`
[-]eem`

The Electronegativity Equalization Method
(EEM) [1Mortier, W. J.; Ghosh, S. K.; Shankar, S.

*J. Am. Chem. Soc.* **1986**, *108*, 4315-4320.]
enables the determination of atomic charges that are sensitive to the
molecule's topology and three-dimensional structure.

The EEM approach is found to be a very powerful way to obtain ab initio quality atomic charges of different kinds in organic molecules, without the computational cost of the ab initio approach. [Mulliken: J. Phys. Chem. A 2002, 106, 7887-7894. CHELPG, MK, NPA, Hirshfeld: J. Phys. Chem. A 2002, 106, 7895-7901. AIM: J. Phys. Chem. A 2004, 108, 10359-10366.]

Given the 3D structure of a molecule with *N* atoms and total charge
*Q*, the Electronegativity Equalization Method
(EEM) estimates the partial atomic charges
*q*_{1} …
*q _{N}* and the average molecular electronegativity

| (1) |

where *r _{i,j}* is the distance between atoms

EEM is based on the electronegativity equalization
principle, [4Sanderson, R. T.

*Science* **1951**, *114*, 670−672.,
5Sanderson, R. T.

*Science* **1955**, *121*, 207−208.]
which has received theoretical grounding within the density functional
theory (DFT), [6
Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E.

*J. Chem. Phys.* **1978**, *68*, 3801−3807.,
7Politzer, P.; Weinstein, H.

*J. Chem. Phys.* **1979**, *71*, 4218-4220.,
8Parr, R. G.; Bartolotti, L.

*J. Am. Chem. Soc.* **1982**, *104*, 3801-3803.,
9Parr, R. G.; Pearson, R. G.

*J. Am. Chem. Soc.* **1983**, *105*, 7512−7516.,
10Nalewajski, R.

*J. Phys. Chem.* **1985**, *89*, 2831-2837.,
11Parr, R.; Yang, W.

*Density-Functional Theory of Atoms and Molecules*.

Oxford University Press: New York, 1989, p. 90.]
and which states that the electronegativity of all atoms is equalized
throughout a molecule:

χ_{1} = χ_{2} = … =
χ = … =
_{i}χ
| (2) |

Within EEM, the electronegativity *χ _{i}*
of each atom

χ = (_{i}χ_{i}^{0} +
Δχ) + 2 (_{i}η_{i}^{0}
+ Δη) _{i}q + _{i}k
N
∑
i≠j
q
_{j}r
_{i,j} | (3) |

The first term is the electronegativity of the isolated atom
*χ _{i}*

χ = A +
_{i}B + _{i}q_{i}k
N
∑
i≠j
q
_{j}r
_{i,j} | (4) |

Additionally, the total molecular charge *Q* is the sum of all partial
atomic charges *q _{i}*:

Q =
N
∑
i=1
q
_{i} | (5) |

Taken all together, eqs (2), (4), and (5) can be expressed as a system
of coupled linear equations, eq (1), from which the partial atomic charges
*q _{i}* and the molecular electronegativity

The main limitation of the EEM approach is inherent to its empirical nature. EEM relies on empirical parameters fitted to reference QM data. As such, when employing a particular set of EEM parameters, it is important to consider the nature of the reference QM data, as well as the particular fitting strategy used in the development of the set of EEM parameters. In general, one cannot expect that EEM charges will outperform QM charges.

- "Electronegativity Equalization Method for the Calculation of
Atomic Charges in Molecules"

Mortier, W. J.; Ghosh, S. K.; Shankar, S.*J. Am. Chem. Soc.***1986**,*108*, 4315-4320. - "Rapid Calculation of Accurate Atomic Charges for Proteins via the
Electronegativity Equalization Method"

Ionescu, Crina-Maria; Geidl, Stanislav; Svobodová Vařeková, Radka; Koča, Jaroslav*J. Chem. Inf. Model***2013**,*53*, 2548-2558. - "AtomicChargeCalculator: interactive web‐based calculation of
atomic charges in large biomolecular complexes and drug-like
molecules"

Ionescu, Crina-Maria; Sehnal, David; Falginella, Francesco L.; Pant, Purbaj; Pravda, Lukáš Bouchal, Tomáš Svobodová Vařeková, Radka; Geidl, Stanislav; Koča, Jaroslav*J. Cheminform***2015**,*7*, 50-62. - "An Interpretation of Bond Lengths and a Classification of
Bonds"

Sanderson, R. T.*Science***1951**,*114*, 670−672. - "Partial Charges on Atoms in Organic Compounds"

Sanderson, R. T.*Science***1955**,*121*, 207−208. - "Electronegativity: The density functional viewpoint"

Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E.*J. Chem. Phys.***1978**,*68*, 3801−3807. - "Molecular Electronegativity in Density Functional Theory"

Politzer, P.; Weinstein, H.*J. Chem. Phys.***1979**,*71*, 4218-4220. - "On the Geometric Mean Principle for Electronegativity
Equalization"

Parr, R. G.; Bartolotti, L.*J. Am. Chem. Soc.***1982**,*104*, 3801-3803. - "Absolute hardness: companion parameter to absolute
electronegativity"

Parr, R. G.; Pearson, R. G.*J. Am. Chem. Soc.***1983**,*105*, 7512−7516. - "A Study of Electronegativity Equalization"

Nalewajski, R.*J. Phys. Chem.***1985**,*89*, 2831-2837. -
Parr, R.; Yang, W.
*Density-Functional Theory of Atoms and Molecules*. Oxford University Press: New York, 1989, p. 90. - "Molecular electronegativity in density functional
theory (I)">br />Yang, Z.; Shen, E.
*Science in China. Series B, Chemistry***1995**,*38*, 521−528.

- AtomicChargeCalculator: Conformationally Dependent Atomic Charges of Quantum Mechanics Quality
- EEM SOLVER and ABEEM SOLVER, Version 1.0 (accessed November 12, 2015) Version 1.0
- Electronegativity (Wikipedia) (accessed November 12, 2015)