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Computational data analysis shows that key developments towards the periodic system occurred in the 1840s

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The periodic system arose from knowledge about substances, which constitute the chemical space. Despite the importance of this interplay, little is known about how the expanding space affected the system. Here we show, by analysing the space between 1800 and 1869, how the periodic system evolved until its formulation. We found that after an unstable period culminating around 1826, the system began to converge to a backbone structure, unveiled in the 1860s, which was clearly evident in the 1840s. Hence, contrary to the belief that the ``ripe moment'' to formulate the system was in the 1860s, it was in the 1840s. The evolution of the system is marked by the rise of organic chemistry in the first quarter of the nineteenth-century, which prompted the recognition of relationships among main group elements and obscured some of transition metals, which explains why the formulators of the periodic system struggled accommodating them. We also introduced an algorithm to adjust the chemical space according to different sets of atomic weights, which allowed for estimating the resulting periodic systems of chemists using one or the other nineteenth-century atomic weights. These weights produce orderings of the elements very similar to that of 1869, while providing different similarity relationships among the elements, therefore producing different periodic systems. By analysing these systems, from Dalton up to Mendeleev, we found that Gmelin's atomic weights of 1843 produce systems remarkably similar to that of 1869, a similarity that was reinforced by the atomic weights on the years to come.
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Computational data analysis shows that key
developments towards the periodic system occurred in
the 1840s
Wilmer Leal1,2, Eugenio J. Llanos1,2,3, Andr´es Bernal2,4,
Peter F. Stadler1,2,5,6,7,8, J¨urgen Jost2,8& Guillermo Restrepo2,5
October 11, 2021
1Bioinformatics Group, Department of Computer Science, Universit¨at Leipzig, H¨artelstraße 16-18, 04107
Leipzig, Germany
2Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
3Corporaci´on SCIO, Calle 57b 50-50 bloque d22 of. 412, 111321 Bogot´a, Colombia
4Departamento de Ciencias B´asicas, Universidad Jorge Tadeo Lozano, Carrera 4 # 22-61, 110311 Bogot´a,
Colombia
5Interdisciplinary Center for Bioinformatics, Universit¨at Leipzig, H¨artelstraße 16-18, 04107 Leipzig, Germany
6Institute for Theoretical Chemistry, University of Vienna, W¨ahringerstraße 17, 1090 Vienna, Austria
7Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogot´a, Colombia
8The Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, New Mexico 87501
Abstract
The periodic system arose from knowledge about substances, which constitute the chemical space. De-
spite the importance of this interplay, little is known about how the expanding space affected the system.
Here we show, by analysing the space between 1800 and 1869, how the periodic system evolved until its
formulation. We found that after an unstable period culminating around 1826, the system began to converge
to a backbone structure, unveiled in the 1860s, which was clearly evident in the 1840s. Hence, contrary to
the belief that the “ripe moment” to formulate the system was in the 1860s, it was in the 1840s. The evolu-
tion of the system is marked by the rise of organic chemistry in the first quarter of the nineteenth-century,
which prompted the recognition of relationships among main group elements and obscured some of transition
metals, which explains why the formulators of the periodic system struggled accommodating them. We also
introduced an algorithm to adjust the chemical space according to different sets of atomic weights, which
allowed for estimating the resulting periodic systems of chemists using one or the other nineteenth-century
atomic weights. These weights produce orderings of the elements very similar to that of 1869, while pro-
viding different similarity relationships among the elements, therefore producing different periodic systems.
By analysing these systems, from Dalton up to Mendeleev, we found that Gmelin’s atomic weights of 1843
produce systems remarkably similar to that of 1869, a similarity that was reinforced by the atomic weights
on the years to come.
Introduction
Meyer and Mendeleev’s periodic systems culminated a series of attempts at building Systems of Chemical
Elements (SCEs) [1], which resulted from ordering and classifying elements [2] through the knowledge of their
compounds [3, 4]. Thus, by finding the smallest common combining weight of a large set of compounds containing
a reference element, atomic weights were determined and used to order elements [5]. Likewise, compounds played
a major role in assessing chemical resemblance among elements, which was mainly determined on the basis of
similarities of empirical and molecular formulae [3, 4]. Thus, SCEs refer not just to chemical elements, but to
substances in general.
Every discovered substance enlarges the set of known chemicals, which we call the chemical space [6]. Given
the central role of this space for the formulation of the SCE, every discovery of new elements and compounds,
may affect the SCE by introducing or perturbing similarities among chemical elements or by affecting the
ordering of their atomic weights. Up to now there is no account of how the evolution of the chemical space
affected the SCE. Nevertheless, historians have concluded that the ripe moment for formulating the system
came in the 1860s [7, 1], thanks largely to the normalisation of molecular formulae through the standardised
set of atomic weights resulting from the 1860 Karlsruhe conference.
Here we analyse how the expansion of the chemical space between 1800 and 1869 affected the SCE by using
two approaches: presentist and retrodictive. The first one assesses the effect of the amount of chemical data
according to current standards and solves the question of when the size and diversity of the chemical space
allowed the emergence of the SCE. The second approach focuses on the evolution of the atomic theory and
solves the question on when the theory led to the emergence of the SCE. Taken together, these approaches help
us to determine whether specific changes in the 1860s chemical space actually led to the SCE; or whether the
patterns of the SCE were already present earlier in history, which leads to ponder whether the SCE could have
been formulated earlier.
Figure 1: Chemical elements, growth and diversity of the chemical space up to 1869. a) Current system of
chemical elements (SCE) depicting elements known by 1869 (black), undiscovered elements (grey) and mixtures
that were thought to be elements (red) (Supporting Information). Elements in black were considered in this
study. b) Absolute (left axis [l.a.]) and cumulative values (right axis [r.a.]) of new substances and combinations.
c) Percentage of chemical space spanned by some elements. These percentages are non-additive because a single
substance adds to each one of its elements, e.g. H2O contributes to both H and O counts. d) Percentage of
chemical space spanned by different combinations. e) Percentage of chemical space spanned by substances made
of nelements. After 1811 the number of uncombined forms (unary substances) in which elements appeared
exceeded the number of known elements as a consequence of the allotropic forms and polymorphs of elements.
For instance, by 1868 sulfur had nine uncombined forms. f) Cumulative number of elements (r.a.) and percentage
of theoretical combinations of different sizes actually observed (l.a.) (Materials and Methods)
Evolution of the chemical space (1800-1868)
Gmelin and Beilstein’s Handbooks, initiated in the nineteenth-century, gather records of extractions, synthesis
and properties of substances [6, 8]. Nowadays Reaxys c
, a large electronic database of chemical information,
which merges these two handbooks plus several other sources of chemical information, constitutes a suitable
corpus for historical studies of chemistry [6, 8].
We collected records from Reaxys1(January 2017) from 1771 up to 1868, that is two months before the
publication of the first Mendeleev’ SCE [9]. These amounted to 11,356 substances involved in 21,521 single-
step reactions (Materials and Methods), mainly reported in Gmelin’s Handbook and gathered from leading
1Copyright c
2021 Elsevier Limited except certain content provided by third parties. Reaxys is a trademark of Elsevier Limited.
Reaxys data were made accessible to our research project via the Elsevier R&D Collaboration Network.
nineteenth-century journals [10]. These substances span a growing number of elements over time, from nine in
1800 up to 60 in 1868 (Figure 1a and Interactive Information). The most complete system was formulated by
Mendeleev [11], including the 60 elements of Figure 1a plus Er, Yt and Di [12]. Nonetheless, we excluded these
three elements because of their unreliable information by 1869: Yt (currently Y [13]) first reported reaction
dates back to 1872. Er and Di were later found to be mixtures of other elements [14] (Supporting Information).
Chemists expanded the chemical space at an exponential rate, from a handful of new substances in 1800 up
to the 11 thousand of 1868 [6] (Figure 1b). From each substance, we extracted its element combination, that is
HOS for H2SO4. We used the number of combinations as a measure of diversity. Figure 1b shows that although
combinations also grew exponentially [6], unlike substances their growth was reduced after 1830, indicating
decreasing diversity. After this year, substance discovery focused on fewer combinations, so that by the end of
the period 36% of the combinations covered 80% of the chemical space (Figure 1b). Figures 1c-d provide further
details about the 1830 turning point: at the dawn of the century the chemical space was mainly populated by
compounds of C, H, O and N; then, during the first quarter of the century, chemists found new combinations,
which reduced the percentage of chemical space spanned by each combination (Figure 1d, Figure S1). This is a
period where the number of new substances and of combinations grew hand in hand (Figure 1b). A minimum
was reached for CHO and CHNO compounds around 1830. Afterwards, there was again a clear emphasis
on CHO and CHNO (Figure 1d), which resulted in a less rapid production of new combinations (Figure 1b).
More CHO and CHNO substances distributed over a slow growing number of combinations increased the space
spanned by these combinations (Figures 1d and S2). This is clearly a consequence of the organic revolution
[5, 15]: before 1830 most new combinations were metallic, while afterwards most were organic (Figure 1d,
Figures S1 and S3, Table S1). The importance of organic chemistry after 1830 is observed in Figures S4 and
S5, where substances containing typical organic chemistry molecular fragments skyrocketed, in contrast with
those containing inorganic ones.
Another attribute of a combination is its size, that is the number of elements present in it. The theoretical
number of combinations depends on the available elements. Thus, by 1800, with 11 elements, there were 2,036
possible combinations (Materials and Methods), which grew up to 1.15 ×1018 by 1868 with 60 elements. We
found that despite the growth of new combinations (Figure 1b), chemists reported compounds of no more than
eight elements (Figure 1e). During the first quarter of the nineteenth-century the chemical space was mainly
populated by compounds of size 2-3, presumably due to the prevalence of dualism in chemical theories [15].
Afterwards there was a surge in the number of larger combinations involving 4-5 elements, mostly organic.
By analysing how close were chemists to actually realising the theoretical combinations of different sizes,
we found that during the first years of the nineteenth-century, where a rapid discovery of elements took place
(Figure 1f), the amount of theoretical combinations skyrocketed causing a rapid drop of the proportion of re-
alised combinations. Once the discovery of new elements slowed around 1820, more combinations were actually
observed increasing the proportion of theoretical combinations realised (Figure 1f). In the mid 1840s came
another batch of new elements, reducing again the proportion of realised combinations, which coincides with
a strong drop in the number of new substances, from 300 in 1842 to 163 in 1846 (Figure 1b). After a decade,
chemists were again discovering more combinations and increasing this proportion. As expected, given its rela-
tively small number, binary combinations were always closer to their theoretical possibilities than combinations
of more elements. By 1825, after the stabilisation of the number of elements, about 13% of the theoretical
number of binary compounds was reported (Figure 1f, inset), a growing percentage not even affected by the
emphasis on compounds of three and four elements (Figure 1e). In fact, by 1868 about 23% of the possible
binary compounds (made with combinations of 60 elements) were already known (Figure 1f, inset).
Evolution of the system of chemical elements (1800-1868)
We analysed the interplay between the chemical space and the SCE from two perspectives, one contemporary
or presentist and another historical or retrodictive. The presentist approach “sees” the chemical space of the
nineteenth-century through the eyes of twenty first-century chemistry. Here nineteenth-century formulae, for
example Dalton’s OH for water, are replaced by their contemporary versions. Reaxys data suit this approach.
The retrodictive approach considers the evolution of the chemical space as historically witnessed. It acknowledges
the historical construction of consent on atomic weights and its associated formulae. Therefore, when analysing
the chemical space, for instance of 1810, it attempts to use the formulae by the leading chemists of that time,
for example Dalton. This approach allows for studying possible SCEs according to several nineteenth-century
chemists.
Presentist approach to the evolution of the system of chemical elements
Figure 2 explains our approach to quantifying similarity among chemical elements (Supporting Information).
We associate similarity with the possibility of substituting one element by another in an empirical formula.
This follows from Mendeleev’s idea that “the elements, which are most chemically analogous, are characterised
by the fact of their giving compounds of similar form RXn” [16].
As SCEs intend to display only the most remarkable similarities among elements, we display only maximum
similarities for each element. This choice is justified because SCEs are customarily presented as tables in which
similarities between neighbouring elements are the largest. If this is the case, non-maximal but important
similarities can be recovered from sequences of maximum similarity relationships, for instance Li being most
Chemical space
VCl3O
CH2CBr2
HAuCl4
CH2CCl2
NaBr
NH2Cl
K3CrCl6
CHBrCHBr
NaCl
KBrO3
MoBr4
HgOBr2
Arranged formulae
AuHX4
H2NX
FCl
FBr
s(Cl Br )=|FClFBr|
|FCl
|=3
7
s(Br Cl)=|F
Br
F
Cl
|
|F
Br
|=3
6
KClO3
OVX3
CrK3X6
C2H2X2
MoX4
HgOX2
C2H2X2
NaX
KO3X
Figure 2: Similarity among chemical elements. Toy chemical space of 13 substances. Each compound provides
an arranged formula for an element in the given formula when Cl or Br is replaced by X and the elements are
lexicographically ordered. Arranged formulae of element X are gathered in FX, which is a multiset as elements
may appear more than once, e.g. C2H2X2appears twice in FBr (Supporting Information). The similarity of
element xto element yis given by s(xy), which is the probability of xhaving a common arranged formula
with y. In chemical terms, it is a measure of substitutability. This similarity is an asymmetric relation [17]
e.g. s(Br Cl) > s(Cl Br). For instance, by 1869 we have s(Br Cl)=344/659=0.52, while s(Cl
Br)=349/1556=0.22 (Interactive Information). This means that Br could be substituted by Cl to obtain a
known compound in roughly half of Br combinations, whereas Cl could be substituted by Br in about one
fourth of those of Cl. This similarity measure generalises that presented in [18]
similar to Na and Na to K means that likely Li is quite similar to K as well (Figure 3). Therefore, elements
related by maximum similarities correspond to the notion of families (groups) of elements on periodic tables.
Having determined the key similarities among chemical elements, all that remains is to arrange them accord-
ing to their atomic weights to retrieve the SCE of each year between 1800 and 1868. We depict these systems
as similarity networks. Figure 3a-c present three of them. All 69 networks can be found in the Interactive
Information.
Despite the increase in the number of elements (Figure 1f), the amount of “most similar” relationships
decreased over time, dropping from a maximum of 166 in 1818 down to 69 in 1862 (Figure S6). This indicates
that as chemists expanded the chemical space, they were converging towards a core set of similarity relationships.
To better assess this convergence, we calculated the similarity between SCEs of different years (Figure 4a,
Materials and Methods).
The reddish region around the diagonal in Figure 4a indicates continuity in the evolution of the SCE,
as the most similar periodic system of any year is always one of an adjacent year. Nevertheless, it also shows
qualitative shifts, the most visible of which appears in 1826, that suggest convergence to a stable SCE (Interactive
Information). The dark blue regions around the early years indicate that the SCEs of those years did not stand
the test of the time: they transformed completely within the span of few years and are essentially different from
the SCEs at the end of the period (Interactive Information). Similarities in this early quarter of the century were
mainly related to substitutions in chlorides, oxides, hydroxides, sulfates and other typical inorganic compounds
(Interactive Information). But then, in 1826, there was a sharp stabilisation of the SCE, as revealed by the
light blue-yellow square in Figure 4a, which indicates that more than 40% of the similarities found by 1826
remained in the SCE all the way to the end of the period. Some of these early known similarities were Ag
K and Pt Pd, caused mainly by their inorganic compounds (Interactive Information). Other similarities
showing up a decade later were K Na, Hg Cu, Si Ti, Fe Co and Ni Co, which were also mainly
caused by inorganic compounds (Interactive Information). Interestingly, famous nineteenth-century SCEs as
those published by Meyer and Mendeleev in the 1860s, depict Cu and Ag as similar elements (Figure S7),
mainly due to the similar low oxygen content of their oxides [19]. However, our results show that, ever since 40
years earlier, Cu had been more related to Zn group, mainly for its dominating +2 valence, and Ag to K, for
its dominating +1 valence (Figure 3, Interactive Information). Also, by 1826, halogens and Fe, Co, Ni became
SCE families (Figure 3a-c).
The reddish region between columns 1826-1860 and rows 1835-1845 (Figure 4a) shows that about 80% of the
similarities of the SCE observed between 1835 and 1845 were present since 1826 and lasted until 1860. During
the 1860s, this resemblance dropped down to about 60%. The period after 1845 shows that the similarities
observed after this year lasted, but that there were also some transient similarities, for instance those of Nb,
Ta, Rb and Cs (Interactive Information).
The mechanisms behind this convergence were of substance discovery and tie-breaking. In the early years
of the century not enough compounds were known to determine the similarities that unveil the patterns of the
SCE. For example, up to 1825 no combinations of Ce were known, which caused this element to be similar to
almost all the rest (Figure 3a). In 1826 Ce2S3, the first Ce compound, was reported, which caused its similarity
to collapse on elements that presented the same kind of sulfides. The discrete shift on 1826 is due largely to this
particularity of Ce. The same mechanism operated all across the expanding chemical space, eventually leading
Ag
Al
As
Au
B
Ba
Be
Bi
Br
C
Ca
Cd
Cl
Co
Cr
Cu
F
Fe
H
Hg I
Ir
K
Li
Mg
Mn
N
Na
Ni
O
Os
P
Pb
Pd
Pt
Rh
S
Sb
Se
Si
Sn
Sr
Ta
Te
Ti
U
W
Zn
Zr
Ce
Ag
Al
As
Au
B
Ba
Be
Bi
Br
C
Ca
Cd
Ce
Cl
Co
Cr
Cu
F
Fe
H
Hg
I
Ir
K
Li
Mg
Mn
Mo
N
Na
Ni
O
Os
P
Pb
Pd
Pt
Rh Sb
Se
Si
Sn
Sr
Ta
Te
Th
Ti
U
V
W
Zn
Zr
S
1840
1820
Pb
Mg
Os
Ru
V
Ce
La
Cs
Na
Li
H
Be
Ca
K
Rb Ag
Tl Ba
Sr Zr
Ti
Si
Hg
Cu Zn
Cd
Mn Fe
Ir
Rh
Co Ni
Al
Pt
Pd In
U
Cr
COB
S
Se
Te Sn
Th
Ta W
Mo
Bi Au
As
P
NF
Cl
Br
I
Nb Sb
a
b
d
B
Br
C
Cl
Cu
F
Fe
H
Hg
K
N
Na P
Pt
S
XSO4
XWO4
XSb2O6
XSiO3
XO
X3N2
XCr2O4
XU2O7
XSnO4
XC4H4O6
X2O3XS2
K2XO4
XSO4
XCO3
X2P
XN
X2As
XMoS4
XC4H4O6
X2O5
XH3
Cu3X
X2Se3
Sr3(XO4)2
Co2X
Ca3X2
X2Zn3PtX2
FeX
XO2H2X2
X4N4XCl4
XS3FeX2
NiX
MoX2
XSn
ThX2
XO3
HX
C2H5X
AgXO4
C9H9O3X
UO2X2
SrX2
BX3
PtX4
S2X2
XO2XI4XCl2XCl6[X(NH3)4Cl2]*2Cl
XS2XO2*2H2O
XP2K2XCl62NH4*[XBr6]
I
O
X2SO4
X3BO3
X2C4H4O6
X2MnO4
X2O
X2TeO3
X3SbO3
X2MoO4
X2SiO3
X2WS4
1868
c
Li
Ag Rb
Cs
Be
Mg
Ca
Sr
Tl Ba
Cd
Zn
Pb
Sn
Ti
Ce
Si
Zr Ta W
U
Th
Mo
Cr
Mn
La
Au
Al
In
Co Ni
Ru RhPd
Os Ir
Bi
Sb
As Nb
V
Se
Te
Figure 3: Evolution of the system of chemical elements (SCE). a-c) SCEs of three different years. Arrows xy
indicate that xis most similar to y. Node (element) size is proportional to the number of substances composed
by the element. Similarities of Ce are coloured in light grey for the sake of readability. In Figure a, all Ce
similarities are collapsed for the sake of simplicity. Some of the formulae shared by elements with the same
colour (X) are shown in c. Readers can also select in the Interactive Information any set of elements to retrieve
the formulae making similar the elements in any particular year. d) Backbone of the SCE depicting the pairs
of most similar chemical elements appearing in more than 60% of the SCEs between 1800-1869 (Materials and
Methods)
to the pattern observed in the period 1837-1845 that already reproduced 80% of the similarities observed up to
the 1860s. This suggests that a fairly accurate SCE could have been proposed as early as the 1840s. However,
the problem of uncertainty on atomic weights still needs to be addressed, and we shall do it in the next section.
A system of elements containing the most frequent pairs of most similar elements is depicted in Figure
3d, which we regard as the backbone of the periodic system from 1800 up to 1868. It shows salient families of
elements including alkali metals, halogens, chalcogens, pnictogens (without N) and {Fe, Co, Ni}, plus well-known
families of transition metals such as {Pd, Pt, Ir}and {Mo, W, Ta}.
Regarding the magnitude of similarities among chemical elements, that is their actual similarity values,
Figure S8 shows that they were very weak. In fact, all over the history here analysed more than 80% of the
similarities had values lower than 0.1. That is, over the history less than 10% of the formulae of any element
have been shared with its most similar element(s). The lowest similarity values ever recorded corresponded to
those of organogenic elements (Interactive Information). This fits Mendeleev’s concept of “typical elements”
[12, 20], today called singularity principle or uniqueness of second period elements [21], which indicates that
these elements possess weak similarities with elements of their families [22].
If the similarities were so small, how could they become so noticeable to chemists? This is even more
surprising if we consider that each nineteenth-century chemist may not have had the complete knowledge
provided to us by the database. We believe it has to do with ubiquity: these similarities extend over the
whole spread of the chemical space, so that they are equally visible in any reasonably-sized portion of the
chemical space. To test this hypothesis, we took random samples of different sizes of the space, for every
year, and analysed how often the “most similar” relationships among elements were present in the samples
(Materials and Methods). We found that most of the similarities observed in the first quarter of the nineteenth-
a
Size of chemical space sample (s%)
100
80
60
40
20
0
95 50 575 25 95 50 575 25
Similarity
b
1825 1840 1868
O S
S O
I Cl H K
P As
F Cl
Se S As P
Na K
Sr Ba
Pb Ba
Cr S Ba Pb
Si Ti
Al Fe
Ti Si
Cl I
Cd Hg
C Se
K H
W S B As
Zr Si
Rh Zn
Be Co
U W
Te S
Pt Pd
N Cl
Os Se
Br I
Ce Sn
Ce Cu
Ce Se
Ce F
Ce Te
Ce H
Ce Fe
Ce Zn
Ce Pd
Ta Sb
Ce Hg
Ce I
Ce Ag
Ce Ba
Ce P
Ce Cd
Ce Ni
Os S
Ce Li
Ta Ir
Ce Bi
Ta Sn
Ce Pt
Os Cr
Ta As
Os As
Ta Pt
Ce Al
Mo S
Ce K
Ce Si
Ce Na
Ce Rh
Ce Cl
Mo Cr
Ce B
Ta Si
Bi Hg
Mo W
Ce Zr
Ce Ti
Ce Ir
Ce W
Ce C
Ta C Ce Pb
Ta P
Ce Co
Ce Sb
Ce S
Ce Sr
Ta Fe
Ta W
Ce Mg
Bi Pb
Ce Cr
Ta Ti
Ce O
Sn Ba
Fe Hg
Ce Os
Ce Au
Ce As
Au B
Bi Cu
Ta I
Cu Hg
Au P
Mn Co
Mn Pb
Li K
Au Fe
Mn Sn
Ni Fe
Hg Ba
Mn Ba
Zn Hg
Ir Sn
Au As
Au Al
Sb K
Co Cu
Ir Pt
Mg Ba
Li Na
Sb As
Pd Pt
Co Ba
Mg Pb
Pd Hg
Mg Zn
Zn Ba
Ca Ba
Ni Ba
Ca Hg
Ag K Pd Ba
Ag H
Pd Zn
O S
S O
Na K
As P
Br Cl
I Cl
Se S
P As
F Cl
K Na
H K
Rh Fe
Co Fe
Fe Co
Ca Ba
Ir Pt
W S
Pb Ba
Ce As
Sb As
Bi Fe
Si Ti
Ti Si
Cr S
Mo W
Ag K
Au As
Ce K
Sr Ba
Th Sn
N I
B As
Ta W
V C
Mn Fe
Zn Cu
Ba Ca
Sn Co
Hg Cu
Pd Pt
Li Na
Ce Al
Ce Cr
Ce Sb
Be Ba
Ce Au
Os Ir
Al Fe
Cl Br
Ce Co
Ce Ir
Ce Sn
Mg Ba
Ce Bi
Pt Pd
Ce B
U W
Ni Co
C S
Cu Hg
U Cr
Te Se
Zr Sn
Zr Si
Zr Th
Zr Pt
Zr Te
Cd Zn
Br Cl
Na K
O S
Cl Br
Se S
S O
K Na
P As
As P
Pt Pd
Pd Pt
N Cl
F Cl
I Cl
Ba Ca
H K
Mo W
Mg Ca
Ag K
Mn Fe
Fe Co
Cd Zn
C S
Bi Sb
Ir Pt
Sb As
Te S
Li Na
Co Fe
Rb K
Pb Ba
Sr Ca
Th U
Tl K
W Mo
Cu Zn
Al Fe
Ni Co
La Fe
Ti Sn
Ru Fe
Be Mg
V P
Ta W
In Al
Rh Fe
Si Ti
Cs Na
B As
Zr Si
Ce Sb
Ce Tl
Ce Co
Ce Cr
Ca Ba
Cr Fe
Ce Ti
Ce Fe
Ce Th
Ce Sn
Hg Cu
Os Fe
Nb Sb
Au Al
Nb P
Au Fe
Zn Mg
Sn Fe
U W
U Cr
Sn Pb
Os Cr
Hg Zn
U Mo
95 50 575 25
Ubiquity of similarities
Figure 4: Similarity among systems of chemical elements (SCEs) and ubiquity of element resemblances. a)
Resemblance between SCEs. The heatmap depicts similarity from the SCE of the column to the SCE of the row
(Materials and Methods). Any row yindicates how similar the SCEs are, year after year, to the SCE of year y.
Any column xshows which fraction of the SCE, year after year, is similar to the SCE of year x. b) Ubiquity of
the similarities of the SCEs of 1825, 1840 and 1868. The ubiquity of each similarity xycorresponds to the
percentage of appearance of such similarity in the sampled space of size s% (Materials and Methods). Plots for
all years 1800-1868 are found in Figure S6
century required more than 50% of the chemical space to be detected, indicating that in this period similarities
of different elements were focused on different regions of the chemical space, hindering the discovery of the
patterns of the SCE (Figures 4b and S9). As time went by, especially after 1830, similarities became more
ubiquitous and easier to detect. This effect is particularly intense for similarities among organogenic elements,
as they were spread among the increasingly large number of organic compounds, which promptly became the
majority of the chemical space. For instance, the similarity S O, detected as early as 1800, required at least
65% of the 1800 space to be observed, while by 1840 this fraction plummeted to 10% and dropped to 5% by
1868 (Figures 4b and S9). In contrast, Ba Ca required in 1800 three quarters of the space, by 1840 60%
and by 1868 a quarter, that is five times more chemical space than S O to be detected (Figures 4b and
S9). Therefore, the redundancy of the space on organogenic compounds facilitated the detection of similarities
among organogenic elements, which contrasts with those of the transition metals, whose detection demanded
examination of a larger fraction of the chemical space.
This explains why nineteenth-century chemists, such as Meyer and Mendeleev, struggled with similarities
among transition metals [23, 24, 25, 26, 27, 28, 29, 12, 20] (Figure S7, Table S2). Mendeleev also faced problems
with the similarities of In and the rare earths he included in his system (Table S2) [30]. Remarkably, detecting
In Al by 1869, as Meyer did, required more than 75% of the chemical space (Figure 4d). Examples of other
similarities requiring large amounts of chemical space to be detected were Zn Mg, Nb P and Nb Sb. The
first of these is explicit in Mendeleev and Meyer’s 1869/70 systems (Figure S7), and the other two are explicit
in Meyer’s system and discussed as similarities by Mendeleev [20] (Figure S7, Table S2). Overall, we found
that about 53% of the similarities among chemical elements arising from the chemical space were recovered by
Meyer in his 1864 and 1868 systems (true positives, Supporting Information, Table S3). Almost a quarter of
non similarities of the 1864 chemical space were observed as similarities by Meyer (false positives, Table S3).
This fraction plummeted in 1868 to about 7%. At any rate, the best agreement between Meyer’s systems and
the system allowed by the chemical space was achieved in 1869/70, when 62% of the similarities of the space
were gauged by his system, while there were only 6% non similarities observed as similarities. Mendeleev, in
turn, attained 58% and 10% of true and false positives, respectively (Table S3). Note that the (dis)agreements
here discussed are based on the similarities reported by the two chemists in their systems, which were abundant
and detailed in Mendeleev’s case and very seldom discussed by Meyer, in which case similarities needed to be
interpreted from his periodic tables. Also, the greater detail of Mendeleev’s discussions on similarity is expected
to yield a higher rate of false positives, due to our methodology being based on maximum similarities.
Retrodictive approach to the evolution of the system of chemical elements
The presentist approach to the evolution of the SCE takes for granted a stable set of atomic weights and of
empirical and molecular formulae corresponding to current standards. Nevertheless, analysing the historical
evolution of the chemical space and its influence upon the SCE requires considering the history of the atomic
theory. That is, it requires considering the various nineteenth-century competing sets of atomic weights asso-
ciated to different theoretical and experimental settings [31, 5], which led to a chaos of formulae [32]. Hence,
different atomic weights produce different orderings of the elements and different formulae, so that different
chemists working with different sets of atomic weights could find widely different SCEs, even if they worked
with the same experimental data. Here we analyse the possible SCEs resulting from different perspectives of the
nineteenth-century chemical space spawned by several distinct sets of atomic weights proposed over the period.
In the nineteenth-century, empirical data on composition came in the form of mass percentages for each
element. For instance, Dalton knew that water was made of 88% and 12% by weight of oxygen and hydrogen,
respectively. From Dalton on, chemists assumed formulae for key compounds such as water, ammonia and oxides.
Thus, chemists selected an element and assigned a reference atomic weight to it, and recorded atomic weights
of other elements relative to that one. The initial assumptions thus propagate through all the calculations,
therefore creating a different chemical space for each chemist (Figure 5a). For example, Dalton’s reference was
an atomic weight of 1 for hydrogen. He assumed HO as the formula of water, therefore yielding an atomic
weight of 7 for oxygen. This leads to molecular formulae of oxides whose coefficients are around half of those
we know today. The determinations were made even more difficult by the varying quality of the experimental
data [31, 5].
We gathered 13 sets of atomic weights (Table S4), corresponding to data published by Dalton (1810) [33],
Thomson (1813) [34], Berzelius (1819 [35] and 1826 [36, 37, 38]), Gmelin (1843) [23], Lenßen (1857) [24], Meyer
(1864 [25], 1868 [39] and 1869/70 [27]), Odling (1864) [28], Hinrichs (1867) [29] and Mendeleev (1869) [12], plus
the currently accepted atomic weights. Starting with Gmelin, these sets of atomic weights were proposed by
authors who actually devised SCEs [1]. Although neither Dalton, nor Thomson nor Berzelius aimed at devising
SCEs, they were some of the key figures in the development of the atomic theory [31, 5], which is why we also
explored the effects of their atomic weights upon the SCEs that could have been obtained from their respective
chemical spaces. Figure S10 shows the elements comprised by each system of atomic weights, which range from
30 for Dalton to 60 for Mendeleev. Information on the selection of these elements is found in Table S5.
As any SCE is based on ordering and similarity of its chemical elements [2], we analysed the different
orderings of elements associated to each set of weights. In all cases they agreed in more than 80%, even with
the current atomic weights (Table S6). This indicates that the ordering relationships among elements were
rather stable since the beginning of the nineteenth-century. To determine element similarities it is necessary
to reconstruct the formulae spanned by each system of atomic weights (Figure 5a). As there is no systematic
record of the chemical formulae corresponding to the assumptions of each chemist, we devised an algorithm to
obtain approximate formulae meeting the assumptions of the chemists here analysed (Materials and Methods).
This entails, for instance, approximating the current Fe2O3to FeO3according to Dalton (Figure 5a). Our
procedure takes all Reaxys formulae known by the time of publication of each chemist’s atomic weights and
rescales the modern formulae to fit chemist’s atomic weights within 20 different levels of tolerance (Materials
and Methods, Supporting Information). Often, the higher the tolerance, the lower the perturbation of Reaxys
formulae.
For each chemist’ set of atomic weights and level of tolerance we obtained a corresponding chemical space,
which led to an associated SCE holding a set of similarities among chemical elements. In order to quantify how
close was a chemist’ set of atomic weights of gauging the similarities allowed by the actual chemical space of
chemist’s time (calculated with our contemporary atomic weights), we computed the fraction depicted in the red
plot of Figure 5b (see also Figure S11). This corresponds to the true positives rate, indicating to which extent
the old atomic weights sharpened our ancestors’ capabilities of discovering the SCE of 1868. As a chemist’
space could lead to several transient similarities not remaining until 1868, we also quantified chemist’s fraction
of similarities of this sort (Figures 5b, blue and S12). They correspond to the false positives rate (Figure 5b,
blue).
By inspecting Figure 5b, we observe how, as the century progressed, SCEs resulting from fitting chemists’ sets
of atomic weights contain more and more 1868 similarities and how transient similarities were further reduced.
There is a remarkable leap with Gmelin, who becomes a turning point in the trends, separating SCEs with
H2O
Fe2O3V2O5La2O3
In2O3
HO
FeO3
V2O15
InO
In2O3
Fe2O3
H2O
V2O5
LaO
H2O
Fe2O3
HO
V2O5
H2O
Fe2O3
V2O15
Fe2O3
In2O3
V2O5
H2O
Fe2O3
H2O
Fe2O3
V2O5
Chemical space as we
know it actually
was
Chemical space
as regarded by each chemist
a
b
Figure 5: Contrast between systems of chemical elements (SCEs) calculated with nineteenth-century and with
modern atomic weights. a) Examples of modified formulae according to the atomic weights of (left to right)
Dalton (1810), Gmelin (1843), Meyer (1864, green; 1869/70, purple) and Mendeleev (1869). For every chemist
publishing a set of atomic weights in year y, known Reaxys substances (Sy1) up to year y1 (inclusive)
were retrieved and the corresponding SCE Py1was obtained. Afterwards, formulae of substances Sy1were
transformed to fit chemist’s atomic weights within 20 different tolerance values (τ), each τyielding a SCE with
similarities gathered in Pτ
y1(Materials and Methods, Supporting Information). b) Red: efficacy of chemist’s
atomic weights in approaching P1868, measured as |Pτ
y1P1868|/|Py1P1868 |; a value of 1 means that they
are just as effective as our modern atomic weights. Blue: fraction of transient similarities in Pτ
y1, that is
similarities not observed by 1868. These were calculated as |Pτ
y\P1868|/|Pτ
y|; a small value means that most
of chemist’s SCEs obtained from his atomic weights were observed in 1868. Boxplots depict median (black
horizontal line) and min/max values as whiskers
many transient similarities and few standing the test of the time (on Gmelin’s left in Figure 5b) from SCEs rich
in 1868 similarities and with very few transient similarities (on Gmelin’s right in Figure 5b). Gmelin’s atomic
weights lead to SCEs containing about 78% of the 1868 similarities and about 40% of the similarities of those
SCEs are transient. This is actually an improvement, when contrasted with the SCEs obtained with the atomic
weights of Gemlin’s predecessors. For instance, the SCEs obtained with Dalton’s weights have about 10% of
1868 similarities and 93% of transient ones, and those of Berzelius (1826) 60% and 73%, respectively. The lack
of accuracy of pre-Gmelin SCEs is caused by the many changes the chemical space underwent. Nevertheless,
in those times the SCEs obtained using Berzelius’ 1819 weights stand out. In spite of their 75% of transient
similarities, Berzelius’ atomic weights lead to SCEs with 63% of 1868 similarities.
The remarkable separation of the two plots after Gmelin (Figure 5b) shows the strong relationship between
the theoretical and experimental advances the atomic theory brought about and the raise of the backbone of
the periodic system. Interestingly, this is particularly evident in the 1840s and not in the 1860s as traditionally
accepted, which agrees with the results of our presentist approach.
By analysing the SCEs obtained from Meyer and Mendeleev’s atomic weights, we found that each new
version of Meyer’s weights achieves more 1868 similarities and reduces the amount of transient similarities. His
last set of atomic weights leads to SCEs with no transient similarities matching 82% of the 1868 similarities. In
turn, Mendeleev’s atomic weights produce SCEs with 83% of 1868 similarities and 6% of transient similarities.
These results coincide with the different stances the two chemists had regarding the SCE. Meyer favoured
accurate atomic weights and experimental information and Mendeleev completeness [11, 40], as noted in the
several elements left aside by Meyer that were included by Mendeleev.
Conclusion
Contrary to common opinion, we found that different systems of atomic weights in vogue in the nineteenth-
century did not affect to a large extent the ordering of elements in a system of chemical elements (SCE). In
contrast, similarity played a major role in shaping the SCE.
By analysing the size and diversity of the chemical space between 1800 and 1869 we found that before
1830 the expansion of the space involved discovering new instances of a wide variety of combinations, which
allowed observing, as early as 1826, several similarities standing the test of the time. The rise of organic
chemistry after 1830 caused a strong emphasis on the expansion of the chemical space towards compounds of
organogenic elements, mainly O, H, C, N and S. This facilitated the detection of similarities among organogenic
elements even with low fractions of the chemical space, but hindered the recognition of some similarities among
metals, which required large fractions of the chemical space to be observed. This explains why chemists in the
nineteenth-century struggled to detect similarities among metals but readily observed those among organogenic
elements.
All sets of atomic weights proposed across the nineteenth-century ultimately converged towards the same
similarity patterns among the elements, much faster than previously thought. Disagreements regarding atomic
weights turn out to be less critical than it seems: it is consistency within the system that matters, rather than
its absolute accuracy.
By 1837-1845 a large core of stable similarities arose, which was to remain until Meyer and Mendeleev’s
formulation of their SCEs. This “golden period” turns out to be a ripe moment to devise SCEs similar to
theirs, which challenges the traditional account that the 1860s were the proper time for the periodic system
to arise [7, 1]. Here we have shown that, in terms of the material system of chemistry to which the chemical
space belongs [8], the ripe moment was in the 1840s. In fact, this potential materialised to a significant extent
in Gmelin’s V-shaped SCE [23]. As the SCE had to wait about three further decades to be formulated, the
question arises of whether the social and semiotic conditions for its formulation were still not ripe.
This study shows the interplay between the chemical space and the SCE and highlights the difficulties of
formulating it before the 1840s as a consequence of the many changes of the chemical space of those times.
Likewise, it justifies post-1840s SCEs supported by a stable chemical space and by sharper and accurate atomic
weights.
Regarding Meyer and Mendeleev, both chemists were active in times of a mature chemical space and of
rather stable atomic weights, which led to their SCEs. Although their systems coincide to a large extent with
the possible SCEs of their times, the underlying reasons they had to finally arrange elements as they did cannot
be reduced solely to the chemical space. For instance, both chemists regarded Cu and Ag as very similar (Figure
S7), which does not agree with the chemical space of their time. Mendeleev believed in Tl and Cs similarity,
a thought Meyer shared until 1869/70, when he arranged a new family containing Tl (current group 3). Yet,
the SCEs resulting from Meyer and Mendeleev’s weights show that Tl is most similar to K. Likewise, by 1869
the similarity between Pd and Pt was detectable with only 5% of the chemical space, but Mendeleev did not
include it in his system, nor commented upon it, while Meyer’ system included it. This indicates that both
chemists were not guiding their inquiries exclusively by the chemical space, as it is actually observed in the
physical properties of substances they made reference to [20, 27]. How was the interplay between chemical and
physical evidence leading them to the details of their systems?
We believe the data driven approach presented here to study the evolution of the SCE opens the door to
further studies on the current status of the periodic system. As we have shown elsewhere [6], the chemical space
of the twentieth- and early twenty first-centuries kept the emphasis on organic substances. Does it mean that
the current SCE is very similar to that of 1869? Or do we rather have a very different system?
From a more general perspective, this study contributes to the ongoing computational approaches to the
history of science and the evolution of knowledge [41, 8]. We suggest the methods presented here can complement
and be complemented by more conventional approaches to the history of science.
Data
We retrieved 21,521 single-step reactions with publication year before 1869 from Reaxys. These reactions had
11,451 associated substances with their respective formulae. Some of them were curated and others discarded
(Supporting Information), leading to 11,356 substances. We associated each of these substances with its earliest
publication year (in a chemical reaction) and with its molecular formula.
Theoretical combinations
For nknown elements in a given year, its theoretical number of combinations of size sis theo(n, s) = n
s. Hence,
the theoretical number of combinations of nelements is theo(n) = Pn
s=2 n
s. This is a rough upper bound
disregarding valency and compound stability. The percentage of theoretical combinations actually observed
(Figure 1f) corresponds to exp(n, s)/theo(n, s), where exp(n, s) is the number of reported substances with n
elements whose combinations size is s.
Backbone of the system of chemical elements
Figure 3d depicts similarities ijappearing in more than 60% of the SCEs containing iand j. This percentage
is computed as (f(ij)/1868 y)×100, where f(ij) is the number of SCEs containing ijand yis
the first year in which iand jappear in a SCE. The normalisation factor 1868 yrepresents the time window
where the similarity ijcould have been observed.
Similarity between systems of chemical elements
A system of chemical elements is devised as described in Figure 2 and stored as a collection Nof pairs of elements
(ei, ej), indicating the similarity of element eiwith respect to element ej(eiejin Figure 3). Each year xhas
an associated network Nx. We quantify the relative fraction of similarities of Nxobserved in another network
Nyas s(x, y) = |NxNy|/|Nx|, where |Nx|indicates the number of pairs (ei, ej) in Nx. Whenever a network Ny
is calculated from a chemical space approximated with a tolerance τ(see retrodictive approach), the similarity
of such a network regarding the corresponding network to 1868 is given by sτ(y, 1868) = |Nτ
yN1868|/|N1868 |.
Sampling the chemical space
For each year we randomly took s% of the space and determined the most similar element(s) for each element.
This experiment was carried out 100 times. For each similarity xyresulting for the whole space of that year,
we counted in how many of the 100 experiments xyappeared. The higher this number, the more stable
the similarity is. We carried out this analysis for 19 sample sizes (95%, 90%, 85%, . . ., 5%). The higher these
numbers for different values of s%, the higher the ubiquity of xyin the chemical space (Figure 4b).
Chemical spaces from atomic weights
As contemporary atomic weights are related by simple fractions with atomic weights of different chemists (Ta-
ble S4), we adjusted a contemporary chemical formula F=XxYx. . .Zzto FA=XxfA(X)YyfA(Y). . .ZzfA(Z)[eq. 1].
Here, X, Y,. . ., Z are chemical elements and x, y, . . . , z their stoichiometric coefficients in F;fA(X), fA(Y), . . . , fA(Z)
are the respective coefficients modifying x, y, . . . , z to yield the formula FA, as an approximation to that regarded
by chemist A. Coefficients fAare calculated as follows: knowing the current (W(e)) and chemist’s (A(e)) atomic
weights of element e(Table S4), as well as the respective values for hydrogen (W(H) and A(H)), we calculate
the ratios (W/A)(e)=(W(e)/W (H))/(A(e)/A(H)) and (A/W )(e)=(A(e)/A(H))/(W(e)/W (H)). Our aim is
determining the simplest fraction fapproximating either (W/A)(e) or (A/W )(e). As these ratios either fall in
the real interval (0,1] or correspond to figures of the form α+β, where αis an integer and βis a real number in
the interval (0,1], we need to find a 0 < f 1 that best approximates either βor the ratio falling in the interval
(0,1]. The best fcorresponds to a fraction of a Farey sequence [42] (Supporting Information) minimising the
relative error of the approximation (error(r, f ) = |rf|/r, with reither (W/A)(e) or (A/W )(e)). We allowed
20 different error tolerances τfor the approximation, from 1 to 20% of relative error, in such a manner that
for each τ, the selected fraction falways approximates rwith an error τ. Hence, for a given τa fraction
fis found, which corresponds to the coefficient fA(e)in eq. 1. By applying this algorithm to each element of
the contemporary formula F, the respective fractions are found and the adjusted formula FAof chemist Ais
found (Further details in the Supporting Information). By applying this method it is found, for instance, that
contemporary Fe2O3corresponds to FeO3according to Berzelius’ table of atomic weights of 1819 (Table S4).
Acknowledgements
We thank RELX Intellectual Properties SA for the reaction dataset; W.L. acknowledges support from the
German Academic Exchange Service (DAAD): Forschungsstipendien-Promotionen in Deutschland, 2017/2018
(Bewerbung 57299294). E.J.L. was supported by the Fundaci´on para la Promoci´on de la Investigaci´on y la
Tecnolog´ıa from Banco de la Rep´ublica (Colombia), Project 4.225. G.R. is grateful to Rainer Br¨uggemann,
Michael Gordin, Douglas Klein, Ursula Klein, Farzad Mahootian, Alan Rocke, Eugen Schwarz and Peter Willett
for their comments.
Author information
Contributions
G.R. conceived the idea; W.L. and G.R. designed the research; W.L. dumped and analysed data; W.L., E.J.L.,
P.F.S. and G.R. devised similarity measure; W.L. and E.J.L. computed and analysed similarities; W.L. and
G.R. designed method to adjust chemical space to given atomic weights. A.B. and E.J.L. implemented data
visualisations in the Interactive Information; W.L., E.J.L., A.B., P.F.S., J.J. and G.R. discussed the results;
G.R. wrote the original draft; W.L., E.J.L., A.B., P.F.S., J.J. and G.R. reviewed and edited it.
Corresponding author
Correspondence to Guillermo Restrepo (email: restrepo@mis.mpg.de).
Ethics declarations
Competing interests
The authors declare no competing interests.
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Article
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The periodic system of chemical elements was historically devised by assessing order and similarity relationships among the elements from their compounds, that is, using the accumulated results of chemical practice and knowledge. However, the current approach to the system is based on an ontology of isolated atoms where similarities, especially, are addressed through resemblances of electronic configurations. Here we show how the historical approach can be combined with computational tools for data analysis to build up the system based on the compounds reported by chemists. The approach produces well-known similarities of chemical elements when applied to binary compounds. The results come from the analysis of 4,700 binary compounds of 94 chemical elements, whose resemblances are quantified based on the elements they form compounds with and the proportions of those combinations. It is found that similarities do not always correspond to columns of the conventional periodic table and that besides robust similarities such as those of alkali metals, halogens and lanthanoids, there are other mixed similarities involving transition metals and actinoids, some of which were already known for a long time. These similarities are described. Finally, the advantages and disadvantages of the electronic and the compound approach to the system are discussed. It is concluded that the current data availability and computational facilities make possible to think of a periodic system closer to the chemical milieu of compounds, bringing chemistry back to the system.
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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.
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The periodic table of elements is among the most recognizable image in science. It lies at the core of chemistry and embodies the most fundamental principles of science. In this new edition, Eric Scerri offers readers a complete and updated history and philosophy of the periodic table. Written in a lively style to appeal to experts and interested lay-persons alike, The Periodic Table: Its Story and Its Significance begins with an overview of the importance of the periodic table and the manner in which the term "element" has been interpreted by chemists and philosophers across time. The book traces the evolution and development of the periodic table from its early beginnings with the work of the precursors like De Chancourtois, Newlands and Meyer to Mendeleev's 1869 first published table and beyond. Several chapters are devoted to developments in 20th century physics, especially quantum mechanics and and the extent to which they explain the periodic table in a more fundamental way. Other chapters examine the formation of the elements, nuclear structure, the discovery of the last seven infra-uranium elements, and the synthesis of trans-uranium elements. Finally, the book considers the many different ways of representing the periodic system and the quest for an optimal arrangement.
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Without dwelling on issues of priority regarding the discovery of the periodic system of the elements, this study offers a connected narrative regarding Lothar Meyer’s investigative pathway from the spring and summer of 1856 until the end of 1869, in his gradually deepening understanding of periodic relationships among the elements. Dmitrii Mendeleev’s route to periodicity has been the subject of extensive investigation and debate; by contrast, there is nothing in the literature that takes a similarly detailed look at Lothar Meyer’s personal pathway to the periodic system. This study strives toward a deeper understanding of the history of the discovery of the archetypical symbol of chemistry as a whole, the periodic table; it concludes by offering a wider object lesson.
Article
Chemical research unveils the structure of chemical space, spanned by all chemical species, as documented in more than 200 y of scientific literature, now available in electronic databases. Very little is known, however, about the large-scale patterns of this exploration. Here we show, by analyzing millions of reac- tions stored in the Reaxys database, that chemists have reported new compounds in an exponential fashion from 1800 to 2015 with a stable 4.4% annual growth rate, in the long run nei- ther affected by World Wars nor affected by the introduction of new theories. Contrary to general belief, synthesis has been the means to provide new compounds since the early 19th cen- tury, well before Wöhler’s synthesis of urea. The exploration of chemical space has followed three statistically distinguishable regimes. The first one included uncertain year-to-year output of organic and inorganic compounds and ended about 1860, when structural theory gave way to a century of more regular and guided production, the organic regime. The current organometal- lic regime is the most regular one. Analyzing the details of the synthesis process, we found that chemists have had preferences in the selection of substrates and we identified the workings of such a selection. Regarding reaction products, the discovery of new compounds has been dominated by very few elemental com- positions. We anticipate that the present work serves as a starting point for more sophisticated and detailed studies of the history of chemistry.
Book
3. 4. 2. "SOMETHING ON CERIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3. 4. 3. THE DISCOVERY OF LANTHANUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3. 4. 4. THE DISCOVERY OF DIDYMIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3. 4. 5. THE NAME DIDYMIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3. 4. 6. THE DISCOVERY OF TERBIUM AND ERBIUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3. 5. The Cork Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3. 6. Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3. 7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 4. THE 50 YEARS FOLLOWING MOSANDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 F. SZABADVARY and C. EVANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4. 2. The Terbium Dispute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4. 3. Samarium and Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4. 4. The Division of Erbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4. 5. Separating the Twins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4. 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4. 7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 5. ELEMENTS NO. 70, 71 AND 72: DISCOVERIES AND CONTROVERSIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 HELGE KRAGH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5. 2. The ytterbium earths unti11905 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5. 3. Auer von Welsbach: aldebaranium and cassiopeium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5. 4. Urbain: neo-ytterbium and lutecium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5. 5. The ytterbium controversy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5. 6. Celtium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5. 7. Hafnium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5. 8. New light on old elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5. 9. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5. 10. Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5. 11. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Chapter 6. THE SEARCH FOR ELEMENT 61 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 JACOB A. MARlNSKY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6. 2. Separations and Identifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6. 3. Discovery Confirmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6. 4. Announcing, Claiming and 'Naming Element 61 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6. 5. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 vii PART II - APPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Chapter 7. CARL AUER VON WELSBACH A PIONEER IN THE INDUSTRIAL APPLICATION OF RARE EAR THS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 E. BAUMGARTNER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter
I have no idea who discovered the periodic system of chemical elements, and I am going to tell you why. When you open a chemistry textbook today, you can often find, next to its periodic table, a sidebar with a grizzled bearded man who is depicted as “the discoverer” of the periodic law, the formula-tor of the table whose checkered countenance greets you from the wall of every chemistry laboratory in the world. Almost always, that bearded man is Dmitrii Ivanovich Mendeleev (1834–1907), a chemist from St. Petersburg who published his version of this system in 1869—or maybe in 1871, depending on how you figure it. Sometimes he shares the space with the grizzled beard of Julius Lothar Meyer (1830–1895), who published his version in 1864, or 1868,1 or 1870.2 A hundred years ago, German textbooks might simply have presented Meyer, and some esoteric texts would have also depicted John Newlands, or Gustav Hinrichs, or one or two others—grizzled beards all. The textbooks are endowed with a certainty I do not have; they know what the periodic table is, and therefore they know who discovered it first.
Chapter
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.