The Inversion Barrier of Ammonia

The inversion barrier of ammonia is the energy difference between two extreme conformations, pyramidal and planar, during the out-of-plane motion of the nitrogen atom. Experimentally, this quantity is equal to 

77 kcal/mol, which is a very small part of the total enei of the molecule (about 35.500 kcal/mol). Recently, two ab initio calculations in fairly good agreement with experiment have been presented. Unfortunately, their conclusions are rather contradictory. 

The first one by Rauk et al. (5), is a pure SCF calculation with an extended basis set of GTO s including polarization orbitals on nitrogen and hydrogen atoms and optunization of the geometry. In the opinion of the authors, the success of their calculations (a barrier of 5.08 kcal/ mol) definitely proves that an independent particle model of the SCF t3q e can account for inversion barriers, provided that polarization orbitals are included and the basis is sufficiently flexible otherwise. 

An important point put forward by the study of ammonia is the choice of a well-balanced basis set. For the calculation of effects such as barriers it is important to use a basis as saturated as possible — or, if this cannot be achieved, at least equally well adapted to the different conformations to be considered. This requirement may be a cause of trouble, especially if the different geometrical configurations belong to different symmetry point groups. By symmetry reasons, the mixing of some atomic orbitals in a given molecular orbital may be forbidden for certain conformations and not for others. 

For example, in methylene (CH2) a, ny and %-orbitals are separated by symmetry in the linear form, whereas they are not in the bent form. In the case of ammonia, the more symmetrical planar form Das seems to be favoured with respect to the pyramidal one Ca by SCF calculations with basis sets limited to s and p orbitals, and the inversion barrier may be found to be negative (7). 

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The inversion barrier of ammonia is calculated by MM3 to be 5.5 kcalmol-1, in very good agreement with the experimental value of 5.8 kcalmol 1. ... 

The inversion barrier of ammonia is repulsive dominant Fee and Fnn increase more in the TS than the attractions Vne, the largest variation being that of Fee- Thus NH3 is pyramidal in part because the lone-pair repels the N—H bonding electrons. 

As in other areas of organic chemistry, computational investigations have provided important insights into the nature of carbanions, and the results complement the experimental studies. For example, ab initio calculations suggest that the inversion barrier of a methyl anion is ca. 2.2kcal/mol and that the inversion barrier of the ethyl anion is 3.3 kcal/mol. These values contrast with the <0.2 kcal/mol inversion barrier of the resonance-stabilized cyanomethyl anion on the one hand and the ca. 15 kcal/mol barrier for inversion of the cyclopropyl anion via a highly strained transition structure on the other hand. By comparison, the inversion barrier of ammonia is about 5.5 kcal/mol. ... 

In the preceding sections, we discussed the energy differences associated with atomizations and chemical reactions. In the present section, we consider the smaller differences associated with conformational changes [101 the barrier to linearity of water in Section 15.9.1, the inversion barrier of ammonia in Section 15.9.2 and the torsional barrier of ethane in Section 15.9.3. All barriers have been studied at the Hartree-Fock, MP2, CCSD, CCSD(T) and CCSDT levels of theory in the cc-pVXZ, aug-cc-pVXZ and cc-pCVXZ basis sets, with the valence electrons correlated in the valence... 

We now consider the inversion barrier of ammonia - that is, the difference in energy between the planar and pyramidal conformations of the molecule. Again, since nitrogen undergoes rehybridization when the molecule becomes planar, we would also expect this barrier to be large. However, from spectroscopic measurements, the barrier of ammonia has been determined to be 24.2(1) kJ/mol [12]. From theoretical studies, the zero-point vibrational contribution has been estimated to be 2.9 kJ/mol [10,13,14], giving an electronic barrier of 21.2 kJ/mol - that is, about six times smaller than that of water. The calculated inversion barriers are listed in Table 15.38. 

Contrary to pyrrole, phospholes are not planar, due to the high inversion barrier of the tricoordinate phosphorus (cf. the 6 kcal/mol inversion barrier of ammonia with the 35 kcal/mol inversion barrier of phosphine). As a consequence, unfortunately phospholes are not aromatic (Mathey, F.). Although the aromaticity of phospholes has been disputed in the past, Mislow considered first that phospholes with pyramidal phosphorus are nonaromatic while with planar tricoordinate phosphorus aromatic phospholes could be obtained. It was just recently found that phosphorus can be flattened or even fully planarized (as discussed comprehensively ), resulting in aromatic systems (see section IV.B.l). 

As with conformational energy differences, SYBYL and MMFF molecular mechanics show marked differences in performance for rotation/inversion barriers. MMFF provides a good account of singlebond rotation barriers. Except for hydrogen peroxide and hydrogen disulfide, all barriers are well within 1 kcal/mol of their respective experimental values. Inversion barriers are more problematic. While the inversion barrier in ammonia is close to the experimental value, barriers in trimethylamine and in aziridine are much too large, and inversion barriers in phosphine and (presumably) trimethylphosphine are smaller than their respective experimental quantities. Overall,... 

On the other hand, the Hamiltonian described in this paper does not lend itself to a parametrization of the experimental data with a precision approaching the requirements of the high-resolution spectroscopy. However, if one wants to use these data as fully as possible to obtain physically reliable information on the potential function, then an approach such as described in this paper is required. Determination of the value of the inversion barrier in ammonia which is approximately by 200 cm lower than the value determined previously (Section 5.3) shows on the importance of such approach. 

The primary structural determinant is therefore seen to be the identity of the Group 15 element. Nitrogen is different from P and As in its tendency to pyramidalize, as measured by inversion barriers and by bond angles. The inversion barrier in ammonia is 5 kcal/mol, and it is 30 kcal/mol in phosphine and arsine. The inversion of the trans bent form (which goes through the planar form)... 

The inversion barrier of phosphine has not been determined experimentally. The best quantum chemical calculations yield a barrier of 141 kJ mol , i.e. more than five times higher than in ammonia [2]. Since the barrier to internal rotation in Si2H is smaller than in ethane, it may seem surprising that the inversion barrier of PH3 is higher than in NH3. The reason may be that the pyramidal structure of NH3 is significantly destabilized by repulsion between the H atoms. 

There are two bound vibrational states pertaining to the inversion vibration of ammonia. These two levels are split by tunneling through the barrier into inversion doublets. The splitting of the lower doublet corresponds to a wavelength 1.25 cm... 

Fig. 15.20. The electronic inversion barrier of ammonia (kJ/mol) calculated at the Hartree-Fock level (thick grey line), the valence-electron MP2 level (dotted line), the valence-electron CCSD level (dashed line) and the valence-electron CCSD(T) level (full line).

Repeat your analysis for the sequence of structures corresponding to inversion of trimethylamine. Is the inversion barrier smaller, larger or about the same as that in ammonia If significantly different, speculate on the origin of the difference. 

The distinction between atomic orbitals and basis functions in molecular calculations has been emphasized several times now. An illustrative example of why the two should not necessarily be thought of as equivalent is offered by ammonia, NH3. The inversion barrier for interconversion between equivalent pyramidal minima in ammonia has been measured to be 5.8 kcal mol However, a HF calculation with the equivalent of an infinite, atom-centered basis set of s and p functions predicts the planar geometry of ammonia to be a minimum-energy structure ... 

The simpliest and most important molecule with a low barrier to inversion is ammonia, NH3. In its ground electronic state, NH3 has a pyramidal equilibrium configuration with the geometrical symmetry described by the point group C3V (Fig. 1). Configuration B which is obtained from A by the symmetry operation E is separated from A by an inversion barrier of about 2000 cm . A large amplitude... 

Associated with the greater deviation from nitrogen planarity (compared to ammonia) is an increase in the barrier to inversion. We have not made a study of the Czv form (with planar nitrogen) but previous theoretical calculations 30,53,54) jg d to estimates in the range 15.5— 18.3 kcal/mol. Experimental values of inversion barriers in simple substituted aziridines 5) are in the range 18—21 kcal/mol. For comparison, the experimental inversion barrier in ammonia 35) is 5.8 kcal/ mol. 

The inversion barrier is found to be an example of a Case II energy change for the molecules NH3, PH3, HjO", and HjO (Table 6.5). Only the first and last of these molecules is discussed in detail. The A-H internuclear separations in ammonia and water are found to decrease when the pyramidal or bent geometry is transformed into its respective planar or linear form, by 0.0130 A in NH3 and by 0.0180 A in HjO. The approach of the protons towards the A nucleus, while resulting in a lowering of the electron-nuclear... 

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