502, dipole moment

Dipole moments are taken from microwave measurements where possible, else from solution studies. 

A quantitative measure of the polarity of a bond is its dipole moment (fx), which is the product of the charge Q and the distance r between the charges  

To maintain electrical neutrality, the charges on both ends of an electrically neutral diatomic molecule must be equal in magnitude and opposite in sign. However, in Equation (10.1), Q refers only to the magnitude of the charge and not to its sign, so p, is always positive. Dipole moments are usually expressed in debye units (D), named for Peter Debye. The conversion factor is 

Diatomic molecules containing atoms of different elements (for example, HCl, CO, and NO) have dipole moments and are called polar molecules. Diatomic molecules containing atoms of the same element (for example, H2, O2, and F2) are examples of nonpolar molecules because they do not have dipole moments. For a molecule made up of three or more atoms both the polarity of the bonds and the molecular geometry determine whether there is a dipole moment. Even if polar bonds are present, the molecule will not necessarily have a dipole moment. Carbon dioxide (CO2), for example, is a triatomic molecule, so its geometry is either linear or bent  

The arrows show the shift of electron density from the less electronegative carbon atom to the more electronegative oxygen atom. In each case, the dipole moment of the entire molecule is made up of two bond moments, that is, individual dipole moments in the polar C=0 bonds. The bond moment is a vector quantity, which means that it has both magnitude and direction. The measured dipole moment is equal to the vector sum of the bond moments. The two bond moments in CO2 are equal in magnitude. Because they point in opposite directions in a Unear CO2 molecule, the sum or resultant dipole moment would be zero. On the other hand, if the CO2 molecule were bent, the two bond moments would partially reinforce each other, so that the molecule would have a dipole moment. Experimentally it is found that carbon dioxide has no dipole moment. Therefore, we conclude that the carbon dioxide molecule is linear. The linear nature of carbon dioxide has been confirmed through other experimental measurements. 

Each carbon-to-oxygen bond is polar, with the electron density shifted toward the more electronegative oxygen atom. However, the linear geometry of the molecule results in the cancellation of the two borKi moments. 

The charge distribution of neutral polar molecules is characterized by a dipole moment which is defined classically by jx = E, , , where the molecular charge distribution is defined in terms of the residual charges (qt) at the position r,. The observed molecular dipole moment provides useful information about the charge distribution of the ground state and its ionic character. 

In order to compare calculated and observed dipole moments, we should replace the classical expression of the dipole moment by its quantum analogue jx = f F x1Ir dr where /I is the dipole moment operator (given by jx = —eri + . eZ-Blj with i and j running over the electronic and nuclear coordinates, respectively, and — e the electron charge). The actual calculation of a VB dipole moment is described below. 

Exercise 1.7. Evaluate the dipole moment for the HF molecule using the parameter of Table 1.1, and examine the change of the calculated dipole moment with the change of A (e.g., A = 640 and 2000). 

Recall that a polar covalent bond arises when the electronegativity difference between the bonding atoms is sufficient to cause partial charges on the bonding atoms (but not so large as to produce an ionic bond). 

A nonpolar covalent bond formed between identical atoms. 

A polar covalent bond formed when there is an electronegativity difference between the atoms 

The polarity of the bond manifests itself in a measurable physical quantity called the dipole moment. A dipole moment, i, is a vector quantity that has both magnitude and direction (bold letters are used for vector quantities). 

Dipole moments for some other molecules are given in Table 1. 

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Values of dipole moment y are listed in the compilation by McClellan (1974). 

McClellan, A. L., Tables of Experimental Dipole Moments, W. H. Freeman, San Francisco (1963-74). 

VSTR = O Connell characteristic volume parameter, cm /g-mol ZRA = Rackett equation parameter RD = mean radius of gyration, A DM = dipole moment, D R = UNIQUAC r Q = UNIQUAC q QP = UNIQUAC q ... 

DIPOLE MOMENT OF COMPONENT I fDEBYES ASSOCIATION OR SOLVATION PARAMETER FOR T E (I.JI PAIR... 

REDUCED DIPOLE MOMENT PRIME. ALSO. REDUCED DIPOLE MOMENT IN EARLIER PART OF THE PROGRAM. EFFECTIVE NON-PQLAR ACENTRIC FACTOR. 

Although a diatomic molecule can produce only one vibration, this number increases with the number of atoms making up the molecule. For a molecule of N atoms, 3N-6 vibrations are possible. That corresponds to 3N degrees of freedom from which are subtracted 3 translational movements and 3 rotational movements for the overall molecule for which the energy is not quantified and corresponds to thermal energy. In reality, this number is most often reduced because of symmetry. Additionally, for a vibration to be active in the infrared, it must be accompanied by a variation in the molecule s dipole moment. 

McConnell et al. [196] and Andelman and co-workers have predicted [197,198] an ordered array of liquid domains in the gas-liquid coexistence regime caused by the dipole moment difference between the phases. These superstructures were observed in monolayers of dipalmitoyl phosphatidylcholine monolayers [170]. 

Because mole numbers are additive, it follows that the product A. A V will be an additive quantity provided that a for each species remains constant during the course of the reaction. This last condition implies, essentially, that the effective dipole moments and hence the orientation of each species remain constant, which is most likely to be the case at constant film pressure. Then... 

We have two interaction potential energies between uncharged molecules that vary with distance to the minus sixth power as found in the Lennard-Jones potential. Thus far, none of these interactions accounts for the general attraction between atoms and molecules that are neither charged nor possess a dipole moment. After all, CO and Nj are similarly sized, and have roughly comparable heats of vaporization and hence molecular attraction, although only the former has a dipole moment. 

The atomic unit (AU) of dipole moment is that of a proton and electron separated by a distance equal to the first Bohr orbit, oq. Similarly, the au of polarizability is Oq [125]. Express and o for NH3 using both the cgs/esu and SI approach. 

The heat of immersion is measured calorimetrically with finely divided powders as described by several authors [9,11-14] and also in Section XVI-4. Some hi data are given in Table X-1. Polar solids show large heats of immersion in polar liquids and smaller ones in nonpolar liquids. Zetdemoyer [15] noted that for a given solid, hi was essentially a linear function of the dipole moment of the wetting liquid. 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Therefore, it has at most five independent components, and fewer if the molecule has some synnnetry. Syimnetric top molecules have only one independent component of 0, and, in such cases, the axial component is often referred to as the quadnipole moment. A quadnipolar distribution can be created from four charges of the same magnitude, two positive and two negative, by arranging them m the fonn of two dipole moments parallel to each other but pointing in opposite directions. Centro-syimnetric molecules, like CO2, have a zero dipole moment but a non-zero quadnipole moment. 

The charge redistribution that occurs when a molecule is exposed to an electric field is characterized by a set of constants called polarizabilities. In a imifonn electric field F, a component of the dipole moment is... 

The dipole polarizability tensor characterizes the lowest-order dipole moment induced by a unifonu field. The a tensor is syimnetric and has no more than six independent components, less if tire molecule has some synnnetry. The scalar or mean dipole polarizability... 

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

The leading tenn in the electrostatic interaction between the dipole moment of molecule A and the axial quadnipole moment of a linear, spherical or synunetric top B is... 

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

If molecule A is a linear, spherical or synnnetric top that has a zero dipole moment like benzene, then the leading induction tenn is the quadnipole-mduced-dipole interaction... 

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

McClellan A L 1963 Tables of Experimental Dipole Moments vol 1 (New York Freeman)... 

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