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Schwarz E, Müller U, Kraus F. The Good Reasons for a Standard Periodic Table of the Chemical Elements. Z Anorg Allg Chem 2022. [DOI: 10.1002/zaac.202200008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
| | | | - Florian Kraus
- Philipps-Universitat Marburg Fachbereich Chemie Chemie Hans-Meerwein-Straße 4 35032 Marburg GERMANY
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2
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Chen K, Li WL, Schwarz WHE. d- and s-orbital populations in the d block: unbound atoms in physical vacuum versus chemical elements in condensed matter. A Dronskowski-population analysis. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION B-A JOURNAL OF CHEMICAL SCIENCES 2021. [DOI: 10.1515/znb-2021-0139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
The electron configurations of Ca, Zn and the nine transition elements M in between (and their heavier homologs) are reviewed on the basis of density functional theory and experimental facts. The d-s orbital energy and population patterns are systematically diverse. (i) The dominant valence electron configuration of most free neutral atoms M0 of groups g = 2–12 is 3d
g−2
4s
2
(textbook rule), or 3d
g−14s
1. (ii) Formal M
q+
cations in chemical compounds have the dominant configuration 3d
g−q
4s
0
(basic concept of transition metal chemistry). (iii) M0 atoms in metallic phases [M∞] of hcp, ccp(fcc) and bcc structures have intermediate populations near 3d
g−1
4s
1
(lower d populations for Ca (ca. ½) and Zn (ca. 10)). Including the 4p valence orbitals, the dominant metallic configuration is 3d
g−δ
4(sp)
δ
with δ ≈ 1.4 (±0.2) throughout (except for Zn). (iv) The 3d,4s population of atomic clusters M
m
varies for increasing m smoothly from single-atomic 3d
g−24s
2 toward metallic 3d
g−14s
1. – The textbook rule for the one-electron energies, i.e., ns < (n−1)d, holds ‘in a broader sense’ for the s block, but in general not for the d block, and never for the p block. It is more important to teach realistic atomic orbital (AO) populations such as the ones given above.
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Affiliation(s)
- Kaixuan Chen
- Chair of Solid-State and Quantum Chemistry , Institute of Inorganic Chemistry, RWTH Aachen University , 52056 Aachen , Germany
| | - Wan-Lu Li
- Department of Chemistry and Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education , Tsinghua University , Beijing 100084 , P. R. China
| | - W. H. Eugen Schwarz
- Tsinghua University, Theoretical Chemistry Center , Beijing 100084 , P. R. China
- University at Siegen, Physical and Theoretical Chemistry Group , 57068 Siegen , Germany
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3
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Cao C, Vernon RE, Schwarz WHE, Li J. Understanding Periodic and Non-periodic Chemistry in Periodic Tables. Front Chem 2021; 8:813. [PMID: 33490030 PMCID: PMC7818537 DOI: 10.3389/fchem.2020.00813] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Accepted: 08/03/2020] [Indexed: 12/15/2022] Open
Abstract
The chemical elements are the "conserved principles" or "kernels" of chemistry that are retained when substances are altered. Comprehensive overviews of the chemistry of the elements and their compounds are needed in chemical science. To this end, a graphical display of the chemical properties of the elements, in the form of a Periodic Table, is the helpful tool. Such tables have been designed with the aim of either classifying real chemical substances or emphasizing formal and aesthetic concepts. Simplified, artistic, or economic tables are relevant to educational and cultural fields, while practicing chemists profit more from "chemical tables of chemical elements." Such tables should incorporate four aspects: (i) typical valence electron configurations of bonded atoms in chemical compounds (instead of the common but chemically atypical ground states of free atoms in physical vacuum); (ii) at least three basic chemical properties (valence number, size, and energy of the valence shells), their joint variation across the elements showing principal and secondary periodicity; (iii) elements in which the (sp)8, (d)10, and (f)14 valence shells become closed and inert under ambient chemical conditions, thereby determining the "fix-points" of chemical periodicity; (iv) peculiar elements at the top and at the bottom of the Periodic Table. While it is essential that Periodic Tables display important trends in element chemistry we need to keep our eyes open for unexpected chemical behavior in ambient, near ambient, or unusual conditions. The combination of experimental data and theoretical insight supports a more nuanced understanding of complex periodic trends and non-periodic phenomena.
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Affiliation(s)
- Changsu Cao
- Department of Chemistry, Tsinghua University, Beijing, China
| | | | - W. H. Eugen Schwarz
- Department of Chemistry, Tsinghua University, Beijing, China
- Department of Chemistry, University of Siegen, Siegen, Germany
| | - Jun Li
- Department of Chemistry, Tsinghua University, Beijing, China
- Department of Chemistry, Southern University of Science and Technology, Shenzhen, China
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4
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Scerri E. Recent attempts to change the periodic table. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190300. [PMID: 32811365 DOI: 10.1098/rsta.2019.0300] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/11/2020] [Indexed: 06/11/2023]
Abstract
The article concerns various proposals that have been made with the aim of improving the currently standard 18-column periodic table. We begin with a review of 8-, 18- and 32-column formats of the periodic table. This is followed by an examination of a possible, although rather impractical, 50-column table and how it could be used to consider the changes to the periodic table that have been predicted by Pyykkö in the domain of superheavy elements. Other topics reviewed include attempts to derive the Madelung rule as well as an analysis of what this rule actually provides. Finally, the notion of an 'optimal' periodic table is discussed in the context of recent work by philosophers of science who have examined the nature of classifications in general, as well as the notion of natural kinds. The article takes an unapologetically philosophical approach rather than focusing on specific data concerning the elements. Nevertheless, some pragmatic issues and educational aspects of the periodic table are also examined. This article is part of the theme issue 'Mendeleev and the periodic table'.
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Affiliation(s)
- Eric Scerri
- Department of Chemistry & Biochemistry, University of California Los Angeles, Los Angeles, CA 90095, USA
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5
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Joy J, Danovich D, Kaupp M, Shaik S. Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding. J Am Chem Soc 2020; 142:12277-12287. [PMID: 32571021 DOI: 10.1021/jacs.0c03957] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s2(n - 1)p6 semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d10 core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.
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Affiliation(s)
- Jyothish Joy
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - David Danovich
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie - Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Sason Shaik
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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6
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Cao CS, Hu HS, Li J, Schwarz WHE. Physical origin of chemical periodicities in the system of elements. PURE APPL CHEM 2019. [DOI: 10.1515/pac-2019-0901] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Abstract
The Periodic Law, one of the great discoveries in human history, is magnificent in the art of chemistry. Different arrangements of chemical elements in differently shaped Periodic Tables serve for different purposes. “Can this Periodic Table be derived from quantum chemistry or physics?” can only be answered positively, if the internal structure of the Periodic Table is explicitly connected to facts and data from chemistry. Quantum chemical rationalization of such a Periodic Tables is achieved by explaining the details of energies and radii of atomic core and valence orbitals in the leading electron configurations of chemically bonded atoms. The coarse horizontal pseudo-periodicity in seven rows of 2, 8, 8, 18, 18, 32, 32 members is triggered by the low energy of and large gap above the 1s and nsp valence shells (2 ≤ n ≤ 6 !). The pseudo-periodicity, in particular the wavy variation of the elemental properties in the four longer rows, is due to the different behaviors of the s and p vs. d and f pairs of atomic valence shells along the ordered array of elements. The so-called secondary or vertical periodicity is related to pseudo-periodic changes of the atomic core shells. The Periodic Law of the naturally given System of Elements describes the trends of the many chemical properties displayed inside the Chemical Periodic Tables. While the general physical laws of quantum mechanics form a simple network, their application to the unlimited field of chemical materials under ambient ‘human’ conditions results in a complex and somewhat accidental structure inside the Table that fits to some more or less symmetric outer shape. Periodic Tables designed after some creative concept for the overall appearance are of interest in non-chemical fields of wisdom and art.
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Affiliation(s)
- Chang-Su Cao
- Department of Chemistry , Theoretical Chemistry Center, Tsinghua University , Beijing 100084 China
| | - Han-Shi Hu
- Department of Chemistry , Theoretical Chemistry Center, Tsinghua University , Beijing 100084 China
| | - Jun Li
- Department of Chemistry , Theoretical Chemistry Center, Tsinghua University , Beijing 100084 China
- Department of Chemistry , Southern University of Science and Technology , Shenzhen 518055 China
| | - W. H. Eugen Schwarz
- Department of Chemistry , Theoretical Chemistry Center, Tsinghua University , Beijing 100084 China
- Physical Chemistry Lab , S&T Faculty, Siegen University , Siegen 57068 Germany
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7
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8
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Rahm M, Hoffmann R, Ashcroft NW. Atomic and Ionic Radii of Elements 1
–96. Chemistry 2016; 22:14625-32. [DOI: 10.1002/chem.201602949] [Citation(s) in RCA: 160] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Indexed: 11/09/2022]
Affiliation(s)
- Martin Rahm
- Department of Chemistry and Chemical Biology Cornell University Ithaca New York 14853 USA
| | - Roald Hoffmann
- Department of Chemistry and Chemical Biology Cornell University Ithaca New York 14853 USA
| | - N. W. Ashcroft
- Laboratory of Atomic and Solid State Physics Cornell University Ithaca New York 14853 USA
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9
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Wolters LP, van Zeist WJ, Bickelhaupt FM. New Concepts for Designing d10-M(L)nCatalysts: d Regime, s Regime and Intrinsic Bite-Angle Flexibility. Chemistry 2014; 20:11370-81. [DOI: 10.1002/chem.201403237] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 11/09/2022]
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10
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Hojilla Atienza CC, Milsmann C, Semproni SP, Turner ZR, Chirik PJ. Reversible Carbon–Carbon Bond Formation Induced by Oxidation and Reduction at a Redox-Active Cobalt Complex. Inorg Chem 2013; 52:5403-17. [DOI: 10.1021/ic400352r] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
| | - Carsten Milsmann
- Department of Chemistry, Princeton
University, Princeton,
New Jersey 08544, United States
| | - Scott P. Semproni
- Department of Chemistry, Princeton
University, Princeton,
New Jersey 08544, United States
| | - Zoë R. Turner
- Department of Chemistry, Princeton
University, Princeton,
New Jersey 08544, United States
| | - Paul J. Chirik
- Department of Chemistry, Princeton
University, Princeton,
New Jersey 08544, United States
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11
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Su J, Zhang K, Schwarz WHE, Li J. Uranyl-Glycine-Water Complexes in Solution: Comprehensive Computational Modeling of Coordination Geometries, Stabilization Energies, and Luminescence Properties. Inorg Chem 2011; 50:2082-93. [DOI: 10.1021/ic200204p] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jing Su
- Department of Chemistry and Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Kai Zhang
- Department of Chemistry and Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China
| | - W. H. Eugen Schwarz
- Department of Chemistry and Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jun Li
- Department of Chemistry and Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China
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12
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An Introduction to Relativistic Quantum Chemistry. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-1-4020-9975-5_1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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13
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Wang SG, Schwarz W. Symbol der Chemie: Das Periodensystem der chemischen Elemente im jungen Jahrhundert. Angew Chem Int Ed Engl 2009. [DOI: 10.1002/ange.200800827] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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14
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Wang SG, Schwarz W. Icon of Chemistry: The Periodic System of Chemical Elements in the New Century. Angew Chem Int Ed Engl 2009; 48:3404-15. [DOI: 10.1002/anie.200800827] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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15
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Polestshuk PM, Dem’yanov PI, Ryabinkin IG. The electronic structure and energetics of V+-benzene half-sandwiches of different multiplicities: Comparative multireference and single-reference theoretical study. J Chem Phys 2008; 129:054307. [DOI: 10.1063/1.2955741] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Grochala W, Hoffmann R, Feng J, Ashcroft NW. The Chemical Imagination at Work inVery Tight Places. Angew Chem Int Ed Engl 2007; 46:3620-42. [PMID: 17477335 DOI: 10.1002/anie.200602485] [Citation(s) in RCA: 258] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Diamond-anvil-cell and shock-wave technologies now permit the study of matter under multimegabar pressure (that is, of several hundred GPa). The properties of matter in this pressure regime differ drastically from those known at 1 atm (about 10(5) Pa). Just how different chemistry is at high pressure and what role chemical intuition for bonding and structure can have in understanding matter at high pressure will be explored in this account. We will discuss in detail an overlapping hierarchy of responses to increased density: a) squeezing out van der Waals space (for molecular crystals); b) increasing coordination; c) decreasing the length of covalent bonds and the size of anions; and d) in an extreme regime, moving electrons off atoms and generating new modes of correlation. Examples of the startling chemistry and physics that emerge under such extreme conditions will alternate in this account with qualitative chemical ideas about the bonding involved.
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Affiliation(s)
- Wojciech Grochala
- ICM and Department of Chemistry, Warsaw University, Warsaw 02-106, Poland.
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17
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Grochala W, Hoffmann R, Feng J, Ashcroft N. Chemie unter höchsten Drücken: eine Herausforderung für die chemische Intuition. Angew Chem Int Ed Engl 2007. [DOI: 10.1002/ange.200602485] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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18
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Bitter T, Ruedenberg K, Schwarz WHE. Toward a physical understanding of electron-sharing two-center bonds. I. General aspects. J Comput Chem 2006; 28:411-22. [PMID: 17143871 DOI: 10.1002/jcc.20531] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
In 1916, Lewis and Kossel laid the empirical ground for the electronic theory of valence, whose quantum theoretical foundation was uncovered only slowly. We can now base the classification of the various traditional chemical bond types in a threefold manner on the one- and two-electron terms of the quantum-physical Hamiltonian (kinetic, atomic core attraction, electron repulsion). Bond formation is explained by splitting up the real process into two physical steps: (i) interaction of undeformed atoms and (ii) relaxation of this nonstationary system. We aim at a flexible bond energy partitioning scheme that can avoid cancellation of large terms of opposite sign. The driving force of covalent bonding is a lowering of the quantum kinetic energy density by sharing. The driving force of heteropolar bonding is a lowering of potential energy density by charge rearrangement in the valence shell. Although both mechanisms are quantum mechanical in nature, we can easily visualize them, since they are of one-electron type. They are however tempered by two-electron correlations. The richness of chemistry, owing to the diversity of atomic cores and valence shells, becomes intuitively understandable with the help of effective core pseudopotentials for the valence shells. Common conceptual difficulties in understanding chemical bonds arise from quantum kinematic aspects as well as from paradoxical though classical relaxation phenomena. On this conceptual basis, a dozen different bond types in diatomic molecules will be analyzed in the following article. We can therefore examine common features as well as specific differences of various bonding mechanisms.
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Affiliation(s)
- T Bitter
- Theoretical Chemistry, University Siegen, D-57068 Siegen, Germany
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19
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Kaupp M. The role of radial nodes of atomic orbitals for chemical bonding and the periodic table. J Comput Chem 2006; 28:320-5. [PMID: 17143872 DOI: 10.1002/jcc.20522] [Citation(s) in RCA: 90] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
The role of radial nodes, or of their absence, in valence orbitals for chemical bonding and periodic trends is discussed from a unified viewpoint. In particular, we emphasize the special role of the absence of a radial node whenever a shell with angular quantum number l is occupied for the first time (lack of "primogenic repulsion"), as with the 1s, 2p, 3d, and 4f shells. Although the consequences of the very compact 2p shell (e.g. good isovalent hybridization, multiple bonding, high electronegativity, lone-pair repulsion, octet rule) are relatively well known, it seems that some of the aspects of the very compact 3d shell in transition-metal chemistry are less well appreciated, e.g., the often weakened and stretched bonds at equilibrium structure, the frequently colored complexes, and the importance of nondynamical electron-correlation effects in bonding.
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Affiliation(s)
- Martin Kaupp
- Institut für Anorganische Chemie, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.
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