## Journal Articles | |

5. | Zhikol, Oleg; Shishkin, Oleg Estimating stacking interaction energy using atom in molecules properties: Homodimers of benzene and pyridine (Journal Article) International Journal of Quantum Chemistry, 112 (18), pp. 3008-3017, 2012. (Abstract | Links | BibTeX | Tags: Atom-atom interaction, Hydrogen bonds, Quantum chemistry) @article{Zhikol20123008, title = {Estimating stacking interaction energy using atom in molecules properties: Homodimers of benzene and pyridine}, author = {Zhikol, Oleg A. and Shishkin, Oleg V.}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84864448848&partnerID=40&md5=c4f32b35768fb6d05283e020f3a58fa9, http://doi.wiley.com/10.1002/qua.24189}, year = {2012}, date = {2012-01-01}, journal = {International Journal of Quantum Chemistry}, volume = {112}, number = {18}, pages = {3008-3017}, abstract = {An attempt is presented to infer the stacking interaction energy from the atom in molecules (AIM) properties computed in all critical points of electron density found between interacting molecules. In this study, benzene and pyridine homodimers in coaxial and parallel displaced configurations were used as model structures. We classify the structures and briefly discuss their peculiarities in the AIM theory framework. The maximum absolute error of 2 kcal/mol achieved for 300 potential energy surface point set indicates that a more sophisticated algorithm for estimating atom-atom interactions is needed still. © 2012 Wiley Periodicals, Inc.}, keywords = {Atom-atom interaction, Hydrogen bonds, Quantum chemistry}, pubstate = {published}, tppubtype = {article} } An attempt is presented to infer the stacking interaction energy from the atom in molecules (AIM) properties computed in all critical points of electron density found between interacting molecules. In this study, benzene and pyridine homodimers in coaxial and parallel displaced configurations were used as model structures. We classify the structures and briefly discuss their peculiarities in the AIM theory framework. The maximum absolute error of 2 kcal/mol achieved for 300 potential energy surface point set indicates that a more sophisticated algorithm for estimating atom-atom interactions is needed still. © 2012 Wiley Periodicals, Inc. |

4. | Luzanov, Spin-free quantum chemistry: What one can gain from fock's cyclic symmetry (Journal Article) International Journal of Quantum Chemistry, 111 (15), pp. 4042-4066, 2011. (Abstract | Links | BibTeX | Tags: Quantum chemistry, Spin-flip model, Wave functions) @article{Luzanov20114042, title = {Spin-free quantum chemistry: What one can gain from fock\'s cyclic symmetry}, author = {Luzanov, A V}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-80053553075&partnerID=40&md5=07980ca2b188c8248be183e8c497f147, http://doi.wiley.com/10.1002/qua.22943}, year = {2011}, date = {2011-01-01}, journal = {International Journal of Quantum Chemistry}, volume = {111}, number = {15}, pages = {4042-4066}, abstract = {The spin-free wave function due to Fock (Zh Eksp Teor Fiz, 1940, 10, 961) is re-examined with a stress on the reduced density matrix (RDM) theory. The key notion of the Fock approach is the cyclic symmetry of wave functions. It is a specific algebraic identity involving transpositions of numbers taken from two different columns of the corresponding Young tableau. We show first how to construct symmetry adapted states by accounting for high-order cyclic symmetry conditions. For Young\'s projectors, it gives a new expression including nothing but antisymmetrizers. Next, transforming the Fock spin-free state by a duality operator (the star operator in exterior algebra), we arrive at the representation closely related to spin-flip models. In such spin-flip models, a coupling operator is the basic object for which we show that the cyclic symmetry is transformed into a tracelessness of the coupling operator. The main results are related to the spin-free theory of spin properties. In particular, the theorem previously stated (Luzanov and Whyman, Int J Quantum Chem, 1981, 20, 1179) is refined by an explicit general representation of spin density operators through spin-free (charge) RDMs. Some applications implicating high-order RDMs (collectivity numbers, the unpaired electron problem, cumulant spin RDMs, spin correlators, etc.) are also considered. For spin-free RDM components, a new projection procedure without constructing any symmetry adapted state is proposed. An unsolved problem of constructing orthogonal representation matrices within the Fock theory is raised. © 2010 Wiley Periodicals, Inc.}, keywords = {Quantum chemistry, Spin-flip model, Wave functions}, pubstate = {published}, tppubtype = {article} } The spin-free wave function due to Fock (Zh Eksp Teor Fiz, 1940, 10, 961) is re-examined with a stress on the reduced density matrix (RDM) theory. The key notion of the Fock approach is the cyclic symmetry of wave functions. It is a specific algebraic identity involving transpositions of numbers taken from two different columns of the corresponding Young tableau. We show first how to construct symmetry adapted states by accounting for high-order cyclic symmetry conditions. For Young's projectors, it gives a new expression including nothing but antisymmetrizers. Next, transforming the Fock spin-free state by a duality operator (the star operator in exterior algebra), we arrive at the representation closely related to spin-flip models. In such spin-flip models, a coupling operator is the basic object for which we show that the cyclic symmetry is transformed into a tracelessness of the coupling operator. The main results are related to the spin-free theory of spin properties. In particular, the theorem previously stated (Luzanov and Whyman, Int J Quantum Chem, 1981, 20, 1179) is refined by an explicit general representation of spin density operators through spin-free (charge) RDMs. Some applications implicating high-order RDMs (collectivity numbers, the unpaired electron problem, cumulant spin RDMs, spin correlators, etc.) are also considered. For spin-free RDM components, a new projection procedure without constructing any symmetry adapted state is proposed. An unsolved problem of constructing orthogonal representation matrices within the Fock theory is raised. © 2010 Wiley Periodicals, Inc. |

3. | Luzanov, Anatoliy Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity, chirality, and aromaticity (Journal Article) International Journal of Quantum Chemistry, 111 (10), pp. 2196-2220, 2011. (Abstract | Links | BibTeX | Tags: Quantum chemistry, stereochemistry) @article{Luzanov20112196, title = {Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity, chirality, and aromaticity}, author = {Luzanov, Anatoliy V}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-79955435280&partnerID=40&md5=4769f6fd7110d00bd8142d98d38482c6, http://doi.wiley.com/10.1002/qua.22510}, year = {2011}, date = {2011-01-01}, journal = {International Journal of Quantum Chemistry}, volume = {111}, number = {10}, pages = {2196-2220}, abstract = {Quantum information theory is applied to formulate a new technique for dealing with molecular similarity problems. In this technique, the so-called quantum fidelity appears to be a counterpart of the conventional similarity measure due to Carbo (Carbo, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980, 17, 1185). We define many-body spin-free density matrices for atoms and fragments in molecule, and compute corresponding fidelity measures for molecular subsystems. It allows us to treat the problem from the beginning within a many-electron setting. The approach is employed for analyzing similarity between free atoms and atoms in molecule. A new chirality index, as based on the fidelity between molecule and its mirror image, is suggested to be an approximately additive nonnegative quantity. We also examine a local aromaticity by computing the fidelity measures for benzenoid fragments in polyaromatic hydrocarbons. A detailed study of the proposed indices is reported at the ab initio or semiempirical levels. Copyright © 2010 Wiley Periodicals, Inc.}, keywords = {Quantum chemistry, stereochemistry}, pubstate = {published}, tppubtype = {article} } Quantum information theory is applied to formulate a new technique for dealing with molecular similarity problems. In this technique, the so-called quantum fidelity appears to be a counterpart of the conventional similarity measure due to Carbo (Carbo, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980, 17, 1185). We define many-body spin-free density matrices for atoms and fragments in molecule, and compute corresponding fidelity measures for molecular subsystems. It allows us to treat the problem from the beginning within a many-electron setting. The approach is employed for analyzing similarity between free atoms and atoms in molecule. A new chirality index, as based on the fidelity between molecule and its mirror image, is suggested to be an approximately additive nonnegative quantity. We also examine a local aromaticity by computing the fidelity measures for benzenoid fragments in polyaromatic hydrocarbons. A detailed study of the proposed indices is reported at the ab initio or semiempirical levels. Copyright © 2010 Wiley Periodicals, Inc. |

2. | Luzanov, Anatoliy Matrix-covariant representation of high-order configuration interaction and coupled cluster theories (Journal Article) International Journal of Quantum Chemistry, 108 (4), pp. 671-695, 2007. (Abstract | Links | BibTeX | Tags: Approximation theory, Hole-particle Hamiltonians, Polyexciton models, Quantum chemistry, reduced density matrices) @article{Luzanov2008671, title = {Matrix-covariant representation of high-order configuration interaction and coupled cluster theories}, author = {Luzanov, Anatoliy V}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-38449086509&partnerID=40&md5=2e6224b5d4c0895323c43e0ba8a94b7b, http://doi.wiley.com/10.1002/qua.21551}, year = {2007}, date = {2007-01-01}, journal = {International Journal of Quantum Chemistry}, volume = {108}, number = {4}, pages = {671-695}, abstract = {We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix-covariant expressions independent of the basis set used. The corresponding variational Q equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix-covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high-order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin-flip approximation closely related to high-order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three-electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many-body problem. © 2007 Wiley Periodicals, Inc.}, keywords = {Approximation theory, Hole-particle Hamiltonians, Polyexciton models, Quantum chemistry, reduced density matrices}, pubstate = {published}, tppubtype = {article} } We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix-covariant expressions independent of the basis set used. The corresponding variational Q equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix-covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high-order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin-flip approximation closely related to high-order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three-electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many-body problem. © 2007 Wiley Periodicals, Inc. |

1. | Luzanov,; Prezhdo, High-order entropy measures and spin-free quantum entanglement for molecular problems (Journal Article) Molecular Physics, 105 (19-22), pp. 2879-2891, 2007. (Abstract | Links | BibTeX | Tags: Dissociated states, Dissociation, Electronic structure, Entropy, Entropy measure, Fock construction, Quantum chemistry, Quantum entanglement, spin-free quantum chemistry) @article{Luzanov20072879, title = {High-order entropy measures and spin-free quantum entanglement for molecular problems}, author = {Luzanov, A. V. and Prezhdo, O.V.b}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-38849181102&partnerID=40&md5=d17ac9319497ab5ce49bae5dd4e0bd51, http://www.tandfonline.com/doi/abs/10.1080/00268970701725039}, year = {2007}, date = {2007-01-01}, journal = {Molecular Physics}, volume = {105}, number = {19-22}, pages = {2879-2891}, abstract = {A new entropy measure is proposed for the molecular electronic structure theory. The corresponding many-electron, Shannon-like measure reflects quantum entanglement between electronic subsystems with different spins. The related Renyi entropy is introduced, and its connection with the previously considered collectivity analysis is discussed. Investigation of the second-order reduced density matrix (2-RDM) allows one to define an irreducible, size-consistent component of the 2-RDM entropy and to find the irreducible component of the 2-RDM squared norm. Specific computations on several small molecules are carried out at the full configuration interaction level, providing new insights into non-classical, long-range electron correlations and quantum entanglement in these systems. The local spin analysis and the spin-correlator analysis reveal nontrivial spin structure underlying the entangled states.}, keywords = {Dissociated states, Dissociation, Electronic structure, Entropy, Entropy measure, Fock construction, Quantum chemistry, Quantum entanglement, spin-free quantum chemistry}, pubstate = {published}, tppubtype = {article} } A new entropy measure is proposed for the molecular electronic structure theory. The corresponding many-electron, Shannon-like measure reflects quantum entanglement between electronic subsystems with different spins. The related Renyi entropy is introduced, and its connection with the previously considered collectivity analysis is discussed. Investigation of the second-order reduced density matrix (2-RDM) allows one to define an irreducible, size-consistent component of the 2-RDM entropy and to find the irreducible component of the 2-RDM squared norm. Specific computations on several small molecules are carried out at the full configuration interaction level, providing new insights into non-classical, long-range electron correlations and quantum entanglement in these systems. The local spin analysis and the spin-correlator analysis reveal nontrivial spin structure underlying the entangled states. |

# Publications

## Journal Articles | |

5. | Estimating stacking interaction energy using atom in molecules properties: Homodimers of benzene and pyridine (Journal Article) International Journal of Quantum Chemistry, 112 (18), pp. 3008-3017, 2012. |

4. | Spin-free quantum chemistry: What one can gain from fock's cyclic symmetry (Journal Article) International Journal of Quantum Chemistry, 111 (15), pp. 4042-4066, 2011. |

3. | Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity, chirality, and aromaticity (Journal Article) International Journal of Quantum Chemistry, 111 (10), pp. 2196-2220, 2011. |

2. | Matrix-covariant representation of high-order configuration interaction and coupled cluster theories (Journal Article) International Journal of Quantum Chemistry, 108 (4), pp. 671-695, 2007. |

1. | High-order entropy measures and spin-free quantum entanglement for molecular problems (Journal Article) Molecular Physics, 105 (19-22), pp. 2879-2891, 2007. |