CHAPTER 19

Complex Compounds

The discussion in the preceding chapter had direct reference only to compounds of the type Rm Xn, in which m positive atoms are combined with n negative atoms, but the principles therein developed are applicable to all combinations of atoms. Our next objective will be to apply these principles to an examination of some of the more complex situations.

Any atom in one of the simple compounds may be replaced by another atom of the same valence number and type. Thus any or all of the four chlorine atoms in CCl4 may be replaced by equivalent negative atoms, producing a whole family of compounds such as CCl3 Br, CCl2 F2 , CClI3 , CF4 , etc. Or we may replace n of the valence one chlorine atoms by one atom of negative valence n, obtaining such compounds as COCl2 , COS, CSTe, and so on. Replacements of the same kind can be made in the positive component, producing compounds like SnCl4 .

Simple replacement by an atom of a different valence type is not possible. Copper, for instance, has the same numerical valence as sodium, but the sodium atoms in a compound such as Na2 O are not replaceable by copper atoms. There is a compound Cu2 O, but the neutral valence structure of this compound is very different from the normal valence structure of Na2 O. Similarly, if we exchange a positive hydrogen (magnetic valence) atom for one of the sodium (normal valence) atoms in Na2 O, the process is not one of simple replacement. Instead of NaHO, we obtain NaOH, a compound of a totally different character.

A factor which plays an important part in the building of complex molecular structures is the existence of major differences in the magnitudes of the rotational forces in the various inter-atomic combinations. Let us consider the compound KCN, for example. Nitrogen is the negative element in this compound, and the positive-negative combinations are K-N and C-N. When we compute the inter-atomic distances, by means of the relations that will be developed later, we find that the values in natural units are .904 for K-N and .483 for C-N.

As stated in Chapter 18, the term “bond” is not being used in this work in any way connected with the subject matter of that chapter: the combining power or valence. The term “valence bond,” or any derivative such as “covalent bond,” has no place in the theoretical structure of the Reciprocal System. However, use of the word “bond” is convenient in referring to the cohesion between specific atoms, atomic groups, or molecules, and in the subsequent discussion it will be employed in this restricted sense. On this basis we may say that the force of cohesion, or “bond strength,” is considerably greater for the C-N bond than for the K-N bond, as is indicated by the difference in the inter-atomic distances.

It has usually been assumed that this force of cohesion is an indication of the strength of the inter-atomic forces, but in reality the relation is inverse. As explained in Chapter 8, the gravitational forces exerted by the atoms, the forces due to the atomic rotation, are forces of repulsion in the time region, and the cohesion is therefore greater when the rotational forces are weaker. The short C-N distance, and the corresponding strength of this bond, are the results of inactive force dimensions in this combination which reduce the effective repulsive force, and require the atoms to move closer together to establish equilibrium with the constant force of the progression of the reference system.

Because of its greater strength, the C-N bond remains intact through many processes which disrupt or modify the K-N bond, and the general behavior of the compound KCN is that of a K-CN combination rather than that of a group of independent atoms such as we find in K2 O. Groups like CN which have relatively high bond strengths and are therefore able to maintain their identity while changes are taking place elsewhere in the compounds in which they exist are called radicals. Inasmuch as the special properties of these radicals are due to the differences between their bond strengths and those of the other bonds within the compounds, the extent to which any particular group acts as a radical depends on the magnitude of these differences. Where the inter-atomic forces are very weak, and the bond is correspondingly strong, as in the C-N combination, the radical is very resistant to separation, and acts as a single atom in most respects. At the other extreme, where the differences between the various inter-atomic forces in the molecule are small, the boundary line between radicals and non-radical atomic groupings is rat per vague.

The stronger radicals are definite structural groups. NH4 is, to a large degree, structurally interchangeable with the sodium atom, OH can substitute for I in the CdI2 crystal without changing the structure, and so on. The weakest radicals, those with the smallest margins of bond strength, crystallize in structures in which the radical, as such, plays no part, and the structural units are the individual atoms. The perovskite (CaTiO3 ) structure is a familiar example. Here each atom is structurally independent, and hence this type of arrangement is available for a compound like KMgF3 in which there definitely are no radicals, as well as for a compound such as KIO3 which contains a borderline group. From a structural standpoint the IO3 group in KIO3 is not a radical, although it acts as a radical in some other physical phenomena, and is commonly recognized as one.

From a thermal standpoint, for example, the IO3 group is definitely a radical at low temperatures, the entire group acting as a unit. But unlike the strong radicals such as OH and CN, which maintain this single unit status under all ordinary conditions, IO3 separates into two thermal units at higher temperatures. Other radical groups are still less resistant to the thermal forces. The CrO3 group, for example, acts as a single thermal unit at the lower temperatures, but in the upper part of the solid temperature range all four atoms are thermally independent. The thermal behavior of chemical compounds, including the examples mentioned, will be discussed in a subsequent volume.

In order to take the place of single atoms in the three-dimensional inorganic structures, the radicals must have three-dimensional force distributions, and where some of the inter-atomic forces are inherently two-dimensional, as is true in some of the lower group elements, for reasons that will be explained later, the three-dimensional distribution must be achieved by the geometrical arrangement. The typical inorganic radical therefore consists of a group of satellite atoms clustered three-dimensionally around one or more central atoms. Inasmuch as the satellite atoms are between the central atom and the opposite component of the compound, the effective valence of the radical must have the same sign as that of the satellite atoms. This limitation on the net valence means that the great majority of these inorganic radicals are negative, as hydrogen is the only element that has a two-dimensional force distribution when acting in a positive capacity. The most important hydrogen radical of this class is ammonium, NH4 , in which hydrogen has the magnetic valence 1 and nitrogen the negative valence 3 for a net group valence of +1. The phosphonium radical is similar, but less common. A variation of NH4 is the tetramethylammonium radical N(CH3 )4 , in which the hydrogen atoms are replaced by positive CH3 groups.

The theoretically possible number of negative radicals is very large, but the effect of probability factors limits the number of those actually existing to a small fraction of the number that could theoretically be constructed. Other things being equal, those groups with the smallest net displacement are the most probable, so we find BO2 -1 commonly, and BO3 -3 less frequently, but not BO4 -5, BO5 -7, or the other higher members of this series. Geometrical considerations also enter into the situation, the most probable combinations, where other features are equal, being those in which the forces can be disposed most symmetrically.

The status of the binary radicals such as OH, SH, and CN, is ambiguous on the basis of the criteria developed thus far, since there is no distinction between central and satellite atoms in their structures, but these groups can be included with the inorganic radicals because they are able to enter into the three-dimensional inorganic geometric arrangements.

Another special class of radicals combines positive and negative valences of the same element. Thus there is the azide radical N3 , in which one nitrogen atom with the neutral valence +5 is combined with two negative nitrogen atoms, valence -3 each, for a group total of -1. Similarly, a carbon atom with the primary magnetic valence +2 joins with a negative carbon atom, valence -4, to form the carbide radical, C2 , with a net valence of -2.

The common boride radicals, the combination boron structures mentioned in Chapter 18, are B2 , B4 , and B6 . The best known B4 compounds are all direct combinations with valence 4 elements of Division I. It can therefore be concluded that the net valence of the B4 combination is -4. Similarly, the role of B6 in such compounds as CaB6 and BaB6 indicates that the net valence of the B6 radical is -2. The status of B2 is not as clearly indicated, but it also appears to have a net valence of -2; that is, it is simply half of the B4 combination. This net valence of -2 could be produced either by a combination of the -3 negative valence with the secondary magnetic valence, +1, or by a combination of the -5 negative valence with the positive valence +3. The same two alternatives are available for B4 . The combination of +1 and -3 valences is also feasible for the radical B6 , and on the basis of these values the valences of all of the boride radicals constitute a consistent system, as shown by the following tabulation:

Positive
Negative
Net
B2
B+1
B-3
- 2
B4
2 B+1
2 B-3
- 4
B6
4 B+1
2 B-3
- 2

On the other hand, the B6 radical cannot be produced by a combination of +3 and-5 valences, and in order to utilize the -5 valence it would be necessary to substitute valence +2 in the positive position. The -3 negative valence thus leads to a more consistent set of combinations, as well as being consistent with the boron valence in the direct combinae lions of boron with positive elements. At least for the present, therefore, it will have to be concluded that the weight of the evidence favors a single negative valence (-3) for boron.

The general principles of compound formation developed for the simpler combinations apply with equal force to compounds contemning radicals of the inorganic class. The basic requirement is that the group valence of the radical be in equilibrium with an equal and opposite valence. A negative radical such as SO4 therefore joins the necessary number of positive atoms to form a compound on the order of K2 SO4 . The positive NH4 radical similarly joins with a negative atom to produce a compound like NH4 Cl. Or both components may be radicals, as in (NH4 )2 SO4

One new factor introduced by the grouping is that the relative negativity of the atoms within the group no longer has any significance. The azide group, N3 , for instance, is negative, and cannot be anything but negative. In the compound ClN3 , then, the chlorine atom is necessarily positive, even though chlorine is negative to nitrogen in direct Division IV combinations such as NCl3 .

In the magnetic valence compounds the negative electric displacement is in equilibrium with one of the magnetic displacements of the positive component. This leaves the positive electric displacement free to exert a directional influence on other molecules or atoms. In its general aspects, this directional effect is similar to the orienting influence of the space-time equilibrium that is required in order to enable atoms of negative elements to join with other atoms in compounds. In both cases there are certain relative positions of the interacting atoms or molecules that permit a closer approach, which results in a greater cohesive force. Neither of these orienting agencies contributes anything to the cohesive forces; they simply hold the participants in the positions in which the stronger forces are generated. Without the directional restrictions imposed by these orienting influences the relative positions would be random, and the greater cohesive forces would not develop.

Since all magnetic valence compounds have free electric displacements, they all have strong combing tendencies, forming what we may call molecular compounds; that is, compounds in which the constituents are molecules instead of the individual atoms or radicals of the atomic compounds. Inasmuch as the free electric displacements are all positive, there is no valence equilibrium involved, and the molecular compounds can be of almost any character, but geometrical and symmetry considerations favor associations with units of the same kind, or with closely related units. Double molecules of a compound are not readily recognized in the solid or liquid states, but in spite of the obstacles to recognition there are many well-known combinations such as FeO, Fe2 O3 , C2 O, CO, etc. Water and ammonia, both magnetic valence compounds, are particularly versatile in forming combinations of this type, and join with a great variety of substances for form hydrates and ammoniates.

There is only one free electric displacement in any binary magnetic valence combination, and the orienting effect is therefore exerted in only one direction. When the active molecular orientation effects, as we will call them, of a pair of molecules such as FeO and Fe2 O3 are directed toward each other, the system is closed, and the resulting Fe3 O4 association has no further combining tendencies. Even where several H2 O molecules combine with the same base molecule, as is very common, the association is between the base molecule and each H2 O molecule individually. A different situation develops where a two-dimensional molecule is formed on the basis of a magnetic valence. Here the inter-molecular distance may be reduced to the point where three molecules are within a single natural unit of space, in which case each molecule exerts an orienting effect not only upon its immediate neighbor in the active direction, but also upon the next molecule beyond it.

Limitation of the effective inter-atomic forces to two dimensions in this class of compounds contributes to the extension of the magnetic orientation effects in two separate ways. First, it reduces the inter-atomic distance by one third, since there is no effective rotational force in the third dimension. In the compound lithium chloride, for example, the distance between lithium and chlorine atoms on a three-dimensional basis would be 1.321 natural units. By reason of the two-dimensional orientation, this drops to .881 units. Then, the distance between molecules 1 and 3 is further reduced by the geometric effect illustrated in Fig. 3. In an aggregate in which the structural units are arranged three-dimensionally, as in (a), molecule 2 interposes its full diameter between molecules 1 and 3. Where the inter-atomic distance is x, the distance between the centers of molecules 1 and 3 is then 4x. But if the structural units are arranged two-dimensionally, as in (b), this distance is reduced to 2y, where y is the distance between adjacent central atoms.

In the case of lithium chloride, this reduction is not sufficient to enable any interaction between molecules 1 and 3, as the 2y distance is 1.398, and no effect is exerted where this distance exceeds unity. But there are other compounds, particularly those of carbon and nitrogen, in which the 2y distance is, or can be, less than unity. The C-C distance, for example, ranges from .406 to .528. With some aid from the geometric

Figure 3

(a)
(b)

arrangement in the case of the greater distances, a large number of carbon compounds based on the magnetic orientation are within the range where the orienting effects of the free electric displacement extend to the third molecule.

These two-dimensional magnetic valence molecules with very short inter-atomic distances are actually stable structures with their negative electric rotations fully counterbalanced by appropriate positive magnetic rotations, and they are therefore capable of independent existence in the manner of the other molecules that we have considered. Because of their strong combining tendencies, however, most of them do not actually lead an independent life more than momentarily if there are other molecules present with which they can combine, and in recognition of the fact that they are normally constituents of molecular compounds rather than molecules in their own right we will hereafter refer to them as magnetic neutral groups.

While there are many atomic combinations with inter-atomic distances less than one half natural unit, or so close to this figure that they can be brought within it by structural modifications, the number of such combinations that can form magnetic neutral groups is limited by various factors such as probability, valence, relative negativity, etc. Thus the combinations CN and OH are excluded because they have active valences; that is, they are negative radicals, not neutral groups. NH2 is excluded by a probability situation that will be discussed later; OH2 is excluded because hydrogen is strongly positive to oxygen, and so on. Furthermore, the binary valence two combinations are subject to an additional restriction. Its exact nature is not yet clear, but its effect is to put CO at the limit of stability, so that combinations such as NO and CS are excluded. The practical effect of these several restrictions, together with the limitations on the inter-atomic distance, is to confine the magnetic neutral groups, aside from CO, almost entirely to combinations of carbon, nitrogen, and boron with valence one negative atoms or radicals.

In the subsequent discussion we will find it convenient to use a diagram which identifies the orientation effects that are exerted by the various structural units, and thus shows how the different types of molecular compounds are held in combining positions; that is, positions in which the inter-group cohesive forces are maximized. In the diagram we will represent valence effects by double lines, as in CH3 =OH, while the primary molecular orientation effect will be represented by single lines, as in CH-CH. The secondary molecular effects exerted on the third group in line will then be shown by connecting lines, with arrows to indicate the direction of the orienting effect.

As this diagram indicates, there is a primary orientation effect between CH groups 1 and 2, and between groups 3 and 4. Because these effects are unidirectional, and paired, there is no interaction between groups 2 and 3. If the CH groups were three-dimensional, like the FeO and Fe2 O3 molecules previously mentioned, there would be no combination between the 1-2 pair and the 3-4 pair, and the result would be two CH-CH molecules. But because group 3 is within one unit of distance of group 1, the orienting effect of the free electric displacement of group 1, which acts at short range against group 2, also acts against group 3 at longer range, as shown in the diagram. Similarly, the 4-3 effect acts at long range against group 2. Thus the 1-2 and 3-4 pairs are held in the combining position by the secondary orientation effects in spite of the lack of any primary effect between groups 2 and 3.

The relation of these orienting influences to the cohesion between the constituents of the atomic or molecular compound can be compared to the effect of a reduced temperature on a saturated liquid. The result of the lower temperature is solidification, and in the solid there is an additional cohesive force between the atoms that did not exist in the liquid, but this new force is not supplied by the temperature. What the change in the temperature actually accomplished was to create the necessary conditions under which the atoms could assume the relative positions in which the inter-atomic forces of cohesion are operative. Similarly, the orienting effects of the valence equilibrium and the free rotational displacement of the magnetic neutral groups do not provide the forces that hold the molecules together; they merely create the conditions which allow the stronger cohesive forces to operate.

When the atoms or neutral groups are subjected to the orienting effects that permit them to establish equilibrium at one of the shorter inter-atomic or inter-group distances, it is the point of equilibrium between the rotational forces and the oppositely directed force due to the progression of the natural reference system that determines the magnitude of the cohesive forces. An important consequence is that the cohesive force between any two specific magnetic neutral groups is the same regardless of whether the orientation results from the short range primary effect, or the long range secondary effect, of the free electric displacements. In the preceding diagram, the magnitude of the cohesive force between groups 2 and 3 is identical with that of the 1-2 and 3-4 forces. It is simply the cohesive force between two CH groups. As we will see later, particularly in Chapter 21, this point is quite significant in connection with the attempts that are being made to draw conclusions concerning the molecular structure from the magnitudes of the inter-group forces.

As the diagram indicates by the arrows at the two ends of the four-group combination, the 2-1 and 3-4 secondary orientation effects are not satisfied, and they are capable of extension to any other atom or group that comes within range. Such a combination of neutral groups is therefore open to further combination in both directions. The system is not closed by the addition of more groups of the same character, since this still leaves active secondary orientation effects at each end of the combined structure. The unique combining power that results from this continuation of the secondary effects gives rise to an extremely large and complex variety of chemical compounds. There is almost no limit on the number of groups that can be joined. As long as each end of the molecule is a magnetic neutral group with an active secondary effect, there are still two active ends no matter how many groups are added.

The necessary closure to form a compound without further combining tendencies can be attained in one of two ways. Enough of these magnetic neutral groups may combine to permit the ends of the chain to swing around and join, satisfying the unbalanced secondary effects, and creating a ring compound. Or, alternatively, the end groups may attach themselves to atoms or radicals which do not have the orienting effects of the magnetic groups. Such additions close the system and form a chain compound. Both the chain and ring structures are known as organic compounds, a name surviving from the early days of chemistry, when it was believed that natural products were composed of substances of a nature totally different from that of the constituents of inorganic matter.

As used herein, the term “organic” will refer to all compounds with the characteristic two-dimensional magnetic valence structure, rather than being defined as usual to cover only carbon compounds with certain exceptions. The excluded carbon compounds are practically the same under both definitions, and the only significant difference is that in this work a few additional compounds, such as the hydronitrogens, which have the same type of structure as the organic carbon compounds are included in the organic classification.

The valence equilibrium must be maintained in the chain compounds, and the addition of a positive radical or atom at one end of the chain must be balanced by the addition of a negative unit with the same net valence at the other end. This equilibrium question does not arise in connection with the ring compounds as all of the structural units in the ring are either magnetic neutral groups or neutral associations of atoms or groups with active valences. Here the complete valence balance is achieved within the groups or associations.

In order to join the two-dimensional magnetic group structures any radicals which are to occupy the end positions must also be two-dimensional. The inherently three-dimensional inorganic radicals such as NO3 , SO4 , etc., do not qualify. The two-atom and three-atom radicals like OH, CN, and NO2 are arranged three-dimensionally in the inorganic compounds, but they are not necessarily limited to this kind of an arrangement, and they can be disposed two-dimensionally. These radicals are therefore available for the two-dimensional compounds.

The two-dimensional structure also reverses the requirement with respect to the net valence of the radicals. The external contacts of the two-dimensional groups are made primarily by the central atoms, and instead of having the same direction as that of the satellite atoms, the net group valence conforms to the valence of the central atom. These groups, the organic radicals, are therefore opposite in valence to their counterparts among the inorganic radicals. Corresponding to the positive ammonium radical NH4 is the negative amine radical NH2 , the negative radical CN- in which carbon has the magnetic valence 2 has an organic analog in the positive radical CN+, in which carbon has the normal valence 4, and so on. Furthermore, the combinations of carbon and the valence one negative elements, including hydrogen, which are inherently two-dimensional, and are therefore precluded from acting as inorganic radicals, are fully compatible with the two-dimensional neutral groups. Since there are a large number of such combinations, the great majority of the organic radicals are structures of this type.

From the foregoing it can be seen that the organic compounds are subject to exactly the same valence considerations as the inorganic compounds. They are, in fact, atomic associations of identically the same general nature. The only difference is that the very short inter-atomic distances in the magnetic valence compounds of the lower group elements permit the existence of secondary orientation effects that enable these compounds to unite into complex structures. This unification of the whole realm of chemical compounds is an example of the kind of simplification that results when the true reason for a physical phenomenon is ascertained. As we saw in Chapter 18, the formation of chemical compounds takes place because the atoms of the purely electronegative elements (Division IV) cannot establish a stable relationship with atoms of other elements except under certain special conditions in which their negative displacement (motion in time) is counterbalanced by an appropriate positive displacement of the elements with which they are interacting. These requirements are equally as applicable to carbon and the other lower elements as to the constituents of the inorganic compounds. All chemical compounds are governed by the same general principles.

The clarification of the nature of the organic compounds will, of course, require some modification of existing chemical ideas. The concept of an electronic origin of the cohesive forces must be abandoned. Electrons are independent physical entities. They are not constituents of atoms, and they are not available to generate cohesive forces, even if they were capable of so doing. (It should be noted that the foregoing statement does not assert that there are no electrons in the atoms. That is an entirely different issue which will be given consideration when we are ready to begin a discussion of electrical phenomena.) The concepts of “double bonds” and “triple bonds” will also have to be discarded, along with the curious idea of “resonance,” in which a system alternating between two possible states is supposed to acquire an additional energy component by reason of the alternation.

Some of the theoretical concepts that are untenable in the light of the new findings, such as the “double bonds” , have been quite useful in practice, and for this reason many chemists will no doubt find it difficult to believe that these ideas are actually wrong. As explained in the introductory discussion, however, much of the progress that has been made in the scientific field has been made with the help of theories that are now known to be wrong, and have been discarded. The reason for this is that none of these theories was entirely wrong. In order to gain any substantial degree of acceptance a theory must be correct in at least some respects, and, as experience has demonstrated in many cases, these valid features can contribute materially to an understanding of the phenomena to which they relate, even though other portions of the theory are totally incorrect.

The necessity of parting with cherished ideas of long standing will be less distressing if it is realized that the “double bonds” and associated concepts that must now be abandoned are not tangible physical entities; they are merely inventions by which certain empirical relations of a mathematical nature are clothed in descriptive language for more convenient manipulation. Linus Pauling brings this out clearly in the following statements:

The structural elements that are used in classical structure theory, the carbon-carbon single bond, the carbon-carbon double bond, the carbon-hydrogen bond, and so on, also are idealizations, having no existence in reality.... It is true that chemists, after long experience in the use of classical structure theory, have come to talk about, and probably to think about, the carbon-carbon double bond and other structural units of the theory as though they were real. Reflection leads us to recognize, however, that they are not real, but are theoretical constructs in the same way as the individual Kekule structures for benzene.68

When a correct theory appears it must include the valid features of the previous incorrect theory. But the identity of these features as they appear in the context of the different theories is often obscured by the fact that they are expressed in different language. In the case we are now considering, current chemical theory says that the cohesion in organic compounds is due to electronic forces. Development of the Reciprocal System of theory now leads to the conclusion that there are no electrons in the atomic structures, and consequently there are no electronic forces. At first glance, then, it would appear that the new findings repudiate the entire previous structure of thought. On closer examination, however, it can be seen that the electrons, as such, actually play no part in most of the explanations of physical and chemical phenomena that are presumably derived from the electronic theory. The theoretical development actually uses only the numerical values.

For example, the conclusions that are drawn from the positions of the elements in the periodic table are currently expressed in terms of the number of electrons. Carbon has a valence of four in its “saturated” condition because it has four electrons in its atomic structure, so the electronic theory says. It is clear from the empirical evidence that there actually are four units of some kind in the carbon atom, whereas the sodium atom has only one unit of this kind. But the empirical observations give us nothing but the numbers 4 and 1; they tell us nothing at all about the nature of the units to which the numerical values apply. The conclusion that these units are electrons is pure assumption, and the identification with electrons plays no part in the application of the theory. The maximum valence of carbon is four, not four electrons.

Moseley's Law, which relates the frequencies of the characteristic x-rays of the elements to their atomic numbers, is another example. It is currently accepted as “definite proof” of the existence of specific numbers of electrons in the atoms of these elements. Conclusions of the same kind are drawn from the optical spectra. In a publication of the National Bureau of Standards entitled Atomic Energy Levels we find this positive statement: “Each chemical element can emit as many atomic spectra as it has electrons.” But, in fact, the empirical evidence in both cases contributes nothing but numbers. Here, again, the observations tell us that certain specific numbers of units are involved, but they give us no indication as to the nature of these units. So far as we can tell from the empirical information, they can be any kind of units, without restriction.

Thus, when we discard the electronic theory in application to these phenomena we are not making any profound change; we are merely altering the language in which our understanding of the phenomena is expressed. instead of saying that there are 11 electrons in sodium, one of which is in a particular “configuration,” we say, on the basis of our theoretical findings, that the total number of effective speed displacement units in the rotational motions of the sodium atom is 11, and that only one of these applies to the electric (one-dimensional) rotation. Carbon has 6 total displacement units in its rotational motions, with 4 in the electric dimension. It follows that in those properties which are related to the total effective speed displacement (the net total quantity of motion in the atom) the number applicable to sodium is 11, and that applicable to carbon is 6, while in those properties which are determined by the displacement in the electric dimension individually the respective numbers are 1 for sodium and 4 for carbon.

It is an equally simple matter to translate the formation of “ionic compounds” from the language of the electronic theory to the language of the Reciprocal System. The electronic theory says that stability is attained by conforming to the “electronic configuration” of one of the inert gas elements, and that potassium and chlorine, for example, accomplish this by transferring one electron from potassium to chlorine, thus bringing both to the status of the inert gas element argon. The Reciprocal System says that chlorine has a negative rotational speed displacement of one unit (a unit motion in time) in its electric dimension, and that it can enter into a chemical combination only by means of a relative orientation in which that negative displacement is balanced at a zero point by an appropriate positive displacement. Potassium has a positive displacement of one unit, and the combination of this one positive unit and the negative unit of chlorine produces the required net total of zero.

So far as the “ionic compounds” are concerned, the Reciprocal System changes practically nothing but the language, as the foregoing example shows. But when the language change is made, it becomes evident that the same theory that applies to this one restricted class of compounds applies to all of the true chemical compounds. On this basis there is no need for the profusion of subsidiary theories that have been formulated in order to deal with those classes of compounds to which the basic “ionic” explanation is not applicable. Instead of calling upon the multitude of different “bonds” –the ionic bond, the ion-dipole bond, the covalent bond, the hydrogen bond, the three-electron bond, and the numerous “hybrid” bonds–that are required in order to adapt the electronic theory to the many types of compounds, the Reciprocal System applies the same theoretical principles to all compounds.

In these cases that we have considered, the translation from electronic language to the language of the Reciprocal System leads to a significant clarification of the mechanism of the processes that are involved. Whatever value there may be in the electronic theory is not lost when that theory is abandoned; it is carried over into the theoretical structure of the Reciprocal System in different language.