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History of Science DOI: 10.1002/anie.201306024
100th Anniversary of Bohrs Model of the Atom**
W. H. Eugen Schwarz*
Dedicated to Professor W. Kutzelnigg on
the occasion of his 80th birthday
atomic spectroscopy · Bohr,Niels · model of the atom ·
periodic system · quantum chemistry
One hundred years ago this autumn, the young 27-year-old
Danish physicist Niels Bohr published his atomic models.[1] In
1911–1912 he had visited the centers of experimental and
theoretical atomic physics: Cambridge (where Thomson, the
Nobel Laureate of 1906, had discovered the electron in 1897)
and Manchester (where Lord Rutherford, Chemistry Nobel
Laureate of 1908 for studies in radioactivity, had discovered
the atomic nucleus in 1911). The harvest of Bohrs postdoc-
toral stay comprised in particular three papers with the
comprehensive title “On the Constitution of Atoms and
Molecules” published in the Philosophical Magazine in the
fall of 1913.[1a] The papers became famous as “Bohrs
Trilogy”. His “investigation of the structure of atoms” earned
him the Nobel Prize in 1922 (Figure 1).[2]
We shall begin the present account by reviewing the
atomistic concepts in chemistry and physics up to the
beginning of the 20th century (Section 1), a time when many
atomistic phenomena were known in detail but remained
physically unexplainable. Some scientists had concluded that
classical physics needed revision and hypothetical suggestions
inconsistent with classical physics appeared. Against this
background we shall then describe Bohrs fundamental steps
and achievements during the period 1912–1913 as regards the
physical structure and spectra of atoms, the periodic ordering
of the elements, and chemical bonding (Section 2). Finally, we
shall identify Bohrs lasting results for chemistry while also
noting those conjectures that were short-lived (Section 3). In
this context we shall highlight the importance of subsequent
physical discoveries for chemistry, notably the electron spin,
the Pauli exclusion principle, and the Heisenberg uncertainty
principle. We shall conclude with some scientific and philo-
sophical observations and also call attention to certain
definitive and chemically relevant insights of Bohr that still
have not yet found their way into many chemistry textbooks.
Recent short accounts of Bohrs atomic models are found
in Refs. [3–5] , a recommendable book in the present context
is Ref. [6], the respective commented writings in “Niels Bohr
Collected Works” are found in Refs. [7,8]. We will focus on
Bohrs chemically relevant electronic theory, without nuclear
chemistry.
1. Atomism in Chemistry and Physics before Bohr
From Antiquity to Maxwells Electrodynamics. The con-
cept that the world is made up of tiny indestructible and
immutable particles which are subject to causal physical laws
was proposed over 2500 years ago in ancient Greece.[9] In the
first century BC, Titus Lucretius Carus in Rome explained
many chemical and physicochemical phenomena with the
atomistic model, of course in a simplistic and qualitative
manner. For a long time this materialistic approach did not
prevail over theological or teleological world views which
embraced Aristoteles continuum model, but it never com-
pletely died out during the Middle Ages.[10,11]
The revival of “causal mechanical” atomism began in the
Renaissance and continued to gain momentum. In 1611 the
German astronomer Kepler explained the symmetry and
structure of hexagonal snowflakes by the close-packing of
Figure 1. Niels Bohr in the year in which he received the Nobel Prize
(1922).[2]
[*] Prof. Dr. W. H. E. Schwarz
Department of Chemistry, University of Siegen
57068 Siegen (Germany)
and
Tsinghua University Beijing
Beijing 100084 (China)
E-mail: schwarz@chemie.uni-siegen.de
[**] I thank the Chemistry Departments of Tsinghua and Siegen
Universities for support. I am grateful to S. Brandt (Siegen), G.
Frenking (Marburg), A. Karachalios (Mainz), H. Kragh (Aarhus), M.
Schmidt (Ames), and particularly to K. Ruedenberg (Ames) for
many constructive comments and to A. Schirrmacher (Berlin) and
H. Schçnherr (Siegen) for help with the graphics.
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12228-12238
hard, ball-like water particles. In 1646 the French physician
Magnien deduced the first realistic value of molecular sizes
from the diffusion of fragrances in the air. In 1661 the English
polymath Robert Boyle advocated that physical elements
should be deduced from experimental chemical analysis—
a goal that was reached towards the end of the 18th century by
a group of French chemists led by A. de Lavoisier. On this
basis, the English scientist John Dalton introduced the
concept of mechanical atomism into early 19th century
chemistry which thereby became one of its fundamental
concepts. Molecules are formed of unalterable nonpenetrat-
ing spherical atoms that stick together when bonded. The
stoichiometric findings of chemical statics could then be
explained quantitatively with the help of relative atomic
weights and integer valence numbers.[9–12]
In the 18th century Daniel Bernoulli laid the basis for the
kinetic theory of gases. This “kinetic” atomism was fully
implemented by Clausius in the mid-19th century and shortly
thereafter culminated in the statistical mechanics of indivi-
sible particles put forth by Boltzmann, Maxwell, and Gibbs.
Chemical reaction kinetics and reaction equilibria could be
explained phenomenologically. Maxwell, also the father of
electrodynamics, explicitly favored the concept of atoms as
“immutable homogeneous hard vibrating bell-like elemen-
tary bodies”, which can absorb and emit electromagnetic
radiation.[11,13]
Speculations on Inter-Atomic Interactions. A further
atomistic concept had been developed starting in the 18th
century, namely a “dynamic” atomism of physical force
centers. Isaac Newton and subsequently the Croatian poly-
math Rud
¯er Bos
ˇkovic
´assumed the atoms to be comparable to
modulated gravitational (or electric) force centers. After
Voltas invention of the electric battery in 1800 and the
subsequent electrolysis of many compounds, Berzelius con-
jectured the heteropolar bonding of multipolar electric atoms.
In 1844 Faraday, the father of electrochemistry, rejected the
mechanical atomism in favor of the dynamic one. In his
influential Faraday Lecture of 1881 in London, H. von Helm-
holtz discussed the problem of how long-range Coulomb
interactions could give rise to short-range homopolar binding
forces between atoms with an electrical structure.[11–14]
Common to all speculations during the century between
Berzelius and Bohr was the notion that bonding is due to
astatic attraction between atoms, possibly derivable from
some electromagnetic potential. Even when internal electric
motions in the atoms were considered for the exchange of
radiation, they did not play a role in chemical bonding. This
presumption survived in the atomic bonding models of Stark
(Figure 2) and of Lewis and Kossel (Figures 3 and 5), and
even in Slaters statement of 1933 that “the mechanism of this
[homopolar] binding is one in which [electronic] charge
concentrates between the nuclei and is attracted electrostati-
cally by both nuclei, this attraction producing the binding”.[15]
The traditional view that valency has a purely electrostatic
origin without contributions due to inner-atomic electronic
kinematics has survived in many chemical textbooks and in
Baders theory of Atoms in Molecules (QTAIM).[16]
Speculations on the Intra-Atomic Structure. In fact, until
1890 nothing was known about atoms other than their gas/
fluid/kinetic dimensions and masses, their chemical behavior
(presumed to be related to electric properties but still
irreducible to physics), and their UV/Vis spectra (of com-
pletely mysterious origin). In 1891 Stoney discussed the
electron as a basic component of atoms and gave it this
name.[20] A milestone toward the elucidation of the internal
atomic structure was Thomsons discovery in 1897 of the
electron as a very light particle.[21] Other physicists had also
detected the electron but were dubious that such tiny particles
could exist at all. In the same year the Dutch physicist
Lorentz, using a model of oscillating electrons, explained the
influence of a magnetic field on atomic spectral lines, which
had been recently discovered by his former student Zee-
man.[11–14]
W. H. Eugen Schwarz received a diploma in
experimental physical chemistry from Ham-
burg University and a PhD in natural
philosophy from Frankfurt University. From
1976 until 2002 he was a professor of
theoretical chemistry at Siegen University.
He worked on quantum chemical theory
and applications (atomic core potentials,
relativistic effects etc), on the elucidation of
basic chemical concepts (bonding, periodic
table), and on the history and philosophy of
chemistry. As an emeritus professor he is
still active at the Theoretical Chemistry
Center of Tsinghua University Beijing.
Figure 2. Stark’s speculative model of electrostatic bonding in the CO
molecule (1915).[17] Similarly complex models had been proposed
repeatedly since Berzelius (1815).
Figure 3. Cubic (left: Lewis)[18] and circular/spherical models (right:
Kossel)[19] of the atomic shell structure (1916), accounting for the
chemical and atom-spectroscopic observations that indicated stable
shells containing two and eight electrons.
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In the first decade of the new century, Perrin in France,
Nagaoka in Japan, and Lodge and Nicholson in England
mentioned planetary atomic models. From the electrostatic
point of view, a central positive point charge surrounded by
negative electrons would collapse. Therefore Thomson sug-
gested his “plum-pudding” model of the atom with “neg-
atively electrified corpuscles enclosed in a sphere of uniform
positive electrification”.[21] From the electrodynamic point of
view, moving electrons would radiate and lose energy. There-
fore, various authors had concluded that stable atoms contain
electrons at rest in symmetric arrangements consisting of
concentric circles or spherical shells, each shell with a max-
imum occupation (Figures 3 and 4). Lewis speculated about
the “cubic atom” and bond formation by completing shells of
eight electrons by interatomic “electron sharing” (Fig-
ure 5).[18] Still today there are few chemistry textbooks (e.g.
Ref. [53b,58]) that mention (dynamic) electron sharing as the
physical origin of covalence.
Regarding the atomic weights, the English physician Prout
had proposed around 1815: 1) that all atoms of an element are
identical and 2) that they are formed by accretion of basic
hydrogen atoms. But this second conjecture seemed to be
disproven by Berzelius accurate determinations of atomic
weights around the same time. The consensus was then that
the masses m(Z) of all atoms of an element Zare equal but
non-integer in terms of the unit m(H). It was intriguing,
however, that many masses were close to integer values.
Crookes had surmised already in 1884 that individual atomic
masses are integer but that “our atomic weights merely
represent a mean value” of what was later called isotopes (a
term introduced in 1913 by the chemist Soddy). In 1901 Lord
Rayleigh estimated a chance of less than 1%for so many
atomic weights having near-integer values, without any
physical reason. The conjectures of Prout, Crookes, and
Rayleigh were eventually confirmed in 1920 by Aston, who
demonstrated the isotopy of many elements by means of the
mass spectrograph.[10–14]
2. Bohr’s Path to a New Atomic Model
When Atoms Were Incomprehensible. Niels Henrik
David Bohr[23–26] was born in Copenhagen in the fall of
1885. His mother Ellen ne Adler descended from a wealthy
Jewish banking family; his father was a professor of physiol-
ogy and, together with his two sons, an early promoter of
soccer in Denmark. After finishing high school with very good
exam grades, at least in the sciences, Niels Bohr enrolled at
Copenhagen University taking courses in physics, mathemat-
ics, astronomy, chemistry, and philosophy. Despite his manual
skills, the chemistry lab course proved not easy for him. Since
his schooldays he was particularly interested in new physical
discoveries such as X-rays (1895), radioactivity (1896), and
the electron (1897). He did not finish his studies in the
shortest time, but he finally completed his theoretical Master
Thesis (1909) and Doctoral Dissertation (spring 1911) on the
electron theory of metals, critically advancing ideas of Drude
and Lorentz. He concluded: “It does not seem possible [… by
the classical] electron theory to explain the magnetic proper-
ties”. Wanting to learn more on recent developments of
electron theory, he applied for a one-year postdoctoral
scholarship from the Carlsberg Brewery Foundation. In the
fall of 1911, he went to the Cavendish Laboratory at
Cambridge directed by Thomson, the “father” of the electron.
He attended lectures and lab courses, but scientific cooper-
ation with Professor Thomson did not develop in the way that
he had hoped.
By that time, the existence of atoms was generally
accepted by physicists and chemists. Moreover, atoms were
no longer thought of as indivisible: All atoms contained
negatively charged, light electrons and a positive part of
unknown mass. There was no evidence, though, on the
number of positive and negative charge units in the atoms.
The atoms could undergo radioactive changes emitting a-, b-,
and g-rays, and they could absorb and emit electromagnetic
IR, Vis, UV, and X-radiation. Substances were known that
were chemically identical but with different mass numbers.
Various atomic models were discussed,[27, 28] foremost Thom-
sons.[21,22] He first assumed the total mass of the atoms to
stem from the electrons, which implied thousands of electrons
per atom. Later it turned out that the number of electrons is of
the order of the atomic mass number.[29] In his “plum-
pudding” model Thomsen assumed that the electrons are
immersed in a heavy positive background charge and
Figure 4. Classical electro- and magnetostatic models of atomic shell
structure around 1900, for repulsive particles in a smoothly attracting
field. Taken over by Thomson from A. J. Mayer’s experimental model of
floating magnets (1878).[21b]
Figure 5. Lewis’ model of double bond formation A
!
B,[18b] showing
both the sharing and the resulting pairing of bonding electrons.
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arranged them in stationary shells (Figure 4). In 1904, the
Japanese physicist Nagaoka proposed the alternative “Sat-
urnian” model of electronic rings around a very tiny
nucleus.[30] Atomic shell models might have explained the
periodicity of the elements, but the classical shell numbers of
Thomson, Nagaoka, and others could not reproduce the
chemical and the atom-spectroscopic proof.
Newtons classical mechanics and Maxwells classical
electrodynamics had been extremely successful in the con-
tinuous macroscopic regime. The conceptual inconsistencies
between the two (e.g. unlimited versus limited velocities) had
been resolved by Einstein in 1905, at the age of 26. In cases
where microscopic discrete atomistic phenomena could not
yet be explained, most physicists, in particular in the
Commonwealth, were hesitant in accepting ad hoc hypoth-
eses violating continuous classical physics.[23–27] However, in
1900–1901 Max Planck proposed discrete energy exchanges
between quantized atoms and the electromagnetic field,
thereby deriving the correct entropy of the observed “black-
body radiation”.[31] In the “Annus Mirabilis” of 1905 Einstein
also extended this idea by quantizing the electromagnetic
field energy, as a “heuristic” guiding principle to explain the
observations of the photoelectric effect.[32] And in 1910,
Arthur Erich Haas[33] tried to explain why the size of all atoms
is in the  range, as first deduced by Loschmidt[34] in 1865
from the kinetic gas theory for the “molecules of air”. Haas
inferred that the size of the atom has a fundamental physical
meaning. Only by combining Plancks constant htogether
with other known natural constants, was he able to obtain
a length of the right order of magnitude. Initially, his
dissertation was ridiculed, however.
Atomic Speculations and Facts. In the fall of 1911, Bohr
happened to meet Professor Rutherford from Manchester,
a center of research in radioactivity. Already in 1908 and 1909,
Rutherfords senior co-worker Hans Geiger and undergrad-
uate Ernest Marsden had measured a low but finite 0.01 %
probability of backscattering of a-particles by thin Pt and Au
foils.[35] Could that be explained by Thomsons atoms
consisting of light electrons? In 1911 Rutherford gave
a well-founded answer.[36] Supported by scattering calcula-
tions, he conjectured that atoms contain a heavy, positively
charged “kernel” 105times smaller than the whole atom. The
physical community was not excited and Thomson even
disbelieved it.
The first evidence on the atomic charge numbers ap-
peared during the year 1911. Based on his analysis of Geiger–
Marsdens data on a-scattering, Rutherford deduced nuclear
charges Zof the order of approximately one-half of the
atomic masses, ZA(Z)/2.[36] From the analysis of X-ray
scattering, the English physicist Barkla deduced total atomic
electron numbers Nof similar magnitudes.[29] The Dutch
lawyer and hobby scientist van den Broek concluded in 1913
that the atomic number in the periodic system is equal to the
nuclear charge and the number of atomic electrons.[37] The
hydrogen atom probably had one electron in the field of
a singly charged nucleus. All these conjectures were still
under discussion, however.
In the spring of 1912, Bohr moved to Manchester where
he worked again experimentally and theoretically.[1,6,7] He
learned a lot about radioactivity from his friend, the
Hungarian chemist von Hevesy, a postdoctoral associate in
Rutherfords laboratory. It was known that a- and b-rays
consist of particles with charges +2 and 1. Bohr believed in
the “nuclear atom” and interpreted both rays as nuclear
phenomena, while many colleagues related b-radiation to the
electrons in the atom. In Bohrs eyes, only the electro-
magnetic spectra and chemistry were due to the atomic
electrons. Bohr even anticipated the radioactive displacement
laws, published a year later independently by the chemists
Fajans and Soddy.
Classical Physics Corrected Empirically by Quantum
Concepts. In the summer of 1912, Bohr integrated his
knowledge of atoms and came up with an atomic model of
a heavy core surrounded by orbiting electrons. He applied
classical theories of mechanics and electrodynamics as far as
consistent with the facts, and added ad hoc assumptions where
needed to reproduce the observed atomic stability and the
discrete radiative transitions. He sent seven handwritten
pages to Rutherford (later called the “Rutherford Memo-
randum”)[6,7, 23, 26] as an outline of his future manuscript “On
the constitution of atoms and molekules”.[1] He prepared to
paint a great picture of the subatomic structure of all matter.
But Rutherford was yet somewhat hesitant in accepting
Bohrs bold visions, but supported the young scholar.
Electronic shell models like those in Figures 3 (right) and
4 were common at the time. In contrast to Thomsons model,
electron rings attracted by a heavy central point charge are
mechanically stable only in the presence of a kinetic rota-
tional centrifugal force. For any stable system held together
by Coulomb (as well as gravitational) forces, the virial
theorem imposes a strict relation between the (negative)
total energy Eand its (positive) kinetic and (negative)
potential contributions Ekin and Epot [Eq. (1)].
E¼Ekin þEpot;Ekin ¼E;Epot ¼2E:ð1Þ
Two problems arise then, one mechanical, the other electro-
magnetic, which were “corrected” by Bohr.
First, the radius of the electron ring in the model atom
depends on the speed of rotation, which is classically
arbitrary, as for the planetary orbits. In order to obtain
theoretically the same radius in the observed  range for all
atoms of a given element, an “appropriate” quantization is
required. Motivated by the quanta hypothesis for electro-
magnetic radiation Ephoton =hnelmag, and the harmonic oscil-
lator hypothesis E=nhnosc, where Ekin =1
=
2E, Bohr at first
considered the quantization of the atomic rotational kinetic
energy as Ekin =(n/2)hnorbit,(n=“quantum” number 1, 2, 3,
…; norbit =orbiting frequency). But the equivalent quantiza-
tion of angular momentum was more elegant and easier to
generalize [Eq. (2)].
¼ðn=2pÞh¼nhð2Þ
The quantization rule had also been introduced in 1912 into
a planetary atomic model by Nicholson,[38] however, within
a complex scheme of unproductive hypotheses.[3,6,7,39]
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Second, a rotating charge would emit radiation according
to classical electrodynamics, and the orbiting electron would
fall into the point nucleus within nanoseconds (Figure 6). The
nonclassical assumption of the quan-
tization of angular momentum en-
sured the stability of the electron
rings. In addition, Bohr posited that
the atomic electrons would not emit
electromagnetic radiation according
to classical theory—neither continu-
ous radiation upon continuous tran-
sition between the stationary orbits,
nor discrete radiation with the rota-
tional frequency of the initial or final
orbits, nor radiation with deforma-
tive vibrations of the rings, a com-
mon assumption of the time. In-
stead, discrete nonclassical radiation
should occur in accordance with the
empirically derived Rydberg–Ritz
combination principle (1888/1908) and the Planck–Einstein
formulas (1901/1905) [Eq. (3)].
Einitialorbit Efinal orbit ¼Erad ¼hvrad ð3Þ
Since his PhD dissertation of 1911, Bohr had been aware
of the failures of classical theory in describing atoms and
metals. Generally known were moreover Plancks nonclass-
ical explanation of thermal radiation (1901), Einsteins non-
classical explanation of the photoelectric effect (1905), and
Einsteins quantization of mechanical molecular vibrations
(1907).[40] The latter explained the vanishing of the specific
heat in solids at zero temperature. The Dutch physicist Peter
Debye finally (1911) derived the accurate T3law from the
quantum hypothesis. Rutherford was critical of Bohrs
quantization assumptions; nonetheless he helped Bohr im-
prove his extended manuscript.[1a] However, Thomson and
other British atomic theoreticians reacted negatively.[6,7]
Accurate Theory of the One-Electron Atom. In Part I of
his trilogy[1a] Bohr discussed the H atom and its spectra, which
were known with high precision. Bohrs model of one electron
eorbiting around a heavy proton p+reproduced the spectral
series reported by Balmer (a Swiss teacher, 1885) and Paschen
(1908) and predicted the Lyman (already in the literature
since 1906), Brackett (1922), and Pfund (1924) series. Bohr
also explained why the Balmer series ended in laboratory
experiments around quantum number n=12. He noted that
the atoms in the excited Rydberg states become too big (in
the mm range) to remain unperturbed at the gas pressure of
a few Torr used in the investigations. He furthermore
recognized that the “hydrogen spectra” described by the
American astronomer Pickering (1897) and the English
physicist Fowler (1910) arose in fact from He+. He explained
with astonishing accuracy the small experimental deviation
from the respective hydrogen lines,[1b] by a factor of fexp =
1.00040, as being due to the ratios of the masses of the
electron (me) and the hydrogen (MH) and helium nuclei (MHe)
[Eq. (4)].
ftheo ¼1þ½meðMHe MHÞ=ðMHe MHÞ ¼ 1:00041 ð4Þ
In addition, Bohr could derive the value of the spectro-
scopic Rydberg constant from the experimental values of e,
me,h,c, and e0at the level of experimental accuracy. The
reactions from the physical community were diverse, from
“pure nonsense” to “there may be a grain of truth in it” to
“brilliant”. The German physicist Sommerfeld was so im-
pressed that he extended Bohrs model of circular orbits to
elliptical orbits (Figure 7) corresponding to different angular
momentum states in modern quantum theory. The relativistic
extension even reproduced the spectroscopic fine structure.
Successes and Failures for Many-Electron Atoms.In
Part II of his trilogy,[1a] Bohr discussed atoms with several
electrons. Since the Pauli exclusion principle (1925) was not
yet known, no safe ground existed for deriving the maximum
electronic occupations of the atomic orbits. Chemical evi-
dence and atomic spectra were of some modest help. In
modern notation, Bohr correctly assumed the configurations
H1s
1,He1s
2,Li1s
22s1,Be1s
22s2, but then his speculations ran
astray: B 1s22s3,C1s
22s4,N1s
42s3,O1s
42s23s2,F1s
42s43s1,Ne
1s82s2, etc. Bohr improved his suggestions over the years, but
his electron configurations for the noble gas atoms proposed
in 1921 (up to element Uuo =118E) were still wrong (Fig-
ure 8).[42]
Remarkably,[42, 43] Bohr was also the first in 1922 to suggest
a 5f-block of elements (see below Figure 12) as the homo-
logue of the 4f-block of rare earth metals, a quarter century
before Seaborg. Regarding the transition metals of the nth
period, he stressed in 1923 that the orbits, now called (n1) d
shells, are more strongly bound than the most loosely bound
electron in the outer valence ns shell of neutral atoms. From
the atomic Vis, UV, and X-ray spectra, he derived the orbital
energy levels of the neutral atoms and plotted them versus the
nuclear charges Z(Figure 9). His deductions were more
realistic than the descriptions in many current chemistry
textbooks. Since he was not sure, for which Zvalues in the d-
or f-blocks the (n1)d or (n2)f levels would fall below the ns
levels, he dotted some of the curves in the respective Zranges.
Figure 6. Bohr (Ruther-
ford Memorandum 1912)
on the instability of
atoms in classical phys-
ics: an orbiting electron
spirals into the nucleus.
Figure 7. Sommerfeld’s spectroscopic orbits of the potassium atom
(41to 62corresponding, in modern nomenclature, to 4s to 6p), from
Bohr’s Nobel Lecture 1922.[41]
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An approximate relation between the wavelengths lKof
the characteristic X-radiation of the elements and their
atomic weights Ahad already been found empirically,
1/ ffiffiffiffiffi
lK
p~A. Several X-ray physicists had suggested “correct-
ing” the chemical Avalues according to their observed
wavelengths or absorbances. Concerning Afor 27Co =58.9,
28Ni =58.7, and 29Cu =63.55, the value for nickel should be
increased by about 21
=
2units and would then lie halfway
between Co and Cu.[29] Bohrs identification of the character-
istic Kaand KbX-ray emissions as being caused by electronic
1s
!
2p,3p orbit jumps became a basic advance. Thereby the
nuclear charges Zcould be derived uniquely and accurately.
In 1913–1914 the young English physicist Moseley[44] mea-
sured the characteristic X-ray lines of “all” elements (from Al
to Au) in Rutherfords lab in Manchester (and later in
Oxford) and, with the help of Bohrs atomic model, he
established the nuclear charges [Figure 10 and Eq. (5)] .
Zz¼const ffiffiffiffiffiffiffi
nKa
pð5Þ
zis a constant accounting for the nuclear screening by the
other electrons. The chemical arrangement of Fe, Co, Ni, Cu
in the periodic table could be verified by the physicists as
following the Zand not the Avalues. Notably, the correct
chemical positions of the lanthanoid elements could be
deduced physically. Thus, the way was opened for a physical
foundation of the periodic system of chemical elements.
Molecules Pose a Real Challenge. Part III of the trilogy[1a]
was devoted to chemical bond formation. Bohr constructed
bonds by “Lewis pairing” the atomic valence electrons on
rings rotating in a quantized fashion around the interatomic
axes. He had graphically displayed his ideas on the theory of
chemical matter already in the “Rutherford Memorandum”
of 1912 (Figure 11). As in the case of the hydrogen atom, Bohr
devised a classical-mechanical model for the molecules and
determined the ground state as a classical-mechanical force
equilibrium (energy minimum) under the condition of the
nonclassical ad hoc constraint of quantized angular momenta.
Single bonds were represented by rotating electron pairs
(Figure 11: the HH bond in H2and the four CH bonds in
Figure 8. Bohr’s electron configurations (1921, still incorrect) for the rare gas elements up to “Niton” (=radon) and E118.[42] nkorbits correspond
to n=k1orbitals (or to nj=k1/2 spinors), for example, 41,4
2,4
3,4
4to 4s, 4p, 4d, 4f.
Figure 9. Plot of Bohr’s atomic orbit energies e(in terms of y¼ffiffiffiffi
IE
p,IE=orbit ionization energy in Rydberg =13.6 eV; strongly bound orbits have
high yvalues) versus nuclear charge, Z=1 through 92 (from 1923).[43] At the top and bottom and on the right of Bohr’s diagram, we have added
the modern orbital symbols 1s, 2s, 2p … 4s, 4p*(=4p1/2), 4p (=2p3/2) etc. corresponding to Bohr’s orbit symbols 11,2
1,2
2…N
I4(1,1),N
II 4(2,1),N
III
4(2,2) etc. We note Bohr’s order of orbit energies when the orbits first become occupied, see the bottom line. For example, for the sixth row of the
periodic table with Z=55, 56, 57, 58 (Cs, Ba, La, Ce) he correctly gives 6s<5d<4f (while chemical textbooks traditionally give 6s <4f<5d). We
also note the change of order of the valence orbit energies for the later lanthanoids and the 5d transition elements, where he correctly gives
4f<5d <6s (while chemical textbooks still teach 6s <4f<5d). Since Bohr was not sure of the exact Zvalue, where these crossings of the orbit
energies occur, he dotted the beginnings of the orbit-energy curves. We have indicated the Zranges, where the orbit(al) energy order changes, by
bold ellipses or circles.
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CH4) and the double bond in O2by a rotating electron quartet
(with six electrons in each O 1s inner core shell). The water
molecule was assumed to be linear, HOH. Remarkably,
Bohr had already a feeling for “structure resonance” in
ozone: he represented O3(again linear) by two different
models.
The H2molecule, only sketched in the “Rutherford
Memorandum”, was treated explicitly in the trilogy. Bohr
obtained R=58 pm for the bond length (correct value 74 pm)
and D=2.7 eV for the dissociation energy (correct value
4.75 eV, without zero-point correction). The HHe and He2
molecules were correctly calculated as unstable, while the
unstable H3molecule was predicted as stable and the stable
H3+molecule as unstable. Since the order of magnitude of the
derived values was correct for H2, there seemed to be a grain
of truth in Bohrs concept of combining classical dynamics
with the “arbitrary” constraint of angular momentum quan-
tization. The quantitative accuracy in the smallest two-
electron molecule was, however, not even remotely compa-
rable to that in the one-electron atoms H and He+. A few
years later Pauli applied Sommerfelds action-quantization to
the one-electron molecule H2+, again assuming an angular
momentum instead of a linear motion through the nuclei with
z=0hand predicted it metastable with a decomposition
energy of D=+61
=
2eV at R=293 pm (correct: D=2.8 eV,
R=106 pm).[45] The Bohr and Sommerfeld models were not
at all reliable for molecules.
The Periodic System of Elements.[6, 8,42] In relating the
chemical elements to the electron configurations, Bohr
included more empirical facts and relations, in particular
from chemistry. He replaced the classical-mechanical shell-
filling by 2, 7, and 10 2 electrons (see Figure 4) and his
symmetry-driven choices (e.g. Figure 8) by the empirical octet
rule, which originated in a suggestion from the German
chemist Abegg in 1904.[46] Among the multitude of graphical
representations of the periodic system in the literature, Bohr
chose a “long table” design, in particular the one which
exhibited the chemical differences and cross-relations be-
tween the s-, p-, d-, and f-block elements; he did not place the
f elements in a footnote (Figure 12). This format had first
been suggested by the English chemist Bayley in 1882 and by
the Danish chemist Thomsen in 1895.[47] Remarkably correct,
Bohr let the 4f elements begin with Ce, the first element
indeed with 4f valence participation, and he first suggested
a 5f block (though beginning only after the first trans-
actinides). Extending his periodic table to element 118, Bohr
discussed the possible structures and stabilities of then
Figure 10. Moseley–Bohr’s law (5) for nuclear charge Zand frequency
of the Karadiation, fixing the atomic numbers of the elements in the
periodic system.[44]
Figure 11. Bohr’s models of H2,O
2and CH4molecules in the “Ruth-
erford Memorandum” of 1912. He reproduced the chemical concepts
of HH and CH single bonds and of O=O double bonds: Angular-
correlated electron pairs rotate around the internuclear connection
line, attracted by nuclei and atomic cores of H+, C(1s2)4+or O(1s6)2+.
Angular momentum quantization was assumed as in the atoms.
Figure 12. Bohr’s periodic table of 1922, for H up to Uuo, showing for
the first time the seventh period including a 5f block.[42]
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unknown nuclei. Atoms of these elements have been synthe-
sized in the past, with element 118 (called Eka-Radon or
Ununoctium) being the heaviest so far.
3. Hindsights and Insights
The Old Quantum Concepts.[6,7] The foundations of
classical physics were completed with Maxwells electro-
dynamics and Boltzmanns statistical thermodynamics in the
decades between 1860 and 1890. During this time, however,
physical spectroscopy and chemical investigations began to
produce a large body of data pertaining to atoms and
molecules that challenged explanation by classical theory.
Some leading scientists such as the Austrian physicist Mach,
the Bohemian chemist Wald, the German chemists Ostwald
and Kolbe, and the English chemist Brodie rejected physical
atomism as being too speculative and anti-positivistic. Many
leading physicists, notably in England, persisted in strictly
applying classical physics in the microscopic regime.
The German-speaking physicists Planck, Einstein, and
Haas realized that certain important microscopic phenomena
could be rationalized by the introduction of “artificial”
quantum concepts. Many scientists were unimpressed or even
contemptuous of such ad hoc assumptions. Indeed, some
speculations put forth at that time turned out to have little
merit. In hindsight Bohrs reasoning differed from that of
others in two respects. He perceived which basic physical
concepts and logic were essential and should be maintained,
and he embedded experimental quantum facts into the
internally consistent classical continuum theory only where
the latter proved to be inadequate or incorrect. While Bohr
was a theoretical physicist by nature, he had experience in
experimental techniques and was familiar with practical
physics as well as chemistry. Several famous chemists such
as Bjerrum, Brønsted, and von Hevesy were among his
lifelong friends.
In the summer of 1912, during his stay with the creative
Rutherford group, Bohr conceived the idea of quantizing both
the stationary motion and the electromagnetic radiation of
the electrons. From this basis, he set out to develop his
ambitious program of explaining all atoms and molecules. He
was aware that classical physics was insufficient and that he
was searching without knowing the final answer. Several
physicists were impressed by the accuracy of his theoretical
results (derivation of the Rydberg constant, spectra of H and
He+) and by the relevance of his semiempirical deductions
(orbit(al) energies in atoms, interpretation of the X-ray
spectra of all elements, splitting of atomic lines by fields, etc.).
It may be noted that Bohr was lucky to benefit from some
“error cancellation”. Instead of quantizing the electronic
motion in three-dimensional space (as Sommerfeld subse-
quently did, obtaining three quantum numbers: the principal,
the angular momentum, and the directional ones), Bohr
quantized only one dimension. He therefore missed some
quantum kinetic zero-point energy, as became apparent much
later on the background of Heisenbergs uncertainty relation.
On the other hand, Bohr assumed the lowest angular
momentum to be 1hinstead of 0h. These two “changes”
cancel in the energy exactly in the case of H-like atoms, but
not in general. Accordingly, Bohrs model did not work well
for many-electron atoms and for molecules.
For most chemists, Bohrs derivations were too compli-
cated, too unusual, or simply unacceptable. For instance, his
hydrogen atom with a planar electron orbit did not fit well
with Daltons model of spherical atoms. Therefore, three-
dimensional images of many-electron atoms were published,
by Sommerfeld starting in 1918, by Bohr starting in 1921, and
by colleagues subsequently.[39, 49] Real models made of balls
and wires were sketched and published.[5, 6] Planetary models
determined the iconography of the atoms for the general
public. In particular, Bohrs model began to be mentioned in
chemistry textbooks after he had received the Nobel Prize in
1922. By that time, however, the shortcomings of Bohrs
approach were already apparent and the search for more
radical modifications of classical physics was under way.
Following the invention of wave mechanics, planetary models
disappeared in the physics community. The chemistry com-
munity failed to absorb some of Bohrs chemically relevant
qualitative insights.
The Periodic System.[8] During the decade after the
trilogy, Bohr and his colleagues laid the foundation for
a physical rationalization of basic chemical concepts, includ-
ing the periodic system, by what may be viewed as an
eclectically mixed theoretical–empirical approach. Bohr–
Moseleys law yielded unique nuclear charges and element
numbers for all elements. The update of Bohrs atomic model
by Sommerfelds three-dimensional action-quantization and
the introduction of the spin and the exclusion principle by
Pauli led to a well-grounded concept of atomic core and
valence shells and to the correct filling numbers of 2, 8, 18,
and 32 electrons for closed shells. Bohr and Pauli introduced
the rules of the “Aufbau principle”. The order and variation of
the atomic orbit(al) level energies for the series of atoms were
correctly derived from the empirical spectroscopic data
(Figure 9).
Since the early 1920s, the orbit(al) energy order of the
atomic inner shells was known:
1s 2s <2p 3s <3p <3d4s <4p <4d <4f 5s ... ð6Þ
In the valence shells the order is different, however.[50] The
experimentally derived (and later theoretically verified)
paradigm for all d- and p-block elements is, for the example
of the 4th period:
...3p 3d<4s <4p ... ð7Þ
The strong nuclear shielding by the core-shells of the first
elements of a period results in a strong energetic destabiliza-
tion of the valence d and f orbitals in the atoms of Groups 2
and 1. For Ca+, as the paradigm of the alkaline earth metals of
Group 2, Equation (8) holds.
...3p 4s <3d<4p <5s ð8Þ
And for K, as the paradigm of the alkali metals of Group 1,
Equation (9) holds.
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...3p 4s <4p <5s <3d ð9Þ
The spectra of the alkali metal atoms were the first after
those of the hydrogen-like elements to be understood and
assigned. The main drawback of Bohrs atomic model was
that accurate values for the orbit(al) energies could not be
obtained theoretically for any many-electron atom. His model
worked only at the qualitative level; that is, it could be used to
extract reliable orbit(al) energies from simply structured
experimental atomic spectra.
Remarkably, the order (8) of the orbital energies of the
alkaline earth metal atoms has since entered all chemistry
textbooks as the standard valence orbital energy scheme for
all other atoms, because it led to a simple (though incorrect)
“physical deduction” of the structure of the periodic system.
Since then, chemistry students have had to learn, in contra-
diction to the Aufbau principle, that in the nth period,
transition metal compounds have an empty ns shell below the
partially occupied (n1)d valence shell, and that the valences
of the main group atoms are due to the active shells ns below
and np above the intermediate, filled (n1)d10 core shell.
Bohr had noticed early on the changes in the atomic level
ordering along the series of elements. However, he was not
yet sure in his Nobel lecture of 1922, for which groups of
elements the reversal of the (n1)d and ns valence levels
would occur (see Figure 9). The valence electron spectra of
the transition metal atoms were too complex to be analyzed
by his model. This became possible only after the invention of
wave mechanics starting in the late 1920s.
Chemical Bonding. Bohrs attempts to understand the
bonding in molecules were less successful since the aspects
that were missing in the “old quantum theory” are in fact
essential for chemical binding. It is now known that there are
three physical mechanisms that can lower the valence
electron energy thereby creating bonds between atoms:
1) an increase in the effective nucleus–electron attraction in
polar bonding, 2) an attenuation of the electron–electron
repulsion in correlation and dispersion bonding, and 3) a
damping of the electronic kinetic zero-point energy in
homopolar bonding.[51] The third of these mechanisms is
related to the uncertainty relation, which was formulated in
1927 by Heisenberg while working in Bohrs group, a mecca
of theoretical physics of the time. In many-electron molecules,
a correct energy assessment also requires taking into account
Paulis exclusion principle which was outlined in 1925. It was
thus only in 1927, after the formulation of new wave
mechanics, that the first sound quantitative determinations
of covalent bonding became possible, namely for H2by
Heitler and London in Germany and for H2+by Burrau in
Denmark. Physical understanding and well-founded explan-
ations of bonding, however, were initiated only 35 years later
when Ruedenberg[52] showed that a basic driving force is the
attenuation of the quantum kinetic energy by “Lewis sharing”
of electrons between atoms, an insight that was later greatly
extended by Kutzelnigg[53] and others (see the collection of
references in Ref. [52c]).
It therefore stands to reason that even the simplest
chemical bond, that in the H2molecule, could not be treated
with sufficient reliability by Bohrs quantum concepts. He
derived the expression of the kinetic energy of his H2model
(Figure 11 top) for minimum angular momenta of z=1hfor
the two electrons in the orbit of radius rin the central plane:
Ekin =h2/mer2. Since this expression is the same as that for two
separated H atoms, bonding is caused by an increase of the
electron–nucleas attraction in Bohrs model—an explanation
that was echoed twenty years later by Slaters conjecture
mentioned above.[44] Although this simple classical electro-
static picture turned out to be flawed, it found its way into
many chemistry textbooks and also into the Wikipedia: “The
bond is caused by the electrostatic force of attraction between
opposite charges”; in other words, electronic correlation and
in particular kinetic energy effects are ignored.
An intriguing aspect of Bohrs models has more recently
been uncovered by Herschbach,[45] who showed Bohrs
expression for Ekin to be the high-dimensional limit of the
wave-mechanical kinetic energy operator. His group deter-
mined reasonably accurate energy curves for many-electron
molecules by a simple wave-mechanical first-order perturba-
tion correction for the three-dimensional reality.
Science-Philosophical and -Historical Annotations. In the
late 19th century, experimental atomic spectroscopy had
reached a high level of reliability and accuracy, but most of
the high-quality data simply gathered dust, since no theoret-
ical framework existed for interpreting, assigning, organizing,
or using them. The surprisingly accurate results of Bohrs
model for the one-electron spectra of H and He+and the
value of the Rydberg constant, and the various semiempirical
deductions of effective one-electron energies instantly con-
veyed physical meaning to the large quantities of existing
spectroscopic observations. It furthermore led to inferences
that were fruitful in chemistry by establishing the reliable
order of elements in the periodic system and by providing the
first steps towards a physical explanation of the chemical
periodicity. Bohrs work is an outstanding example of what
determines the value of new theories, namely three points:
the reproduction of existing experimental observations, the
prediction of new facts, and the formulation of explanatory
concepts that provide qualitative insights for both.
Every natural science is based on experimental facts, but
the symbiosis with appropriate theoretical concepts is also
necessary. If experimental scientists deliberate about the
concepts and theory-based instruments they apply every day,
they will realize that their business is not “purely empirical”
science but heavily “theory-laden”. One example are the so-
called “experimental” molecular structures generated by the
computers with software attached to the XRD and NMR
instruments. On the other hand, representatives of ”basic
physical sciences“ focus on structurally simple sectors of
nature and then believe that more complex fields such as
chemistry can be readily reduced to their science. Physicists
such as Sommerfeld and Dirac thought that chemistry might
become just a branch of applied theoretical physics.[60] In
1912, the young enthusiastic Bohr hoped to explain all atoms
and molecules, despite his own experiences in chemistry and
his close relations to experienced chemists.
Bohrs work is an outstanding example of the value of
trying, in critical cases, “everything that goes” even if it goes
against the grain of certain established, logically consistent
.
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methods, in Bohrs case, however, under the strict constraints
of the observed facts. The success of classical mechanics,
electrodynamics, and thermodynamics had been so over-
whelming that early in the 20th century many physicists
strongly believed that the extrapolation of these macroscopi-
cally successful theories into the microcosmos must also
succeed without any modifications. The other extreme would
have been a theory revolution[56] such as at the beginning of
modern physics in the 17th century by Galilei and Newton or
of modern chemistry at the end of the 18th century by
Lavoisier. Bohr decided for an intermediate option and
developed his theoretical-physical simulations of experimen-
tal facts in a pragmatic and eclectic manner, as is usually more
common among chemists. He was very successful, though
only in a very limited range. Anyhow this success finally
earned him acceptance in the physical community, which soon
perceived that much more radical changes were required.
After a dozen years, Bohrs model was washed away in
physics by the scientific revolution of quantum mechanics,
significantly supported in Bohrs famous discussion circle in
Copenhagen.
Bohrs work had less impact in the chemical community
than in physics. The success of the Bohr–Moseley law was
readily accepted. His suggestion of a 5f-block of elements in
the 7th row of the periodic table from element 87 through 118
was hardly considered until Seaborgs work in 1945.[59] A
disappointing development was that Bohrs successful, basi-
cally correct, description of the atomic orbit(al) level schemes
was incorrectly taken over into chemistry. His molecular
speculations, understandably, did not impress the chemists,
but his predominantly classical model of covalent bonding did
also not impede the development of a similar line of thinking
in the chemical textbooks or in the QTAIM, which is now not
easy for quantum theoreticians to correct (see the endeavors
of Ruedenberg[51,52] and Kutzelnigg[53]). The phenomenon of
“creating facts in a scientific thought collective” without
a counterpart in reality was discussed by Ludwik Fleck
already in the mid-1930s, in other contexts.[57]
Bohrs initiative towards a numerical theory and qualita-
tive concepts for understanding the microworld behind the
macroworld was mainly an enterprise of physically oriented
scientists, although many scholars of different persuasions
participated in the preparatory era. It was also a very
international enterprise, even during the First World War,
with contributions from English-empiristic and Germanic-
theoretical circles as well as from many other European
countries, Japan, and the USA. In physics, Bohr became the
father figure of quantum theory. In chemistry, his insights are
still being digested. His concepts of the atomic core and
valence shells and element numbers were soon adopted.
Bohrs and Sommerfelds atomic orbit models are still useful
in introductory courses, but have in recent decades been
replaced increasingly by the wave-mechanical orbital cloud
model.[3–8] However, even 90 years after Bohrs Nobel lecture,
we are still waiting for many chemistry texts to teach the
correct atomic orbital energy schemes [Figure 9 and Eqs. (6)–
(9)], which can indeed be found in various quantum chemistry
texts (see for example, Levine[58] and Kutzelnigg).[22,50]
Received: July 11, 2013
Published online: &&
&&
,
&&&&
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.
Angewandte
Essays
12 www.angewandte.org  2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2013,52,2–13
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These are not the final page numbers!
Essays
History of Science
W. H. E. Schwarz*
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100th Anniversary of Bohr’s Model of the
Atom
In the fall of 1913 Niels Bohr formulated
his atomic models at the age of 27. This
Essay traces Bohr’s fundamental reason-
ing regarding atomic structure and spec-
tra, the periodic table of the elements,
and chemical bonding. His enduring
insights and superseded suppositions are
also discussed.
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ngewandte
Chemi
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13Angew. Chem. Int. Ed. 2013,52, 2 – 13 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.angewandte.org
These are not the final page numbers!
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... In the above equation, a 0 is interpreted as the radius of an atom after the AE-process, which means the electron has arrived at a stable orbit and a photon has been emitted. Now an explanation for why the a E-ratio (i.e., the alpha energies ratio) equals the fine structure constant can be stated: "For the AE-process to occur such that the electron arrives at a stable orbit and a photon is emitted, the electron must have the energy required to overcome the electrostatic repulsion it will encounter when arriving at a stable orbit that is a distance equal to the fine structure constant away from a stable orbit that already has an electron in it, and, for the electron to have this required energy, v e as given in Eq. (2) and l 0 e 0 as given in Eq. ...
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... In the above equation, a 0 is interpreted as the radius of an atom after the AE-process, which means the electron has arrived at a stable orbit and a photon has been emitted. Now an explanation for why the a E-ratio (i.e., the alpha energies ratio) equals the fine structure constant can be stated: "For the AE-process to occur such that the electron arrives at a stable orbit and a photon is emitted, the electron must have the energy required to overcome the electrostatic repulsion it will encounter when arriving at a stable orbit that is a distance equal to the fine structure constant away from a stable orbit that already has an electron in it, and, for the electron to have this required energy, v e as given in Eq. (2) and l 0 e 0 as given in Eq. ...
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This paper uses a limited scope to present an explanation of how quantum jumps prevent quantum mechanics from being a fundamental theory, and this paper explains how Einstein's theory that radiation conveys inertia between the emitting and absorbing bodies plays a critical role in the presented explanation.
... A proposição do princípio da construção data da década de 1920 (SCERRI, 2019b) para realizar o preenchimento dos níveis de energia que, em termos atuais, seguiria a seguinte sequência: 1s « 2s ‹ 2p « 3s ‹ 3p ‹ 3d « 4s ‹ 4p ‹ 4d ‹ 4f « 5s... (SCHWARZ, 2013). Não é infalível, como mostrado acima, mas, de acordo com Riveros (2013), apresenta-se como um excelente ponto de partida para discussão teórica sobre a estrutura eletrônica dos átomos. ...
... However, Meyer's graphic display of periodicity of numerical atomic volumes (Meyer, 1870), and Mendeleev's correct predictions of various properties of unknown elements and their compounds by interpolation in the table (Mendeleev, 1869a;Mendelejeff, 1871: predictions on scandium, gallium, germanium-in the center of Figure 1-experimentally verified between 1875 and 1886) appeared convincing to the community (Scerri, 2007(Scerri, , 2020Stewart, 2019). A theoretical breakthrough was achieved by Bohr and Coster (1923) with their (semi-)classical atomic model that reproduced the spectroscopic data of hydrogen and cationic helium (He + ) exactly, and paved the way for a qualitative physical rationalization of various chemical trends (Schwarz, 2013). From then on, in principle, the energies and radii (proportional to 3 √ volumes; see Biltz, 1934) of the atomic valence and outer-core shells could be utilized to explain chemistry. ...
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... Since the formulation of the periodic system in the 1860s, the quest for understanding its structure has intensively motivated research in different areas of chemistry and physics. However, almost 150 years after its announcement, the different approaches from quantum chemistry [1,2,3,4,5,6,7,8,9,10,11], group theory [12,13], clustering [11,14,15] and information theory [16,10], to name but a few [17,18], have not led to an unified picture [19]. Instead, they give insights on the possible chemical and physical causes of the patterns depicted by the system but have failed in providing a formal structure for it [19]. ...
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For more than 150 years, the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalized periodic system allows envisioning periodic systems in other disciplines of science and humanities.
... Since the formulation of the periodic system in the 1860s, the quest for understanding its structure has intensively motivated research in different areas of chemistry and physics. However, almost 150 years after its announcement, the different approaches from quantum chemistry [1,2,3,4,5,6,7,8,9,10,11], group theory [12,13], clustering [11,14,15] and information theory [16,10], to name but a few [17,18], have not led to an unified picture [19]. Instead, they give insights on the possible chemical and physical causes of the patterns depicted by the system but have failed in providing a formal structure for it [19]. ...
Preprint
Full-text available
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalised periodic system allows envisioning periodic systems in other disciplines of science and humanities.
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The impact of relativistic effects on the periodicity of elements has significant implications for the prediction of the properties of atoms and their compounds. In this study, (non-) periodic variations...
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“Global Civility,” is a groundbreaking book that proposes a unique and interdisciplinary approach to elevate humanity to new levels of civility through the application of the physical constructal law. Drawing inspiration from the renowned constructal theory introduced by Adrian Bejan, a professor at Duke University, the book delves into the interconnectedness of natural systems and how this concept can be extended to enhance ethical behavior and harmony among human societies. In a world facing complex challenges such as cultural clashes, environmental degradation, and social instability, “Global Civility” offers a fresh outlook on addressing these issues through the application of a scientific concept. By examining various disciplines, historical contexts, and philosophy, the book uncovers insightful parallels between the evolution of natural flows and the development of harmonious human interactions. The book also discusses how embracing the principles of constructal theory can lead to more sustainable economic models, efficient governance structures, and inclusive social frameworks. As an author with an interest in global civility, I have combined my passion with this scientific approach. The book is written to engage a broad readership, including both experts in the field and general readers interested in the intersection of science, ethics, and global affairs. “Global Civility” has the potential to captivate readers with its unique premise and actionable insights. Its interdisciplinary nature and potential for sparking meaningful discussions make it a compelling addition to the current literary landscape. Find the book on Amazon: https://www.amazon.com/dp/B0D5Z2SQBN
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This chapter presents recent progress in developing computational methods and applications of automated mechanism discovery in chemistry. Systematic determination of the reaction mechanisms has been a challenging topic in modern computational chemistry. For this purpose, various computational methods have been developed to find multiple reaction paths starting from a known local minimum (LM). Applying such techniques to various LMs one-after-another explores reaction path networks in a broad sense and rationalizes the mechanisms of the known, unknown, or unexpected reactions. Thus, automated mechanism discovery can guide experimental researchers to develop novel chemical reactions and materials.
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The development of chemical theory in the nineteenth century has been relatively little studied, compared with other sciences and other periods; much remains still to be explored. One notable example is chemical atomism, and its adjuncts such as valence and structure theory. Nonexistent at the beginning of the century, a generation or two later these ideas had moved to the very center of the science, which they still inhabit. The chemical atomic theory embodies outstanding examples of paper tools that provide not only explanatory and expository functions for what is already accepted as known, but also heuristic guidance in the further construction of a science. It may be of interest, therefore, to attempt an analysis of what some recent studies have revealed about this subject, along with indications of where further historical efforts may yield additional rewards.
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THE present discussion is concerned with the chemical and radioactive properties of the heavy elements—that is, the elements with atomic number larger than 88—and especially with the newly discovered transuranium elements. Aside from the obvious importance of these elements from the standpoint of atomic energy, they are of great interest from the viewpoint of pure science. The general study of the chemical properties of these elements, and especially the properties of those which fall in the transuranium region, has led to a greatly increased knowledge of the atomic structure of elements in this region of the periodic table, a matter which was of necessity only very poorly understood a few years ago. Likewise, a study of the radioactive properties of the new isotopes in this region has added greatly to our knowledge of the properties of radioactive isotopes, and the nature of and regularities in these properties have contributed greatly to the knowledge of nuclear ...
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Das Zusammenspiel von kinetischer und potentieller Energie über die Unschärfebeziehung wird zunächst anhand einer Variationsfunktion für den Grundzustand des H-Atoms erläutert. Zur Erklärung des physikalischen Mechanismus für das Zustandekommen der chemischen Bindung dient das H-Ion. Die Ausbildung der chemischen Bindung kann man in drei Teilschritte zerlegen: 1. die quasiklassische (elektrostatische) Wechselwirkung der unveränderten Elektronenladungen der getrennten Atome; 2. die Interferenz der Atomorbitale, die (im Falle positiver Interferenz) zu einer Ladungsverschiebung in die Bindungsregion und einer Erniedrigung der kinetischen Energie führt; 3. eine Deformation der Molekülorbitale zur Wiederherstellung der richtigen Bilanz von kinetischer und potentieller Energie. In einfachen Modellen kann man sich oft auf den zweiten Beitrag beschränken. Die Zweielektronenbindung ist von der Einelektronenbindung nicht grundsätzlich verschieden. In größeren Molekülen können interatomare Beiträge großer und kleiner Reichweite zur chemischen Bindung unterschieden werden. Wenn die erstgenannten klein sind, nämlich bei Molekülen mit unpolaren Bindungen, kann eine Einelektronen-MO-Theorie gerechtfertigt werden. Zum Abschluß wird die Möglichkeit der Beschreibung von Molekülen durch lokalisierte Bindungen diskutiert.
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Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Article
In the absence of any available method of spectrum analysis, the characteristic types of X radiation, which an atom emits if suitably exited, have hitherto been described in terms of their absorption in aluminum. The interference phenomena exhibited by X-rays when scatted by a crystal have now, however, made possible the accurate determination of the frequencies of the various types of radiation. This was shown by W. H. and W. L. Bragg, who by this method analyzed the line spectrum emitted by the platinum target of an X-ray tube. C. G. Darwin and the author extended this analysis and also examined the continuous spectrum, which in this case constitutes the greater part of the radiation. Recently Prof. Bragg has also determined the wave-lengths of the strongest lines in the spectra of nickel, tungsten, and rhodium. The electrical methods which have hitherto been employed are, however, only successful where a constant source of radiation is available. The present paper contains a description of a method of photographing these spectra, which makes the analysis of the X-rays as simple as an other branch of spectroscopy. The author intends first to make a general survey of the principal types of high-frequency radiation, and then to examine the spectra of a few elements in greater detail and with greater accuracy. The results already obtained show that such data have an important bearing on the question of the internal structure of the atom, and strongly support the views of Rutherford and of Bohr. Kaye has shown that an element excited by a stream of sufficiently fast cathode rays emits its characteristic X radiation . He used as targets a number of substances mounted on a truck inside an exhausted tube. A magnetic device enabled each target to be brought in turn into the line of fire. The apparatus was modified to suit the present work. The cathode stream was concentrated on to a small area of the target, and a platinum plate furnished with a fine vertical slit placed immediately in front of the part bombarded. The tube was exhausted by a Gaede mercury pump, charcoal in liquid air being also sometimes used to remove water vapor. The X-rays, after passing through the slit marked S in Fig. I, emerged through an aluminum window 0.02 mm. thick. The rest of the radiation was shut off by a lead box which surrounded the tube. The rays fell on the cleavage face, C, of a crystal of potassium ferrocyanide which was mounted on the prism-table of a spectrometer. The surface of the crystal was vertical and contained the geometrical axis of the spectrometer.