Mulliken,

Mulliken symbols The designators, arising from group theory, of the electronic states of an ion in a crystal field. A and B are singly degenerate, E doubly degenerate, T triply degenerate states. Thus a D state of a free ion shows E and Tj states in an octahedral field. 

The W—W bond energy should be about one-sixth of the sublimation energy (note Section III-IB), and there are various schemes for estimating electronegativities, of which Mulliken s [151,152] is perhaps the most fundamental. 

Mulliken R S 1955 Report on notation for the spectra of polyatomic molecules J. Chem. Phys. 23 1997-2011... 

Mulliken Prof. R S University of Chioago. Fie is the person who oame up with the phrase moleoular orbital and the oonoepts behind it... 

One can note some interesting features from these trajectories. For example, the Mulliken population on the participating atoms in Figure 1 show that the departing deuterium canies a full electron. Also, the deuterium transferred to the NHj undergoes an initial substantial bond stretch with the up spin and down spin populations separating so that the system temporarily looks like a biradical before it settles into a normal closed-shell behavior. 

A simple measure of the election density distribution over the participating atoms is the Mulliken population [60]. For linear Li—H—Li the alpha spin is... 

Figure 7. Alpha Mulliken population on Li(2) as functions of time for different initial conditions.

At the outset of the Partial Equalization of Orbital Electronegativities (PEOE) method [28] is the electronegativity concept in the form of Eq. (11) presented by Mulliken, who put it on a sound theoretical basis [29]. 

The constant k can be adjusted to give best agreement with exper-iinen t. It is I onn d th at a good value to n se is soin ewh at larger th an would be indicated by the Mulliken approximation and a very standard value used by many groups is ... 

The derivation of th is result introduces a generalisation of the Mulliken appro,xirn ation ... 

Mulliken population analysis is a trivial calculation to perform once a self-consistent field has been established and the elements of the density matrix have been determined. 

Ldwdin population analysis avoids the problem of negative populations or populations greater than 2. Some quantum chemists prefer the Ldwdin approach to that of Mulliken as the charges are often closer to chemically intuitive values and are less sensitive to basis set. 

Mulliken, Identification of Pure Organic Compounds, Volumes I-IV, 1904-1922 (J. WUey). 

It is also common to represent these same two-electron integrals in a notation referred to as Mulliken notation in which ... 

Here, the indices i and k, which label the spin-orbital having variables r are grouped together, and j and 1, which label spin-orbitals referring to the r variables appear together. The above permutational symmetries, when expressed in terms of the Mulliken integral list read ... 

Most methods of this type are based on the so-called zero-differential overlap (ZDO) approximation. Their development begins by using an approximation to the atomic-orbital-based two-electron integrals introduced by Mulliken ... 

In spite of its deficiencies, the Mulliken population scheme is very popular. One reason is that it is very easy to implement so it is available in many software packages. Probably the most important reason for its popularity is the fact... 

There is some ambiguity about Mulliken population analysis in the literature. This is because various software packages print different portions of the analysis and may name them slightly differently. The description here follows some of the more common conventions. 

The Lowdin population analysis scheme was created to circumvent some of the unreasonable orbital populations predicted by the Mulliken scheme, which it does. It is different in that the atomic orbitals are first transformed into an orthogonal set, and the molecular orbital coefficients are transformed to give the representation of the wave function in this new basis. This is less often used since it requires more computational work to complete the orthogonalization and has been incorporated into fewer software packages. The results are still basis-set-dependent. 

This results in a population analysis scheme that is less basis set dependent than the Mulliken scheme. Flowever, basis set effects are still readily apparent. This is also a popular technique because it is available in many software packages and researchers find it convenient to use a method that classifies the type of orbital. 

Mulliken analysis is most often used with semiempirical wave functions. 

---