Boranes and Azaborane Boranes and Azaborane with QMCwith QMC

Francesco Fracchia, Francesco Fracchia, Dario Dario BressaniniBressanini, Gabriele Morosi, Gabriele Morosi

Università dell’Insubria, Como, Università dell’Insubria, Como, ITALYITALY

QMC in the Apuan Alps QMC in the Apuan Alps VI 2010 – TTI Vallico VI 2010 – TTI Vallico

SottoSotto

HydridesHydrides

•Hydrides are potential hydrogen storage materials

• If H is bound to light elements (B, N,…) materials with a high hydrogen content per unit weight can be obtained

•Accurate thermodynamic data are required

•Some thermodynamic properties are not known, or their accuracy is not good enough

A short history of A short history of BB22HH66

• 1912: Boranes first studied by Alfred Stock

• 1925: X-ray, diborane, ethane-like structure?

• 1934: diborane is diamagnetic

• 1937: Bauer (electron diffraction), ethane-like

• only 12 valence electrons. What is the structure? (Valence Bond theory)

• Many hypothesis

A short history of A short history of BB22HH66

But diborane does not easily release protons

Ethane-like, but with unpaired electrons

A short history of BA short history of B22HH66

•1940: resonant structures with bridging hydrogens proposed

•1941: added ionic structures

A short history of BA short history of B22HH66

• 1941: Schlesinger in a letter to Pauling

As a result of our work on the metallo borohydrides I definitely feel that a structure for diborane quite different from those generally proposed, would aid in correlating many of the observations we have made […] The structure I have in mind is a bridge structure, in which the two boron atoms are joined to each other through an unusual type of hydrogen bond, perhaps best represented by the following formula

• Pauling’s reply:

A short history of A short history of BB22HH66

I do not feel very friendly toward the structure which you mention in your letter for the diborane molecule. So long as the suggested structure remains vague and indefinite, it is not easy to say that it is eliminated by electron data or other data. However, the force constant for the B-B vibration is I think much stronger than would be expected for a structure of this type, in which there is no direct B-B bond

• Later work by Longuet-Higgins, Hedberg and Shomaker, and especially Lipscomb confirmed the 2 electron 3 center “banana” bond

• 1976: Nobel prize in Chemistry to Lipscomb

Dimerization energy of BHDimerization energy of BH3 3 - - experimentsexperiments

• Dimerization energy BH3 + BH3 → B2H6 difficult to measure

Author D(B2H6) Year Method

Garabedian et al. 38.3 1964 Kinetic

Fehlner et al. 37.1 ± 4 1964 Kinetic

Burg et al. 35.0 1966 Kinetic

Sinke et al. 55 ± 8 1964 Mass spectroscopy

Fehlner et al. 39 1964 Mass spectroscopy

Wilson et al. 59 1967 Mass spectroscopy

Ganguli et al. 59 1969 Mass spectroscopy

Fehlner et al. 36 ± 3 1969 Mass spectroscopy

Ruscic et al. (34.3 - 39.1) ± 2 1988 Many sources

Dimerization energy of BHDimerization energy of BH3 3 – – ab initioab initio

• FN-DMC calculations for BH3, B2H6, BH3CO, BH2+

• Orbitals from B3LYP always slightly better than HF

QMC calculationsQMC calculations

Psi Basis set MO HF MO B3LYP Δ (mhartree)

BH3 1 det DZp -26.5960 (1) -26.5969 (1) -0.9

BH3 1 det Thd+qz3p -26.5971 (1) -26.5979 (1) -0.8

BH3 1 det CH-qz3p -26.5976 (1) -26.5980 (1) -0.4

BH3 2 det CH-qz3p -26.5978 (1) -26.5980 (1) -0.2

B2H6 1 det DZp -53.2596 (4) -53.2639 (2) -4.3

B2H6 1 det Thd+qz3p -53.2625 (2) -53.2654 (2) -2.9

B2H6 1 det CH-qz3p -53.2638 (3) -53.2651 (1) -1.2• The could not be improved by adding determinants

IntermezzoIntermezzo•A single determinant can be improved

using a Backflow Transformation

•However using Backflow alone, on a single determinant is not sufficient, since the topology is still wrong

)()( RR TTBF

nodestwoleastatTT 0)()(

RR

HFWe still must add determinants or use a different functional form

IntermezzoIntermezzo

• If the 2-nodal regions conjecture is true:

•The Kohn-Sham wave function, even with the exact exchange-correlation, has the wrong nodal topology (Nodal regions > 2)

•Wrong but exact density and energy

• In QMC we use from DFT

• Should we trust it?

• Why does it give better nodes than HF?

Dimerization energy of BHDimerization energy of BH3 3 – – QMCQMC

This work FN-DMC -37.04(1)Experimental (-39.1 ~ -34.3) ±2

AzaboraneAzaborane

• Azaborane BH3NH3 is a stable, nontoxic solid

• 19.5% by weight is hydrogen.

• High melting point (110-114°C) due to dihydrogen bond B−Hδ-···δ+H−N

• Can release hydrogen reversibly • nBH3NH3→ [BH2NH2]n+nH2

AzaboraneAzaborane

•However

• No efficient regeneration process is known

• Lack of experimental data

•Dissociation energy has not been measured

• BH3NH3 → BH3 + NH3

•Few ab initio calculations

AzaboraneAzaborane• FN-DMC

• Single determinant, B3LYP orbitals + Jastrow

• ZPE and thermal corrections computed with GAMESS

• Comparison with other calculations

Author Method ΔEbond ΔHdiss(0K) ΔHdiss(298K)

Ricca et al. CCSD(T)/aug-cc-pVTZ 31.1 24.6

Dixon et al. CCSD(T)/CBS 31.64 25.92 27.7

Present work FNDMC 31.6(2) 25.6 27.4

NHNH33, comparison, comparison

Method N basis set Energy (hartree)CCSD(T)/aug-cc-pVTZ 130 -56.497886CCSD(T)/aug-cc-pVQZ 270 -56.527293CCSD(T)/aug-cc-pV5Z 365 -56.538421CCSD(T)/aug-cc-pCV5Z 434 -56.55922FN-DMC CH-qz3p 87 -56.5527 (1)

•Total energy of NH3

Other calculations Other calculations (NH(NH33,NH,NH44

++))

•Protonic Affinity of NH3

• NH3 + H+ → NH4+

•Effect of diffuse functions in basis setBasis set E(NH3) E(NH4

+) PAelec (kcal/mol)

CH-qz3p -56.5527 (1) -56.8914 (2) 212.6 ± 0.25

aug-CH-qz3p -56.5528 (2) -56.8916 (2) 212.6 ± 0.25

Other calculations Other calculations (NH(NH33,NH,NH44

++))

Method basis set PAelec(kcal/mol)

MP2 aug-cc-pVQZ 210.59MP3 aug-cc-pVQZ 212.62MP4 aug-cc-pVQZ 211.48CCSD aug-cc-pVQZ 212.8CCSD(T) aug-cc-pVQZ 211.82CCSD(T) aug'-cc-pV5Z 211.83FN-DMC CH-qz3p 212.6 ± 0.25

ConclusionsConclusions

•Boron compounds are chemically very interesting

•There is still “work to do”

•Rather small molecules

•QMC seems well suited, even for larger boranes