101
|
Chattaraj PK, Giri S. Stability, Reactivity, and Aromaticity of Compounds of a Multivalent Superatom. J Phys Chem A 2007; 111:11116-21. [DOI: 10.1021/jp0760758] [Citation(s) in RCA: 188] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
102
|
|
103
|
Padmanabhan J, Parthasarathi R, Elango M, Subramanian V, Krishnamoorthy BS, Gutierrez-Oliva S, Toro-Labbé A, Roy DR, Chattaraj PK. Multiphilic Descriptor for Chemical Reactivity and Selectivity. J Phys Chem A 2007; 111:9130-8. [PMID: 17715901 DOI: 10.1021/jp0718909] [Citation(s) in RCA: 106] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In line with the local philicity concept proposed by Chattaraj et al. (Chattaraj, P. K.; Maiti, B.; Sarkar, U. J. Phys. Chem. A. 2003, 107, 4973) and a dual descriptor derived by Morell, Grand and Toro-Labbé, (J. Phys. Chem. A 2005, 109, 205), we propose a multiphilic descriptor. It is defined as the difference between nucleophilic (omega(k)+) and electrophilic (omega(k)-) condensed philicity functions. This descriptor is capable of simultaneously explaining the nucleophilicity and electrophilicity of the given atomic sites in the molecule. Variation of these quantities along the path of a soft reaction is also analyzed. Predictive ability of this descriptor has been successfully tested on the selected systems and reactions. Corresponding force profiles are also analyzed in some representative cases. Also, to study the intra- and intermolecular reactivities another related descriptor, namely, the nucleophilicity excess (Deltaomega(g)-/+) for a nucleophile over the electrophilicity in it, has been defined and tested on all-metal aromatic compounds.
Collapse
|
104
|
|
105
|
Chattaraj PK, Roy DR. Aromaticity in Polyacene Analogues of Inorganic Ring Compounds. J Phys Chem A 2007; 111:4684-96. [PMID: 17480062 DOI: 10.1021/jp071030s] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The aromaticity in the polyacene analogues of several inorganic ring compounds (BN-acenes, CN-acenes, AlN-acenes, BO-acenes, BS-acenes, and Na6-acenes) is reported here for the first time. Conceptual density functional theory-based reactivity descriptors and the nucleus-independent chemical shift (NICS) values are used in this analysis. The nature of the site selectivity is understood through the charges and the philicities.
Collapse
|
106
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. Electrophilicity-Based Charge Transfer Descriptor. J Phys Chem A 2007; 111:1358-61. [PMID: 17256919 DOI: 10.1021/jp0649549] [Citation(s) in RCA: 289] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In line with the charge transfer (DeltaNmax = -mu/eta) proposed by Parr et al. (Parr, R. G.; Szentpály, L. V.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922), we propose an electrophilicity-based charge transfer (ECT) descriptor in this paper and validate it through the interaction between a series of chlorophenols and DNA bases. Application of ECT can be extended to the interaction of any toxin with the biosystem.
Collapse
|
107
|
Chattaraj PK, Roy DR. A Possible Union of Chemical Bonding, Reactivity, and Kinetics. J Phys Chem A 2006; 110:11401-3. [PMID: 17020249 DOI: 10.1021/jp0649293] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this communication, we report for the first time the reactivity behavior at the transition state, the connection between the equireactivity configuration and the activation barrier, and a possible principle of reactivity conservation along the reaction paths of typical thermoneutral and exo (endo) thermic reactions.
Collapse
|
108
|
Tanwar A, Pal S, Ranjan Roy D, Kumar Chattaraj P. Minimum magnetizability principle. J Chem Phys 2006; 125:056101. [PMID: 16942262 DOI: 10.1063/1.2227381] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
109
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. Theoretical Study on the Complete Series of Chloroanilines. J Phys Chem A 2006; 110:9900-7. [PMID: 16898692 DOI: 10.1021/jp061436p] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The environmental effects of chloroanilines depend on their physical and chemical properties, and it is therefore important to know their structure-property relationships that allow a complete understanding of their environmental consequences. The chemical reactivity profiles of all 19 chloroanilines have been investigated using the density functional theory for the first time. Global reactivity descriptors, such as hardness, chemical potential, electrophilicity index, and polarizability, and local reactivity descriptors, namely, local philicities, have been calculated in order to gain insights into the reactive nature and the reactive sites of the selected systems. Using AIM theory, the presence of hydrogen bond critical points (HBCPs) and the values of electron density and Laplacian of electron density at the HBCPs have been analyzed to appreciate the presence of intramolecular hydrogen bonding in the selected systems. Structure-toxicity analysis of the selected set of chloroanilines demonstrates the importance of the electrophilicity index in the prediction of reactivity/toxicity.
Collapse
|
110
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. Group philicity and electrophilicity as possible descriptors for modeling ecotoxicity applied to chlorophenols. Chem Res Toxicol 2006; 19:356-64. [PMID: 16544939 DOI: 10.1021/tx050322m] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The search for the best quantitative structure-activity relationship (QSAR) models in ecotoxicology is an ever-topical research activity. Hence, the development of new descriptors and applying them successfully in QSAR studies seems demanding in ecotoxicology. In the present work, group philicities are utilized for the first time in QSAR analysis for ecotoxicological studies on chlorophenols (CPs). It is important to point out that group philicities are capable of providing the best QSAR model for the toxicity of CPs against Daphnia magna. Furthermore, global electrophilicity and group philicities together give the best QSAR models for Brachydanio rerio and Bacillus with the maximum value of coefficient of determination and high internal predictive ability. The developed QSAR models clearly show the importance of the selected density functional reactivity indices as descriptors in ecotoxicological studies.
Collapse
|
111
|
Roy DR, Sarkar U, Chattaraj PK, Mitra A, Padmanabhan J, Parthasarathi R, Subramanian V, Van Damme S, Bultinck P. Analyzing Toxicity Through Electrophilicity. Mol Divers 2006; 10:119-31. [PMID: 16763875 DOI: 10.1007/s11030-005-9009-x] [Citation(s) in RCA: 82] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2005] [Accepted: 12/20/2005] [Indexed: 10/24/2022]
Abstract
The toxicological structure-activity relationships are investigated using conceptual DFT based descriptors like global and local electrophilicities. In the present work the usefulness of electrophilicity in predicting toxicity of several polyaromatic hydrocarbons (PAH) is assessed. The toxicity is expressed through biological activity data (pIC50) defined as molar concentration of those chemicals necessary to displace 50% of radiolabeled tetrachlorodibenzo-p-dioxin (TCDD) from the arylhydrocarbon (Ah) receptor. The experimental toxicity values (pIC50) for the electron acceptor toxin like polychlorinated dibenzofurans (PCDF) are taken as dependent variables and the DFT based global descriptor electrophilicity index (omega) is taken as independent variable in the training set. The same model is then tested on a test set of polychlorinated biphenyls (PCB). A good correlation is obtained which vindicates the importance of these descriptors in the QSAR studies on toxins. These toxins act as electron acceptors in the presence of biomolecules whereas aliphatic amines behave as electron donors some of which are also taken into account for the present work. The toxicity values of the aliphatic amines in terms of the 50% inhibitory growth concentration (IGC50) towards ciliate fresh-water protozoa Tetrahymena pyriformis are considered. Since there is no global nucleophilicity we apply local nucleophilicity (omegamax+) as the descriptor in this case of training set. The same regression model is then applied to a test set of amino alcohols. Although the correlation is very good the statistical analysis reflects some cross validation problem. As a further check the amines and amino alcohols are used together to form both the training and the test sets to provide good correlation. It is demonstrated that the toxicity of several toxins (both electron donors and acceptors) in the gas and solution phases can be adequately explained in terms of global and local electrophilicities. Amount of charge transfer between the toxin and the biosystem, simulated as nucleic acid bases and DNA base pairs, indicates the importance of charge transfer in the observed toxicity. The major strength of the present analysis vis-à-vis the existing ones rests on the fact that it requires only one descriptor having a direct relationship with toxicity to provide a better correlation. Importance of using the information from both the toxin and the biosystem is also analyzed.
Collapse
|
112
|
Parthasarathi R, Padmanabhan J, Elango M, Chitra K, Subramanian V, Chattaraj PK. pKa Prediction Using Group Philicity. J Phys Chem A 2006; 110:6540-4. [PMID: 16706412 DOI: 10.1021/jp055849m] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Acid-base dissociation constants (pK(a) values) are important in understanding the chemical, environmental and toxicological properties of molecules. Though various methods have been developed to predict pK(a) by experimental and theoretical models, prediction of pK(a) is still complicated. Hence, a new approach for predicting pK(a) using the group philicity concept has been attempted. Presence of known functional groups in a molecule is utilized as the most important indicator to predict pK(a). The power of this descriptor in describing pK(a) for the series of carboxylic acids, various substituted phenols, anilines, phosphoric acids, and alcohols is probed. Results reveal that the group electrophilicity is suitable for effectively predicting the pK(a) values.
Collapse
|
113
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. Chemical Reactivity Indices for the Complete Series of Chlorinated Benzenes: Solvent Effect. J Phys Chem A 2006; 110:2739-45. [PMID: 16494385 DOI: 10.1021/jp056630a] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a comprehensive analysis to probe the effect of solvation on the reactivity of the complete series of chlorobenzenes through the conceptual density functional theory (DFT)-based global and local descriptors. We propose a multiphilic descriptor in this study to explore the nature of attack at a particular site in a molecule. It is defined as the difference between nucleophilic and electrophilic condensed philicity functions. This descriptor is capable of explaining both the nucleophilicity and electrophilicity of the given atomic sites in the molecule simultaneously. The predictive ability of this descriptor is tested on the complete series of chlorobenzenes in gas and solvent media. A structure-toxicity analysis of these entire sets of chlorobenzenes toward aquatic organisms demonstrates the importance of the electrophilicity index in the prediction of the reactivity/toxicity.
Collapse
|
114
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. QSPR models for polychlorinated biphenyls: n-Octanol/water partition coefficient. Bioorg Med Chem 2006; 14:1021-8. [PMID: 16214354 DOI: 10.1016/j.bmc.2005.09.017] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2005] [Revised: 09/02/2005] [Accepted: 09/07/2005] [Indexed: 10/25/2022]
Abstract
The logarithmic n-octanol/water partition coefficient (logK(ow)) is an important property for pharmacology, toxicology and medicinal chemistry. Quantitative structure-property relationship (QSPR) model for the lipophilic behaviour (logK(ow)) of the data set containing 133 polychlorinated biphenyl (PCB) congeners is analyzed using the conceptual density functional theory based global reactivity parameter such as electrophilicity index (omega) along with energy of lowest unoccupied molecular orbital (E(LUMO)) and number of chlorine substituents (N(Cl)) as descriptors. A reasonably good coefficient of determination (r(2) = 0.914) and the internal predictive ability (r(cv)(2) = 0.909) values are obtained indicating the significance of the considered descriptors in the property analysis of PCBs. Further, the developed method has widespread applicability from chemical reactivity to toxicity analysis and in studies related to various physicochemical properties in the series of dioxins and other polyaromatic hydrocarbons.
Collapse
|
115
|
Roy DR, Parthasarathi R, Padmanabhan J, Sarkar U, Subramanian V, Chattaraj PK. Careful Scrutiny of the Philicity Concept. J Phys Chem A 2006; 110:1084-93. [PMID: 16420012 DOI: 10.1021/jp053641v] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The philicity concept [J. Phys. Chem. A 2003, 107, 4973] is put in proper perspective. In the present work we analyze different physicochemical problems using philicity. It provides satisfactory results in all such cases. We also compare the relative electro(nucleo)philicity with philicity to show that philicity is better than relative electro(nucleo)philicity when the intermolecular reactivity trends are considered and there is hardly any preference of one above the other as far as the intramolecular reactivities are concerned. On the contrary, the philicity concept has some advantages over the other concept.
Collapse
|
116
|
Padmanabhan J, Parthasarathi R, Subramanian V, Chattaraj PK. Molecular Structure, Reactivity, and Toxicity of the Complete Series of Chlorinated Benzenes. J Phys Chem A 2005; 109:11043-9. [PMID: 16331949 DOI: 10.1021/jp0538621] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The structure and chemical reactivity profiles of all 12 chlorobenzenes have been investigated using the density functional theory and ab initio molecular orbital calculations. Global and local reactivity descriptors such as electrophilicity index and local philicity, respectively, of the selected systems have been calculated in order to gain insights into the reactive nature and the reactive sites of these compounds. Also, the effects of chlorine substitution on the aromaticity of the compounds have been analyzed by calculating the nucleus-independent chemical shift. Interaction through charge transfer between chlorobenzenes and nucleic acid bases/selected base pairs are determined using Parr's formula. The results revealed that the chlorobenzenes act as electron acceptors in their interaction with biomolecules. Structure-toxicity analysis of this entire set of chlorobenzenes demonstrates the importance of the electrophilicity index in the prediction of reactivity/toxicity.
Collapse
|
117
|
Chattaraj PK, Roy DR, Elango M, Subramanian V. Stability and Reactivity of All-Metal Aromatic and Antiaromatic Systems in Light of the Principles of Maximum Hardness and Minimum Polarizability. J Phys Chem A 2005; 109:9590-7. [PMID: 16866412 DOI: 10.1021/jp0540196] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
It is demonstrated that among various possible isomers of all-metal aromatic compounds such as Al(4)(2-) and their complexes the most stable isomer with the minimum energy is the hardest and the least polarizable. A similar situation is observed for different isomers of all-metal antiaromatic compounds such as Al(4)(4-) and their complexes. It is shown that linear Al(4)(4-) is energetically more stable than its cyclic isomer. The reaction energies associated with the complexation processes highlight the stability of those complexes. The difference in energy, hardness, and polarizability between a cyclic molecule and its linear counterpart convincingly shows that an aromatic molecule exhibits negative changes in energy and polarizability but positive changes in hardness as expected from the principles of minimum energy, minimum polarizability, and maximum hardness. Although the aromaticity of Al(4)(2-) is unequivocally established through this study, the antiaromaticity picture in the case of Al(4)(4-) is shown to be poorly understood;however, the present analysis sheds light on this controversy.
Collapse
|
118
|
Roy DR, Parthasarathi R, Maiti B, Subramanian V, Chattaraj PK. Electrophilicity as a possible descriptor for toxicity prediction. Bioorg Med Chem 2005; 13:3405-12. [PMID: 15848752 DOI: 10.1016/j.bmc.2005.03.011] [Citation(s) in RCA: 126] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2005] [Revised: 03/02/2005] [Accepted: 03/02/2005] [Indexed: 11/18/2022]
Abstract
Electrophilicity is one of the cardinal chemical reactivity descriptors successfully employed in various molecular reactivity studies within a structure-activity relationship parlance. The applications of this quantity in the modeling of toxicological properties have inspired us to perform a more exhaustive study in order to test and/or to validate the application of electrophilicity in assessing its chemical and toxicological potential. For this reason the toxicity of a large data set of molecules comprising 252 aliphatic compounds on the Tetrahymena pyriformis is studied. A quantitative structure-activity relationship analysis enabled us to model toxicity in terms of global and local electrophilicities, which provide a reasonably good prediction of aliphatic toxicity. It is heartening to note that the global and local electrophilicity values together can explain the toxicity of a large variety of aliphatic compounds nicely without resorting to any other descriptor or other microscopic/macroscopic physicochemical properties as is the situation in all other QSAR studies.
Collapse
|
119
|
Chattaraj PK, Roy DR. Local Descriptors around a Transition State: A Link between Chemical Bonding and Reactivity. J Phys Chem A 2005; 109:3771-2. [PMID: 16833691 DOI: 10.1021/jp051118a] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this communication, we report for the first time the possible existence of a point of inflection in the profile of a local reactivity descriptor around the transition state. The saddle point of the given reaction coincides with this inflection point which becomes transparent when two such profiles corresponding to bond making and bond breaking processes respectively intersect at the transition state for the thermoneutral reactions. The corresponding ramification of the Hammond postulate for the exo(endo) thermic reactions is also discussed.
Collapse
|
120
|
Parthasarathi R, Subramanian V, Roy DR, Chattaraj PK. Electrophilicity index as a possible descriptor of biological activity. Bioorg Med Chem 2004; 12:5533-43. [PMID: 15465330 DOI: 10.1016/j.bmc.2004.08.013] [Citation(s) in RCA: 266] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2004] [Revised: 07/17/2004] [Accepted: 08/10/2004] [Indexed: 11/28/2022]
Abstract
The purpose of this study is to probe the suitability of DFT based chemical reactivity parameter, electrophilicity index as a possible biological activity descriptor in the development of QSAR. Testosterone derivatives with activity described in terms of various biological activity parameters and the estrogen derivatives by relative binding affinity (RBA) values have been selected as model systems. The implications for the ability of electrophilicity to describe the biological activities are discussed. From the results it is possible to observe that electrophilicity index may be suitable to effectively describe the biological activity.
Collapse
|
121
|
Chattaraj PK, Maiti B, Sarkar U. Philicity: A Unified Treatment of Chemical Reactivity and Selectivity. J Phys Chem A 2003. [DOI: 10.1021/jp034707u] [Citation(s) in RCA: 567] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
122
|
Chattaraj PK, Maiti B. HSAB principle applied to the time evolution of chemical reactions. J Am Chem Soc 2003; 125:2705-10. [PMID: 12603158 DOI: 10.1021/ja0276063] [Citation(s) in RCA: 152] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Time evolution of various reactivity parameters such as electronegativity, hardness, and polarizability associated with a collision process between a proton and an X- atom/ion (X = He, Li(+), Be(2+), B(3+), C(4+)) in its ground ((1)S) and excited((1)P,(1)D,(1)F) electronic states as well as various complexions of a two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion and a proton to give rise to an XH(+) molecule. A favorable dynamical process is characterized by maximum hardness and minimum polarizability values according to the dynamical variants of the principles of maximum hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid, gradually prefers less to interact with X as has been discerned through the drop in maximum hardness value and the increase in the minimum polarizability value when the actual chemical process occurs. Among the noble gas elements, Xe is the most reactive. During the reaction: H(2) + H(+) --> H(3)(+) hardness maximizes and polarizability minimizes and H(2) is more reactive in its excited state. Regioselectivity of proton attack in the O-site of CO is clearly delineated wherein HOC(+) may eventually rearrange itself to go to the thermodynamically more stable HCO(+).
Collapse
|
123
|
Deb BM, Chattaraj PK. Thomas-Fermi-type method for the direct calculation of electronic densities and properties of atoms and ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:1412-1419. [PMID: 9907122 DOI: 10.1103/physreva.45.1412] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
124
|
Deb BM, Chattaraj PK, Mishra S. Time-dependent quantum-fluid density-functional study of high-energy proton-helium collisions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:1248-1257. [PMID: 9905151 DOI: 10.1103/physreva.43.1248] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
125
|
Chattaraj PK. First-gradient corrections in Thomas-Fermi theory. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6505-6508. [PMID: 9903049 DOI: 10.1103/physreva.41.6505] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|