Dedicated to the 150th anniversary of D.I. Mendeleev's discovery of the Periodic Law

One hundred and fifty years have passed since Mendeleev published his article demonstrating the periodic recurrence of atomic properties (called elements in chemistry) with increasing atomic weight. Atomic weight  was  defined by Dmitry Ivanovich as a parameter that determines the periodic nature of changes in the properties of  chemical elements , as well as the simple and complex substances formed from these elements. And today, a century and a half after the great Russian scientist published the first periodic table of chemical elements, as well as predicted the properties of several as yet undiscovered elements (which, after their discovery, turned out to have the properties predicted by Mendeleev), we can confidently state:

Mendeleev's Periodic Law as a universal law of nature, applicable to all currently discovered chemical elements (they are also – in the terminology of physicists – atoms) is incorrect.

What? How? What is this written, and in an anniversary article, too, where it's customary not to criticize the classics, but to praise them! And who is this author of this little article (what's his last name?), to make such bold and clearly ignorant assertions out of the blue? A pygmy, trying to refute a classic, one of the greatest in science! How dare he? Such pseudoscientific—and even more so: an anti-scientific assertion cannot go unpunished.

Esteemed reader. Colleague. And critic. Don't jump to conclusions. Give me a chance to finish my sentence, and you (as they used to say in Odessa, and as some renowned scholars did when defending their positions at seminars, sometimes even stamping their professorial feet) will gradually begin to agree with me. And if you listen to my explanations for even three minutes, the rest will become more or less clear to you without further explanation.

MENDELEEV'S PERIODIC LAW AS A LAW THAT ALLOWS US TO CLASSIFY ALL CHEMICAL ELEMENTS DISCOVERED TODAY IS WRONG – BUT BRILLIANTLY WRONG!

Just as Galileo's Principle of Relativity is ingeniously false when the reference frame moves at a speed close to the speed of light. That is, Galileo's Principle of Relativity is true—but not always. Just as Ohm's Law is ingeniously false—and simultaneously true. Which is undoubtedly a Law of Nature—but only under strictly observed restrictions. Specifically, the conductor carrying the current must be perfectly straight (so that it has no inductance), distant from other conductors (because if the conductor has capacitance, Ohm's Law ceases to apply), and the conductor must maintain a strictly constant temperature (after all, conductors—remember—heat up when current flows through them, changing their resistance, and therefore the voltage ceases to be strictly proportional to the current). If, at the time of George Ohm's 1826  publication    , instruments capable of measuring voltage and current to a few decimal places (as is easily measurable today) had existed, the French scientist might not have risked publishing his discovery. And, examining the meticulously presented measurements, many colleagues would have expressed serious doubts about the discovered law, since it turns out to be true—INDISPUTABLY TRUE—but only approximately. And if it's approximately true, and not exactly correct, then what kind of law is it? Especially not the law of some state, not invented by humans, but the highest of all: the Law of the Universe!

The problem with the Periodic Law has something in common with the examples given above (although each of these Great Problems is unique in its own way). By the time Mendeleev discovered the Periodic Law  (1869)  , 63 chemical elements were known  . The idea that chemical elements and their compounds exhibited periodicity was a brilliant insight! By laying out cards on a table (like solitaire cards), Dmitry Ivanovich managed to classify most of the elements discovered by that time in such a way that the chemical properties of their atoms exhibited periodicity. The Law of Nature discovered by Mendeleev was given the name Periodic because (with the exception of the first two chemical elements: hydrogen and helium), they exhibited a periodicity of chemical properties with a period of eight. That is, an element with an atomic number (assigned to elements in order of increasing mass) k+8 had properties similar to an element with an atomic number k. Processes that have the property of repeating themselves at the same fixed interval are called periodic processes in physics (just as in mathematics, functions that satisfy the equation F(x + Δ ) = F(x)). Therefore, the discovery of the periodicity of the properties of chemical elements was – and continues to be – one of the most grandiose achievements in science!

In Mendeleev's time, most elements fit into the periodic table, devised by the author of the law, which had a rectangular shape (with eight groups/columns). However, as more and more elements were discovered, those that did not fit into the rectangular frame (as they must if the Periodic Law applies to all chemical elements) became more and more numerous. Mendeleev's authority, as well as the now-unshakable formulation of the PERIODIC LAW, exerted such pressure on chemists and non-chemists alike that attempts to squeeze all the elements known at any given time into the periodic (and therefore rectangular) frame became more and more numerous. No matter how they arranged the elements of the so-called d-block, ten each, as well as the lanthanides and actinides, while trying to maintain the rectangularity of the table (required by the periodicity condition), they essentially continued to play solitaire, as D.I. Mendeleev brilliantly did when creating the Periodic Table. However, it is important to understand: THE PERIODIC LAW IS NOT TRUE FOR ALL CHEMICAL ELEMENTS, BUT ONLY FOR THOSE WHOSE OUTER SHELLS CONTAIN (as follows from quantum mechanical analysis) s and p electrons. There are currently forty-eight such chemical elements, whose properties can be divided into eight groups (fifty, along with hydrogen and helium, which form a group of two elements). But these are precisely the elements that enable the overwhelming majority of chemical reactions, both in nature and in human-created technologies, and that make life possible! To squeeze elements that do not possess periodic properties into a periodic system (that is, in accordance with the mathematical definition of a periodic function, having the same period), under the magic of the term PERIODIC SYSTEM, is wrong, absurd and futile.

The fact that the Periodic Law holds for 50 chemical elements is Mendeleev's greatest discovery. Without this periodicity, or if it were different, neither the Earth's surface as it exists today nor could life have arisen on Earth. However, the fact that the remaining chemical elements discovered to date (the so-called d-block elements, ten in each block – designated R1, R2, R3, R4 in Figures 1 and 2 _, as _well as _the lanthanides _and actinides) do not exhibit periodic repeating properties with increasing atomic number is no less fundamental and important than the periodicity of the Fifty.

After the creation of quantum mechanics, the problem of the periodicity of the chemical properties of the elements did not disappear, but rather assumed a fundamental character. From the solution of the Schrödinger equation for atoms, it follows that the number of electrons in the nth shell is equal to 2n2 ^, that is, it increases parabolically. How can this—undeniably correct—result be reconciled with the fact that the chemical properties of atoms repeat (according to the Periodic Law) with a period of eight, meaning that the number of elements in each subsequent period does not increase, but rather remains constant? This problem is largely (though not exclusively) the cause of the divide between physicists and chemists and their mutual, barely concealed, dislike. Physicists consider chemists to be empiricists who understand nothing of the fundamental laws of nature, while chemists consider physicists to be useless (or at best, of little use) dogmatists, out of touch with reality.

To be fair (speaking from physics, to which I belong based on my basic education), it should be noted that the chemists' position is not without foundation. Much in chemistry has failed to be deduced from the fundamental laws of physics. For example, Hund's rule, formulated in 1926 (and Madelung's rule, derived ten years later from it), which determines the order in which electron shells are filled in atoms as a function of the atomic number of the element (n + l), could not be analytically derived from the Schrödinger equation, and for this reason it was declared not a law of nature (like the Periodic Law or Ohm's Law), but an empirical rule. A theoretical ploy stemming from the inability to explain this impressive result analytically.

There are many problems arising between chemistry—an experimental and empirical science—and physics, which attempts to explain events based on the fundamental laws of nature. As both sciences develop, the number of unresolved problems " from the perspective of physics " and " from the perspective of chemistry "—that is, the same problems viewed from different perspectives—doesn't decrease, but rather increases. This article attempts to resolve one of them, freeing itself from the magic of the term "PERIODIC LAW." After this, the problem—at this and only at this level—becomes solvable, revealing new insights almost immediately.

All atoms discovered to date are divided into those with periodic properties, which allow them to be divided into eight groups - depending on the maximum valence that they exhibit in chemical reactions) - and aperiodic atoms, which do not have periodic physical and chemical properties.

Figure 1 shows the periodic table, which includes chemical elements divided into eight groups (except the first, consisting of hydrogen and helium).

Figure 1: Periodic elements of the Periodic Table of Elements

Figure 2 shows aperiodic elements that cannot be classified into groups as a function of their atomic weight.

Figure 2: Aperiodic elements of the Periodic Table of Elements

The periodic law is valid for periodic elements, which, according to quantum mechanics, have s and p electrons in their outer shells. The maximum valence of periodic elements is equal to the group number of the periodic table to which they belong. For groups one through seven, the maximum valence of a chemical element is equal to the sum of the number of s and p electrons in its outer shell. As for elements in which the d and f shells are filled, they are metals, in which, as the number of electrons increases, orbitals are filled with electrons with opposite spins simultaneously. Nothing similar exists in the lanthanides and actinides, nor in the elements in the d -blocks, for example, as chlorine has seven electrons in its outer shell, some or all of which can be valence electrons. Why this happens in nature with aperiodic elements is a problem of exceptional importance, still far from being fully resolved.

Of particular interest are the elements of the rightmost group (the noble gases), sometimes called the eighth group and sometimes the zeroth group. There are reasons for both of these definitions. The number of electrons in the outer shell of the noble gases (closing the shell) is eight. The number of valence electrons in the noble gases, which can react chemically with other elements and chemicals, is zero, since all noble gases (the left vertical line in the Periodic Chemical Elements table) have closed shells. Assigning the number eight to the noble gas group means that the corresponding noble gas completes the period it belongs to. However, assigning the number zero to the noble gas group means that each noble gas is an element of the first group of the next period. The combination of these properties can naturally be graphically represented in three dimensions by arranging the Periodic Elements table in a spiral.

Figure 3 Spiral of periodic elements

Figure 4. Spiral of periodic elements in projection perpendicular to the spiral axis.

Thus, the Periodic Law discovered by Mendeleev is true not for all chemical elements, but for 50 periodic elements, which can be divided into eight groups and represented in three dimensions as the Spiral of the Periodic Elements. These and only these elements can be both donors and acceptors of all electrons located in their outer atomic shells. Electrons with d and f electrons in their outer shells do not possess this periodic property, allowing them to be distributed among groups.

The inclusion of all currently discovered elements in the periodic law—both those with periodically repeating properties and those that do not have periodically repeating chemical and physical characteristics—leads to three- and four-dimensional graphical representations of the Pyramids of the Elements (Figure 5) and cones on which circles and spirals are wound. That is, to regular elements, as in D.I. Mendeleev's Periodic Law, but not periodic, like a rectangular