Upon formation of a H bond Y...H-XZ, intramolecular hyperconjugation n(Z)-->sigma*(X-H) of the proton donor plays a key role in red- and blueshift characters of H bonds and must be introduced in the concepts of hyperconjugation and rehybridization. Intermolecular hyperconjugation transfers electron density from Y to sigma*(X-H) and causes elongation and stretch frequency redshift of the X-H bond; intramolecular hyperconjugation couples with intermolecular hyperconjugation and can adjust electron density in sigma*(X-H); rehybridization causes contraction and stretch frequency blueshift of the X-H bond on complexation. The three factors--intra- and intermolecular hyperconjugations and rehybridization--determine commonly red- or blueshift of the formed H bond. A proton donor that has strong intramolecular hyperconjugation often forms blueshifted H bonds.

Ab initio calculations have been performed to study the structures, binding energies, and bonding properties of the hemi-bonded binary complexes (XH2P···NH2Y)(+) with the substituents X and Y being H, F, Cl, Br, NH2, CH3, and OH. The P···N interactions in these open-shelled systems have typical pnicogen bond characteristics but much stronger than the usual pnicogen bonds in closed-shell systems. This P···N bond can be strengthened by an electron-withdrawing substituent X or an electron-donating substituent Y, the bonding energy varies from 17 kcal mol(-1) of (CH3H2P···NH2F)(+) to 54 kcal mol(-1) of (FH2P···NH2CH3)(+). A nearly linear X-P···N arrangement is required by the pnicogen bond P···N and results in a strong hyperconjugation and charge transfer from the N lone pair to the X-P σ* antibond orbital for α spin, the P···N interaction is described as a single-electron σ bond of β spin. The AIM and NBO analyses revealed that the P···N bonds in the majority of the hemi-bonded complexes are partly covalent in nature. Graphical Abstract The P···N interactions in the open-shelled systems (XH2P···NH2Y)(+) (X, Y=H, F, Cl, Br, NH2, CH3, OH) with bonding energy of 17~54 kcal mol(-1) have typical pnicogen bond characteristics but much stronger than the usual pnicogen bonds in closed-shell systems. This P···N bond can be strengthened by an electron-withdrawing substituent X or an electron-donating substituent Y.

Ab initio quantum mechanics methods were applied to investigate the hydrogen bonds between CO and HNF2, H2NF, and HNO. We use the Hartree-Fock, MP2, and MP4(SDQ) theories with three basis sets 6-311++G(d,p), 6-311++G(2df,2p), and AUG-cc-pVDZ, and both the standard gradient and counterpoise-corrected gradient techniques to optimize the geometries in order to explore the effects of the theories, basis sets, and different optimization methods on this type of H bond. Eight complexes are obtained, including the two types of C...H-N and O...H-N hydrogen bonds: OC...HNF2(C(s)), OC...H2NF(C(s) and C1), and OC...HNO(C(s)), and CO...HNF2(C(s)), CO...H2NF(C(s) and C1), and CO...HNO(C(s)). The vibrational analysis shows that they have no imaginary frequencies and are minima in potential energy surfaces. The N-H bonds exhibit a small decrease with a concomitant blue shift of the N-H stretch frequency on complexation, except for OC...HNF2 and OC...H2NF(C1), which are red-shifting at high levels of theory and with large basis sets. The O...H-N hydrogen bonds are very weak, with 0 K dissociation energies of only 0.2-2.5 kJ/mol, but the C...H-N hydrogen bonds are stronger with dissociation energies of 2.7-7.0 kJ/mol at the MP2/AUG-cc-pVDZ level. It is notable that the IR intensity of the N-H stretch vibration decreases on complexation for the proton donor HNO but increases for HNF2 and H2NF. A calculation investigation of the dipole moment derivative leads to the conclusion that a negative permanent dipole moment derivative of the proton donor is not a necessary condition for the formation of the blue-shifting hydrogen bond. Natural bond orbital analysis shows that for the C...H-N hydrogen bonds a large electron density is transferred from CO to the donors, but for the O...H-N hydrogen bonds a small electron density transfer exists from the proton donor to the acceptor CO, which is unusual except for CO...H2NF(C(s)). From the fact that the bent hydrogen bonds in OC(CO)...H2NF(C(s)) are quite different from those in the others, we conclude that a greatly bent H-bond configuration shall inhibit both hyperconjugation and rehybridization.

Pyridine generally acts as the proton acceptors in the hydrogen bonding interaction by using its lone pair n(N) or pi-electrons. Some previous research indicated that for the N-type H-bond, the ring breathing mode v(1), the N-para-C stretching mode v(6a) and the meta-CC stretching mode v(8a) of pyridine showed a frequency blueshift but the triangle mode v(12) had no change in frequency. Both electrostatic interaction and charge transfer caused by intermolecular hyperconjugation n(N)-->sigma( *)(HX) have contributions to the frequency blue shifts, while charge transfer is predominant at equilibrium intermolecular distance. An intramolecular hyperconjugation between the lone pair n(N) and the two sigma( *)(meta-CC) orbitals in the pyridine ring provides a reasonable interpretation for the effect of charge transfer on the ring stretching modes upon formation of the N-type H-bonding.

H-bonding angle angleYHX has an important effect on the electronic properties of the H-bond Y...HX, such as intra- and intermolecular hyperconjugations and rehybridization, and topological properties of electron density. We studied the multifurcated bent H-bonds of the proton donors H3CZ (Z = F, Cl, Br), H2CO and H2CF2 with the proton acceptors Cl(-) and Br(-) at the four high levels of theory: MP2/6-311++G(d,p), MP2/6-311++G(2df,2p), MP2/6-311++G(3df,3pd) and QCISD/6-311++G(d,p), and found that they are all blue-shifted. These complexes have large interaction energies, 7-12 kcal mol(-1), and large blue shifts, delta r(HC) = -0.0025 --0.006 A and delta v(HC) = 30-90 cm(-1). The natural bond orbital analysis shows that the blue shifts of these H-bonds Y...HnCZ are mainly caused by three factors: rehybridization; indirect intermolecular hyperconjugation n(Y) -->sigma*(CZ), in that the electron density from n(Y) of the proton acceptor is transferred not to sigma*(CH), but to sigma*(CZ) of the donor; intramolecular hyperconjugation n(Z) -->sigma*(CH), in that the electron density in sigma*(CH) comes back to n(Z) of the donor such that the occupancy in sigma*(CH) decreases. The topological properties of the electron density of the bifurcated H-bonds Y...H2CZ are similar to those of the usual linear H-bonds, there is a bond critical point between Y and each hydrogen, and a ring critical point inside the tetragon YHCH. However, the topological properties of electron density of the trifurcated H-bonds Y...H3CZ are essentially different from those of linear H-bonds, in that the intermolecular bond critical point, which represents a closed-shell interaction, is not between Y and hydrogen, but between Y and carbon.