The Hydrogen Fluoride Molecule

As usual, the single bond is described by three VB structures, 14-16. 

The F+H (16) structure is expected to be very minor but is nevertheless added for completeness. Table 3 displays the optimal bond lengths and bonding energies calculated at various theoretical levels, in the 6-31+G basis set and in an additional basis set comparable in quality to the one used by Bauschlicher and Taylor [32]. 

Dissociation energies and optimized equilibrium bond lengths for the FH molecule 

This test calculation, referred to as Extended SD-BOVB in Table 3, results in an improvement of only 1.1 kcal/mol of the bonding energy relative to the standard SD level, thus confirming the assumption of near-constancy of the correlation within inactive electrons. It follows therefore that going beyond the SD-BOVB level is not necessary. 

By nature, the BOVB method describes properly the dissociation process. As a test case, the dissociation curve of the FH molecule was calculated at the highest BOVB level (extended SD-BOVB), and compared with a reference full Cl dissociation curve calculated by Bauschlicher et al. [33] with the same basis set. The two curves, that were compared in Ref. 12, were found to be practically indistinguishable within an error margin of 0.8 kcal/mol, showing the ability of the BOVB method to describe the bonding interaction equally well at any interatomic distance from equilibrium all the way to infinite separation [12]. 

As usual, we choose the F atom at the origin of the coordinate system with the H atom placed on the positive z axis at the experimental bond distance Re = 1.73a0 (Huber and Herzberg, 1979). 

The polarity parameter for ground state HF is then calculated to be  

We now look at the distribution of the two electrons in MO, which gives the atomic charges the a bonding 

Fori 1, 0, and electronic charge will be transferred from H to F, as expected on electronegativity grounds. As we said before, the formal charge 51 can be independently derived from the experimentally observed value (Muenter and Klemperer, 1970 Sileo and Cool, 1976) of the vibrationless electric dipole moment18(/r = 0.72 eaQ), if we attribute the entire value of the dipole to its heteropolar component /rH (Magnasco, 2003)  

18 As usual, we assume fx 0 when the direction of the dipole is from - 8 to + 8. Calculated Hartree-Fock values of fx (0.756eao) (Christiansen and McCullough, 1977 Sundholm et al., 1985) corrected for correlation effects (—0.043eao) (Werner and Meyer, 1976 Amos, 1982) agree with the experimental result. 

Orthogonal does not mean not interacting (Footnote 3). This is tantamount to keeping only the exchange part of the exchange-overlap interaction (Magnasco, 2002, 2004a). 

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However, many substances, notably alcohols, have a greater proton affinity than the hydrogen fluoride molecule, and so behave as bases, for example ethanol ... 

The experimental bond length for the hydrogen fluoride molecule is 0.917A. Determine the basis set required to predict this structure accurately. Perform your optimizations at the MP4 level of theory (electron correlation is known to be important for this system). 

Fig. 4.4 shows a representation of the hydrogen fluoride molecule as a dipole. The dipole moment is represented as an arrow, marking the positive end. Since the dipole moment... 

Heteronuclear diatomic molecules (1) The hydrogen fluoride molecule... 

Show how a hydrogen Is atomic orbital and a fluorine 2p atomic orbital overlap to form bonding and antibonding MOs in the hydrogen fluoride molecule. Are they cr or 77 MOs ... 

In this molecule, the hydrogen fluoride molecule, there is a single covalent bond (shared-electron-pair bond), which holds the hydrogen atom and the fluorine atom firmly together. The distance between the nuclei of these two atoms is 0.92A, according to experimental determination made by the study of the spectrum of the gas. 

Consider, as a first example, the hydrogen fluoride molecule (Fig. 39). 

In discussing bonds involving hybrid AO s it is necessary to introduce atomic valence states. If the above description (p. 96) is accepted, the energy of the hydrogen fluoride molecule can be discussed. The bond is... 

Figure 29.3. The hydrogen fluoride molecule dependence of overlap on orbital symmetry, a) Overlap of lobes of same phase leads to bonding. b) Positive overlap and negative overlap cancel each other.

The hydrogen fluoride molecule may be used as a simple example of this approach. Using the 6-31G basis the PA charge on F is -0.395 e. This monopole value yields, when combined with the bond distance of 1.733 au, a dipole moment of 0.685. However, the exact operator dipole obtained from the wavefunction is 0.776. In the cumulative procedure, the difference between these two values is made up with atomic dipoles. From [13] one obtains (w)f = + 0.330 and [w] = +0.446, which of course sum to the exact molecular dipole. Application of Eq. [14] yields cumulative atomic dipoles Mj. = -0.012 and Mh = 0.103. The sum of the PA charge dipole plus the atomic dipoles equals the exact molecular dipole. Analogous procedures are used for higher moments. 

Fig. 3. Relative gain of vibrational-rotational transitions in the hydrogen fluoride molecule for Trot = 300° K and various population ratios -We-z/lV -1. It is seen that the gain is always lower in the R-branch than in the corresponding P-branch transitions... 

P. Politzer and R. S. Mulliken, J. Chem. Phys., 55,5135 (1971). Comparison of Two Atomic Charge Definitions, as Applied to the Hydrogen Fluoride Molecule. 

The procedure of taking a linear combination of atomic orbitals, which we have considered with respect to the H2 molecule, is very fruitful when applied to other covalent bonds. Consider, for example, the hydrogen fluoride molecule, HF, formed from a hydrogen atom with one electron in the Is state and a fluorine atom with an electron configuration of ls 2s 2p. Fluorine has an unpaired 2p electron, and we can form a wave function of the Heitler-London type by making use of the atomic orbitals for this 2p electron and for the Is electron in the hydrogen atom ... 

Desaibe the type of chemical bonding that exists between the atoms in the hydrogen fluoride molecule, HR... 

Similar conclusions come from another ideal system (Fig. 14.23b) namely, the hydrogen fluoride molecule is treated as the pendulum of a grandfather clock (the hydrogen atom down, the clock axis going through the fluorine atom) moving over two molecules A and B, each of them may accommodate an extra electron. ... 

Table 3.2 Four points of the CAS(2,2)CCSD PEC relative to FCI (reported in 10 au) in comparison with the CASSCF(2,2), CCSD, and CCSD(T) PECes for the hydrogen fluoride molecule (Re = 1.733 au) In the last row the FCI energies (in au) are shown. The calculations have been performed with the DZV basis set ...

The Hydrogen Fluoride Molecule. The first molecule considered is HF. For any molecule containing F, the Fermi-contact term alone is insufficient to account for the value of the spin-spin coupling constant, and all terms must be included for quantitative agreement with experiment. Thus, the experimental value for the HF coupling constant is 529 23 Hz (30). Our computed value is 515.0 Hz, with the PSO, DSO, Fermi-contact, and SD terms contributing 185.7, 0.5, 326.2, and 2.6 Hz, respectively. 

The hydrogen fluoride molecule (A) and the hydrogen difluoride ion, containing a hydrogen bond (B). 

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