Valence Bond Theory Allows a Generalized Description of Hydrogen Bonding

This paper describes the nature of the hydrogen bond (HB), B:---H–A, using valence bond theory (VBT). Our analysis shows that the most important HB interactions are polarization and charge transfer, and their corresponding sum displays a pattern that is identical for a variety of energy decomposition analysis (EDA) methods. Furthermore, the sum terms obtained with the different EDA methods correlate linearly with the corresponding VB quantities. The VBT analysis demonstrates that the total covalent-ionic resonance energy (RECS) of the HB portion (B---H in B:---H–A) correlates linearly with the dissociation energy of the HB, ΔEdiss. In principle, therefore, RECS(HB) can be determined by experiment. The VBT wavefunction reveals that the contributions of ionic structures to the HB increase the positive charge on the hydrogen of the corresponding external/free O–H bonds in, for example, the water dimer compared with a free water molecule. This increases the electric field of the external O–H bonds of water clusters and contributes to bringing about catalysis of reactions by water droplets and in water-hydrophobic interfaces.

Structures used for FLF (distance between F and H is optimal but wavefunction (orbitals) is taken from the FL∞ calculation and is not reoptimized).FLF is Frozen Lewis state with optimized orbitals from the long-distance calculation FL∞, calculated at the equilibrium distance without allowing the orbitals to relax.FLF rises from Pauli repulsion and the deformation energy of the fragments and stabilized by the electrostatic interaction.
Structures used for YFull (distance between F and H is optimal).YFull is a state that includes optimized orbitals from the Lewis structure and charge transfer structures at the equilibrium distance

Definition of Energies
FLO is a Lewis state with optimized orbitals at the equilibrium distance FLF is a Lewis state with optimized orbitals from the long distance calculated at the equilibrium distance without allowing the orbitals to relax FL∞ is a state with optimized orbitals at long distance YFull is a state that includes optimized orbitals from the Lewis structure and charge transfer structures at the equilibrium distance  Table S12.Total MP2/cc-pVTZ energies for linear and full optimized structures at optimal and long distances.At long distances (10Å) only bond lengths were reoptimized while angles were kept as in the optimal distance.DEt(opt) is the energy difference between total energies at optimal distances for linear and fully optimized structures.DELin and DEFull are the energy differences between the structures at optimal and long distances.is the energy differences between the linear structures at optimal and long distances calculated at the CCSD(T)/cc-pVTZ level.DEt(opt)= Et(opt, linear) -Et(opt,ful), DELin= Et(opt,linear) -Et(long,linear), DEFull= Et(opt,full) -Et(long,full Page S1.Valence Bond diagrams for 9 Hydrogen-Bonded Molecules that Span 2 the Range from Weak to Strong Bonding using BOVB/6-311G(p,d) calculations Figure S1.Energy Diagrams for HB 1-9 2 S2.The B:----H Portion of the HB ( Figure S5.Charges (BOVB in black for 6 structures, in blue for 3 structures 15 (3-5 or 3a-5a) and CCSD in red) S3.The Coulson-Chirgwin weights of the structures from BOVB/6-311G(p,d) 16 calculations with 6 structures S4.Structures with non-zero weights in the 50 structures VBSCF/6-311G(d,p) 18 calculations.S5.Cartesian coordinates (in Å) from CCSD(T)/cc-pVTZ optimized structures 18 References 19 S1.Valence Bond diagrams for 9 Hydrogen-Bonded Molecules that Span the Range from Weak to Strong Bonding using BOVB/6-311G(p,d) calculations.The diagrams show the energy components (in kcal/mol), DEF , DEint , DEdiss, DEPOL, and DECT of the HB in molecules 1-9 (see Scheme 2 in the manuscript).
a) DEdiss was calculated as a difference in the total energies of YFull and FL∞.In the parentheses DEdiss was calculated using equation DEdiss = DEPOL + DECT -DEF .

Figure S3 .
Figure S3.The correlation between RECS and DE'diss values, calculated for the B---H bond portions in BOVB/6-311G(p,d) calculations with 3 structures (structures 3-5 or 3a-5a) from Scheme 3 in the manuscript.Note that the dissociation of this bond is computed with the three structures which constitute the bond (3-5 or 3a-5a).Thus, DE'diss is different than the DEdiss values for the entire VB(6) set.

Figure S4 .
Figure S4.Mulliken charges in the (H2O)4 cluster, at the corresponding optimized structure (a) and for H-O hydrogen bond at 10.0 Å (b).The first line (black color) corresponds to MP2/cc-pVTZ charges in the gas-phase.Numbers in square parenthesizes correspond to MP2/cc-pVTZ charges in water solution.The second line (red color) corresponds to CCSD/cc-pVTZ charges in the gas-phase.Numbers in square parenthesizes correspond to CCSD/cc-pVTZ in water solution.

Table S17 .
Changes in the dissociation energies DDEdiss (kcal/mol ) upon changing the B-H

Table S18 .
The RECS and DEdiss Values (in kcal/mol) for the B----H Portion of the HBs.

The Coulson-Chirgwin weights of the six VB structures (see Scheme 2 in the manuscript) at the BOVB
H portion of HB (B----H-A).Numbers in red correspond to CCSD/cc-pVTZ calculations.The numbers in the bold font near the species correspond to the HB numbers in Scheme 2 in the manuscript.