Dipole moment vector geometry

The three components of the dipole moment vector can be expressed as a series expansion about the equilibrium geometry... 

Fig. 11 Relative size and orientation of dipole moment vectors of the ground state black) and the excited states JMLCT (bJA ), 3IL (b3A"), and 3MLCT (a3A") of [Re(Etpy)(CO)3(bpy)]+, projected onto the optimized ground-state molecular structure. Dipole moment vectors originate in the center of charge calculated using Mulliken population analysis. They lie in the molecular symmetry plane. (Calculated by TD-DFT G03/PBE0/vacuum at the optimized ground state geometry.) Reproduced with permission from [76]...

It gives information on the geometry of the chromophore, the part of the molecule responsible for the NLO response (for an ideal donor/acceptor one-dimensional system DR = 5, for an octupolar molecule, DR = 1.5 whereas for a A-shape molecule, the amplitude of DR depends on the angle between the chromophore as well as on the D/A groups). On the other hand, the EFISHG measurements give information on the projection of the vector part of p on the dipole moment vector ... 

Molecular electronic dipole moments, pi, and dipole polarizabilities, a, are important in determining the energy, geometry, and intermolecular forces of molecules, and are often related to biological activity. Classically, the pKa electric dipole moment pic can be expressed as a sum of discrete charges multiplied by the position vector r from the origin to the ith charge. Quantum mechanically, the permanent electric dipole moment of a molecule in electronic state Wei is defined simply as an expectation value ... 

The dipole moments of the two conformers 146 and 147 of 1-rm-butyl-piperidine-4-spiro-4 (l, 3 -dioxolan) were calculated by vector addition of the moments of 1-fert-butylpiperidine and 4,4-dimethyl-1,3-dioxolan, making reasonable assumptions regarding geometries. This gave 1.15 and 1.93 D as the moments of the two conformers. The observed moment of 1.47 D gave AG° of 0.37 kcal mol-1 in favor of the axial oxygen conformer 146 in cyclohexane solution. AG%2- of 0.26 kcal mol-1 was estimated from low-temperature H-NMR studies.121 The differences between the piperidine and... 

Here the summation of charges times position vectors is replaced by the integral over the total wavefunction T (the square of the wavefunction is a measure of charge) of the dipole moment operator (the summation over all electrons of the product of an electronic charge and the position vectors of the electrons). To perform an ab initio calculation of the dipole moment of a molecule we want an expression for the moment in terms of the basis functions r/j, their coefficients c, and the geometry (for a molecule of specified charge and multiplicity these are the only variables in an ab initio calculation). The Hartree-Fock total wavefunction T is composed of those component orbitals i// which are occupied, assembled into a Slater determinant (Section 5.2.3.1), and the i// s are composed of basis functions and their coefficients (Sections 5.3). Equation (5.206), with the inclusion of the contribution of the nuclei to the dipole moment, leads to the dipole moment in Debyes as (ref. [lg], p. 41)... 

However, a subterfuge enables MM molecular geometries to yield dipole moments the dipole moment of a molecule can be considered to be the vector sum of bond moments, and like bond energies these are with a fair degree of accuracy transferable between molecules. So from the geometry, which gives the relative positions of the vectors in space, a dipole moment can be calculated, purely empirically. 

Because the magnitude of each dipole is equal and their directions are exactly opposed to one another, the two vectors cancel each other out. Therefore, the C02 molecule has no dipole moment. Now, consider the H20 molecule. Since there is an electronegativity difference between H and O, there will be a dipole between each H and the oxygen atom. However, the molecular geometry of the water molecule is bent. This means that the vectors look like the ones in Figure 7.6 ... 

Here i//0 is the ground vibrational wave function and ij/ is the wavefunction corresponding to the first excited vibrational state of the th normal mode /< is the electric dipole moment operator Qj is the normal coordinate for the /th vibrational mode the subscript 0 at derivative indicates that the term is evaluated at the equilibrium geometry. The related rotational strength or VCD intensity is determined by the dot product between the electric dipole and magnetic dipole transition moment vectors, as given in (2) ... 

In Section 1.3, we saw that for molecules with one covalent bond, the dipole moment of the bond is identical to the dipole moment of the molecule. For molecules that have more than one covalent bond, the geometry of the molecule must be taken into account because both the magnitude and the direction of the individual bond dipole moments (the vector sum) determine the overall dipole moment of the molecule. Symmetrical molecules, therefore, have no dipole moment. For example, let s look at the dipole moment of carbon dioxide (CO2). Because the carbon atom is bonded to two atoms, it uses sp orbitals to form the C—O a bonds. The remaining two p orbitals on carbon form the two C—O tt bonds. The individual carbon-oxygen bond dipole moments cancel each other— because sp orbitals form a bond angle of 180°—giving carbon dioxide a dipole moment of zero D. Another symmetrical molecule is carbon tetrachloride (CCI4). The four atoms bonded to the sp hybridized carbon atom are identical and project symmetrically out from the carbon atom. Thus, as with CO2, the symmetry of the molecule causes the bond dipole moments to cancel. Methane also has no dipole moment. 

First determine the geometry of the molecule by VSEPR theory. Then find the individual bond dipoles of the molecule. The overall dipole moment is the vector sum of the individual bond dipoles. All of the examples in this problem have only one polar bond, so the dipole moment lies along the direction of that bond. 

Use VSEPR theory to determine the geometry of the molecule. Assign bond dipoles to any polar bonds. Predict the overall dipole moment by estimating the result of vector addition of the bond dipoles. 

Water, H2O, has two equal H—O bond dipoles. Water has a bent geometry and the vector sum of the bond dipoles does not cancel. The water molecule has a permanent net dipole moment. 

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