were then conducted both in the harmonic and in the anharmonic approximation using the second-order perturbation theory as implemented in Gaussian16.24−26 For the present studies, the 11B and 1H isotopes only were considered. The molar heat capacity CP(T), molar entropy S(T), and molar enthalpy H(T) of each molecule were calculated at P = 1 (bar) using the perfect gas approximation. The temperature dependencies of these quantities were fitted in the 200−900 K temperature range with the NASA functions15,16

a

Available experimental data are also shown. bRovibrational spectroscopy, ref 32. cRovibrational spectroscopy, ref 33.

Table 4. Calculated Structural Parameters and GroundState Rotational Constants (A0, B0, C0) of 11B4H10 (C2v)a

CP(T ) = a1 + a 2T + a3T 2 + a4T 3 + a5T 4 R

a

Available experimental data are also shown. bRotational spectroscopy, ref 34. cGED and X-ray crystallography, ref 37.

a T2 a T3 a T4 a aT ΔH(T ) = a1 + 2 + 3 + 4 + 5 + 6 RT 2 3 4 5 T

B2H6;32,33 (ii) microwave rotational spectroscopy: B4H10,34 B5H9,35 and B6H10;36 (iii) gas-phase electron diffraction (GED): B4H1037 and B5H9;38 and (iv) X-ray crystallography: B4H1037 and B6H10.39 Tables 2−6 allow the comparison of our

a T2 a T3 a T4 S(T ) = a1 ln (T ) + a 2T + 3 + 4 + 5 + a7 R 2 3 4 8787


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Table 5. Calculated Structural Parameters and GroundState Rotational Constants (A0, B0, C0) of 11B5H9 (C4v)a

Table 8. Calculated Harmonic and Anharmonic Vibrational Frequencies (cm−1) and Available Experimental Data for B2H6 (D2h) calc. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

a

Available experimental data are also shown. bGED, ref 38. Rotational spectroscopy, ref 35. dAverage of the values given in Table 9 of ref 35.

c

Table 6. Calculated Structural Parameters and GroundState Rotational Constants (A0, B0, C0) of 11B6H10 (Cs)a

symmetry

harmonic

anharmonic

exp.42

B2u Ag Au B2g B1g B2u B1u B3g B3u Ag B3u B2g B1u Ag B3u Ag B1g B2u

379 819 869 900 972 1010 1017 1072 1228 1231 1746 1889 1996 2198 2646 2653 2706 2723

365 775 819 858 923 914 966 972 1174 1178 1541 1699 1944 2116 2517 2526 2579 2598

369 790 833 860 915 949 973 1020 1172 1183 1603 1760 1925 2088 2520 2530 2596 2609

Table 9. Calculated Harmonic and Anharmonic Vibrational Frequencies (cm−1) and Available Experimental Data for B4H10 (C2v) calc. a

Available experimental data are also shown. bX-ray crystallography, ref 39. cRotational spectroscopy, ref 36.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Table 7. Calculated Harmonic and Anharmonic Vibrational Frequencies (cm−1) and Available Experimental Data for BH3(D3h) calc.a 1 2 3 4

symmetry

harmonic

anharmonic

exp.b

calc.c

A2″ E′ A1 E′

1161 1230 2604 2697

1142 1179 2489 2533

1148 1197

1134 1196 2495 2588

2601

a

This work. bReference 31. cReference 40.

calculated and the experimental structures and rotational constants of these boranes. In all cases, an excellent agreement is observed between calculated and experimental ground-state rotational constants and between the calculated structures and those obtained from rotational and rotational−vibrational spectroscopies. For B4H10 (Table 4) and B5H9 (Table 5), our results emphasize the noticeable overestimation of the B−H bond lengths by the GED and X-ray crystallography methods. For B6H10 (Table 6), our predicted B−H bond lengths thus prevail over the available experimental ones determined by X-ray crystallography. For B4H10, the B1−H3 bond length determined by rotational spectroscopy is actually larger than the optimized bond length and exhibits a large uncertainty, which reflects difficulties tied to the determination of bridge hydrogen coordinates (see ref 34). More generally, given the accuracy demonstrated here by our calculations for BH3, B2H6, B4H10, B5H9, and B6H10, they provide reference data for the 8788

symmetry

harmonic

anharmonic

exp.43

A1 B2 A2 B2 A1 B1 A2 A1 B1 A1 A1 B2 A2 B1 B2 A1 B1 A2 A2 B1 B2 A1 B2 A2 B1 A1 A1 B1 B2 A2 B2 A1 A1

225 379 422 482 572 585 684 693 776 816 874 895 928 931 972 1022 1027 1054 1123 1139 1189 1207 1349 1481 1540 1578 2240 2249 2259 2270 2615 2620 2692

186 361 405 415 541 544 645 672 744 785 840 844 858 887 892 963 992 1015 1042 1063 1118 1148 1239 1317 1362 1437 2138 2138 2132 2146 2511 2516 2572

238

483 559 662 737 785 827 898 868 846 908 965 966 1023 1117 1071 1140 1196 1255 1308 1410 1444 2095 2150 2150 2150 2475 2475 2570


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Table 9. continued calc. 34 35 36

symmetry

harmonic

anharmonic

exp.43

B2 B1 A1

2694 2707 2714

2574 2595 2605

2570 2570 2570

Table 10. Calculated Harmonic and Anharmonic Vibrational Frequencies (cm−1) and Available Experimental Data for B5H9 (C4v)a calc. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

symmetry

harmonic

anharmonic

exp.

B2 E E B1 E E B2 A1 B1 E E B2 A1 A2 E E E E A1 B1 E E A1 A2 E E B2 B1 E E A1 B2 E E A1 A1

481 587 587 624 641 641 712 736 772 806 806 818 822 852 924 924 953 953 1035 1063 1119 1119 1199 1451 1568 1568 1704 1950 1961 1961 2009 2734 2740 2740 2740 2750

460 570 570 608 617 617 686 711 733 784 784 791 800 808 896 896 935 935 1009 1001 1047 1047 1159 1238 1437 1437 1524 1892 1944 1944 1884 2628 2653 2653 2612 2680

470b 569c 569c 599c 618c 618c 701c 741c

Figure 1. Calculated anharmonic IR spectrum of B2H6 (D2h): (Top) comparison with the normalized experimental IR spectrum from the National Institute of Standards and Technology (NIST) Chemistry WebBook46 and (Bottom) contributions from fundamentals and combinations.

785c 799c 890c 890c 918c 918c 985c 1036c 1035c 1035c 1126c 1450d 1410c 1410c 1500d 1870b 1634c 1634c 1844c 2610c 2610c 2610c 2610c 2628c

A weak IR band at 918 cm−1 has been observed but was not assigned; we associate it with the E mode calculated at 935 cm−1. b Reference 44. cReference 41. dReference 45.

Figure 2. Calculated anharmonic IR spectrum of B4H10 (C2v): (Top) comparison with the normalized experimental IR spectrum from the NIST Chemistry WebBook47 and (Bottom) contributions from fundamentals, combinations and overtones.

structures and rotational constants of the other less well experimentally characterized B−H species. 3.1.2. Vibrational Frequencies. Highly accurate results have also been obtained for the vibrational frequencies of the studied molecules from the anharmonic frequency calculations. This is illustrated by the comparison in the following tables of the calculated harmonic and anharmonic frequencies with the exhaustive experimental data available for BH3 (Table 7), B2H6 (Table 8), B4H10 (Table 9), and B5H9 (Table 10).

One observes that, in all cases, the inclusion of anharmonicity is needed to bring the calculated frequencies into an excellent agreement with the experimental data. For BH3, one can also note in Table 7 the very good match between our DFT-calculated anharmonic frequencies and those determined by Martin and Lee40 from a quartic polynomial expansion of the potential energy surface based on highly accurate CCSD(T) calculations. In the case of B5H9, a weak IR band was observed at 918 cm−1 but was not assigned:41 our results

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Table 12. Thermochemistry at T = 300 K and P = 1 Bar of the Gas-Phase Reactions BkHl + B5−kH9−l ⇆ B5H9(C4v), (k,l) ∈ {(1,4)(2,3),(2,4)(2,6),(2,7)}a

Figure 3. Calculated anharmonic IR spectrum of B6H10 (Cs): (Top) comparison with the normalized experimental IR spectrum from the NIST Chemistry WebBook,48 and (Bottom) contributions from fundamentals, combinations and overtones.

Table 11. Estimates of the Room-Temperature Entropy of Hydration of BH4− and B10H2− 10 Obtained from Our Calculated Gas-Phase Entropies and the Available Experimentally Determined Entropies of the Anions in Water53−55 S (J mol−1 K−1) −

BH4 B10H2− 10 B12H2− 12

gas phasea

aqueousb

189.7 342.9 352.9

107 ± 5, 110 251 ± 17e 259 ± 17e c

ΔShyd (J mol−1 K−1) d

≈−80 ± 5 ≈−92 ± 17 ≈−94 ± 17

a

This work, calculated 300 K gas-phase values. bExperimental roomtemperature entropy in water. cReference 53. dReference 54. e Reference 55.

The reaction entropy ΔrS° is in J mol−1 K−1 and the reaction enthalpy ΔrH° and the reaction Gibbs free energy ΔrG° = ΔrH° − TΔrS° are in kJ mol−1. a

3.2. IR and Raman Spectra. Figures 1−3 allow the comparison of the calculated anharmonic and experimental IR spectra of B2H6, B4H10, and B6H10, respectively. For the three molecules, there is a remarkable agreement between the calculated and experimental spectra, which allows for clear-cut identifications of the contributions from fundamentals, combinations, and overtones. The observed agreement makes us quite confident about the accuracy achieved for the determination of both the IR and Raman spectra of the investigated systems (see Supporting Information). 3.3. Thermodynamic Properties. Despite their importance, there is a rather scarce number of accurate experimental thermodynamic/thermochemical data available for molecular B−H species. The entropy of the highly reactive BH3 species has been experimentally determined at 300 K and ambient

Figure 4. Calculated heat capacity CP(T) curve of diborane compared with the experimental data of Stitt published in the Journal of Chemical Physics (this author reported CV(T), with CP(T) = CV(T) + R in the perfect gas approximation)56 and the plot of the NASA function calculated using the tabulated NASA function parameters of Yu and Bauer published in the Journal of Physical and Chemical reference data.12

allow to associate it with the E mode calculated at 935 cm−1 (Table 10). 8790


BH3 BH3− BH4 BH4− B2H3 B2H4 isomer B2H4 isomer B2H5 B2H5− B2H6 B2H7 B3H B3H2 B3H3 B3H5 B3H6 isomer B3H6 isomer B3H7 B3H8− B3H9 B3H10 B4H B4H2 B4H3 B4H4 B4H5 isomer B4H5 isomer B4H5 isomer B4H7 isomer B4H7 isomer B4H7 isomer B4H8 B4H9 B4H10 B5H9 B5H11 B6H10 B6H12 B8H14 B8H8− B9H2− 9 B10H2− 10 B11H14− B12H2− 12

A B C A B C

A B

A B

4.43646625 3.51626969 2.75690268 4.80878961 2.21669916 2.04240931 2.04379152 2.18504002 2.04605446 2.64851285 9.07279464 × 10−1 2.14017355 1.29198847 7.02006816 × 10−1 −2.61505190 × 10−1 −1.28189391 −1.51506009 4.98142227 × 10−1 7.60427779 × 10−1 7.83801266 × 10−1 4.31719851 × 10−1 1.85253850 3.08953875 × 10−1 −1.49006898 −1.45008503 −1.91597228 −1.63470483 −2.38211263 −2.33562715 −2.77357836 −3.86802260 −2.45465439 −2.85164894 −1.31964869 −3.97374108 −3.37543950 −6.21937684 −4.45043454 −9.25712045 −1.05717585 × 101 −1.24015960 × 101 −1.67646723 × 101 1.80362672 × 101 −2.00029105 × 101

a1 −7.34715737 3.41787957 6.77530806 −1.38063288 1.80909315 1.95462075 1.28067728 1.77067045 6.95773848 3.90242088 2.16705961 1.19420229 2.72533564 2.91185730 4.02043832 5.17975644 4.74724730 2.50164610 2.91917219 3.31150340 5.33706886 1.68691508 3.07579788 5.25014897 4.92877986 6.51429263 6.15278359 6.35388385 5.96272229 6.21887652 6.84829445 5.13752984 6.26512970 4.61278735 5.22817757 6.51623062 7.64435521 7.55806736 1.21424164 1.27005298 1.42231461 1.67016990 1.85243695 1.78490914

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

a2 [K−1] 10 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−1 10−1 10−1 10−1 10−1 10−1

−3

3.36216205 5.69329038 1.31144691 6.50008596 −1.50820137 −9.10474574 1.25545362 7.23971437 4.86872153 5.56787255 3.04145966 1.65174428 −3.39111664 −2.45850153 −3.44100344 −5.49280642 −3.73635271 3.57745649 2.86907121 1.68570110 −2.42758148 5.99769614 −1.78590382 −6.74328199 −4.63009233 −8.32870010 −7.48926430 −7.66537515 −4.11013127 −4.71496877 −6.56151834 −3.36992512 −2.99315509 2.43129463 3.34596103 7.36631132 −1.69083198 7.79783604 −5.01284569 −1.16140371 −1.22193332 −1.43328863 −1.39851736 −9.32270797

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

a3 [K−2] 10 10−6 10−5 10−5 10−5 10−6 10−5 10−6 10−5 10−5 10−5 10−6 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−6 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−5 10−6 10−5 10−5 10−5 10−6 10−6 10−6 10−5 10−4 10−4 10−4 10−4 10−5

−5

−3.76287308 −7.07535773 −2.21348044 −7.51198500 4.84636137 −3.87862898 −2.83612361 −2.52536177 −7.71256114 −8.01318548 −6.48078244 −1.67602595 2.16776350 5.84346534 1.09717420 3.07857039 8.35670783 −7.69789757 −6.69389972 −4.77272724 −1.05496823 −3.02053831 −9.91836591 4.16002550 1.45821323 5.31442140 4.61273685 4.60138736 −9.85335732 5.65068724 2.89097660 −4.70452758 −1.66649429 −7.89747607 −1.05480072 −7.64940724 −7.99613718 −8.84548969 −5.55556321 2.65367043 1.55916164 1.55760767 −4.04853619 −8.14761823

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

a4 [K−3] 10 10−9 10−8 10−8 10−9 10−9 10−8 10−8 10−8 10−8 10−8 10−8 10−8 10−9 10−8 10−8 10−9 10−8 10−8 10−8 10−8 10−8 10−9 10−8 10−8 10−8 10−8 10−8 10−10 10−9 10−8 10−8 10−8 10−8 10−7 10−8 10−8 10−8 10−8 10−8 10−8 10−8 10−9 10−8

−8

1.45622595 2.33876733 9.76117263 2.93805256 4.80517193 4.11675726 1.36938361 1.31120001 3.49837356 3.48276191 3.17015472 9.92725495 −5.33384397 2.14810147 1.04860540 −6.49408825 3.07712886 3.80221878 3.28833637 2.31053521 1.03291324 1.72131660 1.06318954 −9.14410110 2.16874272 −1.25356799 −1.06011046 −1.00040903 9.91260739 7.19100268 −3.08829068 2.88185813 1.61692636 4.13635659 5.60911507 4.40709360 4.88558744 5.11787646 4.53110512 1.23014344 2.10180513 2.68122669 3.71584656 7.59519574

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

a5 [K−4] 10−11 10−12 10−12 10−11 10−13 10−12 10−11 10−11 10−11 10−11 10−11 10−12 10−12 10−12 10−12 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−12 10−12 10−11 10−11 10−11 10−12 10−12 10−12 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 10−11 −1.47281413 3.43660996 1.06003734 −2.79220100 1.16283966 1.20873375 1.53064633 1.32626703 1.85026750 1.31708809 2.38513981 1.54349310 1.70691846 2.31595413 2.80325765 3.40815835 3.80622538 2.78437904 2.38279380 2.07340315 2.02493664 1.69413313 2.78010933 3.86449967 3.82947082 4.14617946 3.57155748 4.43368622 4.43262610 4.63953772 5.42010038 4.66478218 4.72926004 3.84676066 6.33242189 5.30707109 7.69030741 6.20139227 9.43397270 1.03439458 1.18905256 1.52338766 1.58759546 1.83484530

a6 [K] × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × 101 101 102 101 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 103 103 103 103 103

−1.62137247 1.74721584 6.68717786 −2.77891582 1.04393087 × 1.08593909 × 1.16702445 × 1.15494013 × 1.28744937 × 9.87391602 1.80626105 × 1.27648239 × 1.56996468 × 1.90004344 × 2.20826645 × 2.61670235 × 2.81908687 × 2.11302145 × 1.91649398 × 1.95556450 × 2.05286862 × 1.50179708 × 2.04554152 × 2.79868350 × 2.86540506 × 3.04639079 × 2.87888157 × 3.22403242 × 3.24172413 × 3.40327228 × 3.76032108 × 3.34361769 × 3.46702493 × 2.84168277 × 3.97788622 × 3.79325316 × 5.02842137 × 4.29664666 × 6.23364913 × 6.56323785 × 7.42280363 × 9.30345994 × 9.79994828 × 1.07790437 ×

a7

101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 102

101 101 101 101 101

Table 13. Parameters (ai, i = 1, ..., 7) of the NASA Functions Used to Fit the Thermodynamic CP(T), S(T), and ΔH(T) = H(T) − H(0 K) Functions in the 200−900 K Range

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pressure:49 Sexp.(300 K) = 187.9 J mol−1 K−1, which our calculated value of Scalc.(300 K) = 188.6 J mol−1 K−1 is in excellent agreement with. Similarly, there is a remarkable agreement between the measured and calculated values of the entropy of B5H9 at 296 K: Sexp.(296 K) = 274.8 J mol−1 K−1 and45,50 Scalc.(296 K) = 276.8 J mol−1 K−1. For a system whose entropy in a given solvent could be experimentally determined, its calculated gas-phase entropy can be used to reliably determine the corresponding solvation entropy, with an uncertainty mostly dictated by the one on the experimental data. This is illustrated in Table 11, wherein we report our best estimates of the entropy of hydration ΔShyd of 2− the anions BH4−, B10H2− 10 , and B12H12 . For the three anions, one notes that ΔShyd < 0, which is consistent with the fact that, upon hydration under ambient conditions, there is an entropy decrease for all types of solutes.51,52 Furthermore, despite their differences, the hydration entropies of the three anions turn out to be very similar. This calls for further investigation of the hydration structure and dynamics in solution of these species. In Figure 4, we plot in the 100−900 K range, our predicted heat capacity CP(T) curve of diborane and compare it with the one obtained from the experimental data of Stitt56 and with the calculated curve by Yu and Bauer.12 Our curve reproduces very well the experimental data and nicely matches the one of Yu and Bauer. The slight difference between the two calculated curves originates from the differing chosen atomic masses. Our calculated thermodynamic data also allow the accurate prediction of the thermochemistry of reactions involving the investigated B−H species. Thus, for the archetypical gas-phase dimerisation reaction of borane

Finally, as a last application of our results, we have characterized the thermochemistry at T = 300 K and P = 1 bar of the gas-phase reactions Bk Hl + B5 − k H 9 − l ⇆ B5H 9(C4v)

with (k,l) ∈ {(1,4)(2,3),(2,4)(2,6),(2,7)}. The results are summarized in Table 12. In all cases, the calculated reaction entropy ΔrS° is negative, as this could have been anticipated from the decrease of the total number of molecules during the reactions; ΔrS° turns out to span a narrow range: −226 J mol−1 K−1 < ΔrS° < −209 J mol−1 K−1. The considered reactions are actually strongly exothermic with −765 kJ mol−1 < ΔrH° < −234 kJ mol−1, and this does more than compensate for the fact that the reactions are entropically disfavored because they are all strongly exergonic.

4. CONCLUSIONS Taking anharmonicity into account allowed us to achieve a highly accurate description of the thermodynamic properties of 44 B−H species involved in the decomposition of hydrogenstorage B−H materials. For all species, the parameters (ai, i = 1, ..., 7) of the NASA functions used to fit the thermodynamic CP(T), S(T) and ΔH(T) = H(T) − H(0 K) functions in the 200−900 K range have been tabulated (Table 13). Their structures, their rotational constants, and their IR and Raman spectra (with the contributions of fundamentals, combinations, and overtones) are made available to the research community as the Supporting Information. An important aspect of the present work is that our theoretical approach can be readily extended to other families of main group compounds, allowing for the accurate prediction of the thermochemistry of species as highly reactive as the investigated B−H species.

2BH3(g) ⇆ B2H6(g)

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McCoy and Bauer determined under ambient conditions (300 K, 1 atm), a reaction entropy of ΔrS°exp.(300 K) = −143.2 J mol−1 K−1,49 with which our predicted value of ° (300 K) = −144.4 J mol−1 K−1, is in excellent ΔrScalc. agreement. The accurate determination of the associated enthalpy of reaction remains challenging both experimentally and theoretically. From their photoionization studies of BH3 and B2H6, Ruščić et al.57 determined the current best experimental estimate of the 0 K dimerization enthalpy of ΔrH°exp.(0 K) = (−143.5 to −163.6) ± 8.4 kJ mol−1. From the ° theoretical point of view, Feller et al.58 predicted ΔrHcalc. (0 K) = −159.4 kJ mol−1 from the results of CCSD(T) calculations extrapolated to the complete basis set limit and the use of experimental and scaled harmonic frequencies for calculating the contributions of the zero-point vibrational ° (0 K) energies (ZPVEs). Karton and Martin59 obtained ΔrHcalc. = −158.6 kJ mol−1 using the W4 theory and calculated anharmonic ZPVEs. Lately, Fracchia et al.60 determined ΔrH°calc.(0 K) = −153.1 kJ mol−1 by combining their quantum Monte Carlo calculation results and the anharmonic ZPVEs of Karton and Martin.59 Our calculations give ΔrHcalc. ° (0 K) = −151.5 kJ mol−1: this value fits quite well in the experimental range and it also quantitatively agrees with the above theoretical values, which probably are the current most accurate high-level theoretical estimates of the 0 K dimerization enthalpy. Such a remarkable agreement makes us quite confident about the accuracy of our results. In particular, our calculated value of ΔrH°calc.(300 K) = −159.6 kJ mol−1 probably constitutes the current best estimate of the 300 K dimerization enthalpy.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b00218. For each of the studied 44 species: structure; equilibrium rotational constants; tabulated harmonic and anharmonic values of the vibrational frequencies, IR intensities and Raman activities; plots of the IR and Raman spectra with the contributions of fundamentals, combinations, and overtones; tabulated and plotted ideal-gas thermodynamic functions CP(T), S(T), and H(T) − H(0) at 1 bar; results of the fits of the thermodynamic functions with the NASA functions; and tables of the optimized values of the NASA parameters (PDF) Comparison between the results obtained for BH3, B2H6, and B4H10 at the B3LYP-D2/cc-pVTZ and B3LYP-D2/ cc-pVQZ levels (selected anharmonic results, harmonic and anharmonic vibrational frequencies, anharmonic IR and Raman spectra) (PDF) Main results obtained for all studied species (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Robert Maillard: 0000-0003-3584-234X Daniel Sethio: 0000-0002-8075-1482 8792


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Hans Hagemann: 0000-0002-7183-8543 Latévi M. Lawson Daku: 0000-0003-1305-6807 Present Address †

Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Swiss National Science Foundation (project number 200021-169033) and by grants from the Center for Advanced Modeling Science (CADMOS; project ID: CTESIM).

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