Int. J. Mol. Sci. 2010, 11(11), 4381-4406; doi:10.3390/ijms11114381

Article
Ionocovalency and Applications 1. Ionocovalency Model and Orbital Hybrid Scales
Yonghe Zhang
American Huilin Institute, 13810 Franklin Ave, Queens, NY 11355, USA; E-Mail: y.zhang.huilin@gmail.com
Received: 27 September 2010; in revised form: 19 October 2010 / Accepted: 21 October 2010 /
Published: 3 November 2010

Abstract

: Ionocovalency (IC), a quantitative dual nature of the atom, is defined and correlated with quantum-mechanical potential to describe quantitatively the dual properties of the bond. Orbiotal hybrid IC model scale, IC, and IC electronegativity scale, XIC, are proposed, wherein the ionicity and the covalent radius are determined by spectroscopy. Being composed of the ionic function I and the covalent function C, the model describes quantitatively the dual properties of bond strengths, charge density and ionic potential. Based on the atomic electron configuration and the various quantum-mechanical built-up dual parameters, the model formed a Dual Method of the multiple-functional prediction, which has much more versatile and exceptional applications than traditional electronegativity scales and molecular properties. Hydrogen has unconventional values of IC and XIC, lower than that of boron. The IC model can agree fairly well with the data of bond properties and satisfactorily explain chemical observations of elements throughout the Periodic Table.
Keywords:
ionocovalency; molecular properties; electronegativity; theoretical chemistry

1. Introduction

In the valence-bond (VB) approach, the molecular wave function is written as a product of the state functions of the constituent atoms. This makes models based on the VB approximation intuitively appealing, as exemplified by the extreme usefulness of Lewis structures of “The Atom and the Molecule” [1] and by the wide acceptance of Pauling’s “Nature of the Chemical Bond” [2]. Before Lewis proposed his theory of the shared electron pair bond, bonding in some compounds could be satisfactorily explained on the basis of simple electrostatic forces between the positive and negative ions which are assumed to be the basic molecular units. The shared electron pair bond is known as the covalent bond, while the other type is the ionic bond.

Over the years, the description of the properties of the covalent and ionic bond remains largely qualitative and Pauling’s scale [3] due to not based on the electron configuration data, left a wide front for arguments and has lead to many different suggestions for the bond strengths [424].

In the present work, we defined and correlated ionocovalency (IC), a quantitative atomic dual nature of ionicity and σ- and spatial-covalency with the quantum-mechanical potential to describe quantitatively the dual properties of bonds. Orbital hybrid IC scale and IC electronegativity XIC scale are proposed wherein the ionicity and the covalent radius are determined by spectroscopy. Being composed of the ionic function I and the covalent function C, the model exhibits quantitatively the dual properties of bond strengths, charge density and ionic potential. Based on the atomic electron configuration, the quantum-mechanical built-up dual parameters and sub-models, which in turn exhibit various specific bond properties, the model formed a Dual Method of the multiple-functional prediction which has much more versatile and exceptional applications than traditional electronegativity scales and molecular properties. Hydrogen has its unconventional values lower than that of boron, residing on the borderline between the weak ionic and the weak covalent ions. The IC model can agree fairly well with the data of bond properties and satisfactorily explain chemical observations of elements throughout the Periodic Table.

2. Methodology

2.1. IC Model

Based on the VB approximation, the bond strengths can be considered mainly about the potential energy: the nuclear charge Z felt by valence electrons at the covalent boundary. And the term of Schrödinger’s Wave Equation incorporating bond strength is the potential energy Ze2ψ/r.

h 2 2 ψ / 8 π 2 m Z e 2 ψ / 4 π ɛ 0 r = E ψ

Ionic bonds are omnidirectional. The nuclear charge Z possesses the power of ionizing radiation and radiates positive charge in all directions. Therefore, the nuclear charge Z is directly proportional to the bond strengths but has the delocalized ionic nature.

The covalent radius, rc is the other important part of the potential here. It is a distance from nucleus to a charge density wherein the bonding atoms are aligned and localized at very specific bond lengths, and it is inversely proportional to the bond strengths. In the case of the hydrogen atom, as Equation (2.1.1) shows, as the electron approaches the nucleus, the potential energy dives down toward minus-infinity, in order for the total energy E to remain constant, and its kinetic energy shoots up toward positive-infinity. So a compromise is reached in which theory tells us that the fall potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius [25]. The calculation of the H2 molecule by Heitler and London showed that as the inter-nuclear distance decreased, the potential energy associated with interactions between nucleus and electrons dropped very markedly until a minimum was reached, and then (owing to the greater effect of internuclear repulsion at much smaller internuclear distances) to rise sharply [26]. The minimum corresponded fairly closely to the experimentally determined value of R, 0.74 Å (covalent radius = 0.37 Å, see below 4.2). Therefore, the covalent radius has the harmoniously localized covalent nature.

As atoms and molecules have the dual nature, ionocovalency, the bond strengths can be considered as a combination of the ionic and the covalent functions [10]. So the ionic function I can be considered as a function of the nuclear charge Z: I(Z); and the covalent function C can be considered as a function of the covalent radius rc: C(rc−1), wherein the reciprocal of rc can be defined as atomic covalency.

Ionocovalently, the bond strengths and electronegativity, therefore, can be accounted for on the basis of the dual nature of bonds, and functionally defined as ionocovalency, a product of the ionic and the covalent functions:

I C = I ( Z * ) C ( r c 1 )

And so the bond strengths, the potential energy and electronegativity have the IC framework of ionocovalency, which shows an effective ionocovalent potential, the attraction power that should be Pauling postulated.

According to the Bohr energy model

E = Z 2 m e 4 / 8 n 2 h 2 ɛ 0 2 = R Z 2 / n 2
we have derived the effective nuclear charge Z* from ionization energy and the effective principal quantum number n* [8,9]:
Z * = n * ( I z / R ) ½
where Iz is the ultimate IE. R is the Rydberg constant, R =2μ42e4/h2 = 13.6 eV, h is Planck’s constant. Substituting Equation (2.1.4) into (2.1.2), we can naturally correlate the bond properties to the quantum-mechanics, and get the IC model:
I ( I z ) C ( n * r c 1 ) = n * ( I a v / R ) ½ r c 1
where the effective principal quantum number n* is related to the electron energy, distribution and the distance from the nucleus. Hence, n* can be considered as an energy of ionic function and also as a spatial distance of covalent function. The n*rc−1, which is related to the spatial overlap, can be defined as spatial-covalency of covalent function (rc−1 is a linear- or σ-covalency).

2.2. IC Electronegativity XIC

As an application of ionocovalency, by Plotting Pauling values of Xp against n*(Iav/R)½rc−1, we obtain a new IC-potential electronegativity

X I C = 0.412 n * ( I a v / R ) ½ r c 1 + 0.387

Based on the above IC model, our previous electronegativity scale Xz [8,9] can be accounted for IC-force:

I C = I ( V ) C ( r 1 ) = I ( Z * ) C ( r 2 ) = n * ( I z / R ) ½ r c 2
X z = 0.241 n * ( I z / R ) ½ r c 2 + 0.775

In Equation 2.1.5 and 2.1.6, Iav is ionicity (the average IE of valence shell electrons) determined by the following IC orbital hybrid bonding procedures. The diagrams are adapted from those in the excellent article by Blaber [27].

2.3. IC Orbital Hybrid Bonding Procedures

(1) Ionization promotion: As a valence shell fills, the successive increased ionization energy of an electron would provide the promotion energy for hybrid orbital formation e.g., consider gaseous molecules of BeF2. The fluorine atom has the electron configuration: 1s22s22p5. The beryllium atom has the electron configuration: 1s22s2.

Ijms 11 04381f3 1024

In the ground state, there are no unpaired electrons. However, the beryllium atom could obtain an unpaired electron by promoting an electron from the 2s orbital to the 2p orbital by its lower first IE (9.32 eV). The beryllium atom can now forms two covalent bonds with fluorine atoms:

Ijms 11 04381f4 1024

(2) Ionicity hybridization: We can combine functions for the 2s and 2p electrons to produce a “hybrid” orbital for both electrons. The charge transfer and charge distribution would occur from the higher energy level of the 2p orbital to the lower energy level of the 2s orbital to form an energy-lower and identical 2sp hybrid orbital. The ideas developed are adequate for calculation of the charge density identically distributed. The IEs of the 2s and 2p electrons can be averaged to result in a hybridizing ionicity, Iav:

I a v = n 1 Σ i = 1 n I i
where Ii is the IE of single electron of valence shell, n is number of valence shell electrons.

By Equation (2.1.9), we get an average IE: Iav = 13.76 eV from the first IE (9.32 eV) and second IE (18.2 eV):

  • first: Be[He](2s)2 → Be+[He] (2s)1 − 9.32 eV

  • second: Be+[He](2s)1 → Be2+[He] − 18.20 eV

of 2s electrons for 2sp electrons:

Ijms 11 04381f5 1024

(3) Ionocovalency: by localizing the hybridized ionicity at the covalent boundary rc to form an ionocovalent bond of 2sp hybrid orbitals:

Ijms 11 04381f6 1024

Hence, for beryllium, IC = I(Iav)C(n*rc−1) = n*(Iav/R)½rc−1 = 1.99(13.76/13.6)½ (0.970)−1 = 2.064 And XIC = 0.412 n*(Iav/R)½ rc−1 + 0.387 = 0.412*1.99(13.76/13.6)½(0.970) −1 + 0.387 = 1.237.

Similarly, an s orbital can also mix with all three p orbitals in the same subshell. For CH4 by Equation (2.1.9), we get ionicity: Iav = 37.015 eV from the first IE (11.26 eV), second IE (24.40 eV), third IE (47.90 eV) and fourth IE (64.50 eV)

  • first: C[He](2s)2(2p)2 → C+[He](2s)2(2p)1 − 11.26 eV

  • second: C+[He](2s)2(2p)1 → C2+[He](2s)2 − 24.40 eV

  • third: C2+[He](2s)2 → C3+[He](2s)1 − 47.90 eV

  • fourth: C3+[He](2s)1 → C4+[He] − 64.50 eV

of the all 2s and 2p electrons and form 2sp3 hybrid orbitals:

Ijms 11 04381f7 1024

The IE is taken from Mackay et al. [28], the covalent radius rc, is taken from Pauling [29], Batsanov [30], Cordero et al. [31], Rappe et al. [32] and the effective principal quantum number n* is from our previous work [8,9]. The ionocovalency scale, IC, calculated from Equation (2.1.5) is listed in Chart 1 and the electronegativity scale, XIC calculated from Equation (2.1.6) are listed in Table 1.

Based on the IC model, ionocovalency can be finally defined as “the effective potential caused by the ionicity on a bonding pair of electrons at the localized covalent boundary in different valence hybrid orbital states, forming an ionocovalent charge density”.

3. Results

3.1. General Trend of Periodic Table

Natural Values: Chart 1 shows that IC has a same value range as that of its atomic core charge. This phenomenon is particularly noticeable for the top period elements which have not yet experienced much shielding effects. The atomic core charge is an effective nuclear charge and is always markedly less than the actual nuclear charge Z, but, as the shielding is not perfect, the core charge increases as Z increases, but more slowly. In the IC model, the effective nuclear charge is determined by natural IE, not from the calculation by shielding constants.

Ionocovalent Continuum: Chart 1 and Table 1 show that the ionocovalency IC and the electronegativity XIC exhibit evidently the ionocovalency character. The greater the IC and the XIC, the more covalent and the less ionic the cation is, and vice versa. Generally, across the period, the more right-hand-side an element is, the more covalent it is. And the more down-ward an element is, the more ionic it is. The IC and XIC increase from the lower left to the upper right of the Periodic Table across the s and p blocks, and decrease down most columns. Trends parallel periodic trends in IE.

The ionocovalency is a continuum which is certainly an improvement over the old ionic-versus-covalent dichotomy. In so-called ‘pure’ ionic bonding, an electron is transferred completely from one atom to another, once this transfer is complete, the IC potential will act to try to pull this electron back to its parent ion. If IC partially succeeds then there will be some electron density, n*(Iav/R)½rc−1, in the region in between the ions, which is the situation in a covalent bond. Thus ‘pure’ ionic and ‘pure’ covalent bonds could be seen as two extremes of an IC continuum. And so a covalent scale has the ionic degree.

Energy-lowered Hybrid Bonding: The ionocovalent bonding procedures runs a charge promotion, charge distribution and energy-lowered hybrid sequence. Using Equation 2.1.5. and 2.1.6., we get the energy-lowered hybrid IC and XIC values which are evidently lower than that of unhybridized values. For example, for carbon we have the energy-lowered 2sp3 hybrid IC = 4.320 and XIC = 2.167. In the unhybridized situation, IC would be as higher as 5.702 and all unhybridized conventional electronegativities are as higher as than 2.5 for carbon.

3.2. Hydrogen

Pauling’s scale is estimated from the bond dissociation energies of two atoms, hydrogen and chlorine, and then arbitrarily extended to all elements not based on the quantitative configuration energy data [3].

Hydrogen has the lowest energy, E = −13.6 eV. Batsanov has an experimental covalent radius of 0.37 Å [30] equal to the Heitler-London’s half H-H value R (R = 0.74 Å) [26]. Based on these spectroscopic data and the IC model (Equation 2.1.5), we reach its IC value of 2.297 eV and its electronegativity, XIC of 1.333 (Table 2 and Figure 1) that is not that conventionally high as 2.2.

The result is strongly supported by the point-charge distribution in hydrides (Table 3) proposed by Mo [33], which shows that in the typical ionic LiH (lithium monohydride) hydrogen gains point charge of 0.783, in the weak ionic BeH (beryllium monohydride) gains only 0.044, but in the covalent BH (boron monohydride) starts to loss point charge. That means that the ionocovalency and the electronegativity of hydrogen are smaller than that of boron. And moreover, the data of electric dipole moments for AlH (aluminum monohydride) (Table 4), proposed by the National Institute of Standards and Technology [34], shows that the aluminum end of the dipole is negative. That means that the ionocovalency and the electronegativity of hydrogen are smaller than that of aluminum.

Hydrogen has one valency orbital and a single electron. It can be an anion to form an ionic bond by gaining another electron and it can be a cation to form a covalent bond by sharing another electron. Therefore, the IC and the XIC values of hydrogen happen to lie on the border between the weaker ionic beryllium and the weaker covalent boron (Chart 1 and Table 1). We can assign the IC value of hydrogen (2.297) as a standard to estimate the ionocovalent character of the cations. The cations with IC values smaller than that of hydrogen we call the ionic cations and those with IC values greater than that of hydrogen we call the covalent cations. The cations with IC values greater than that of beryllium (2.064) and smaller than that of boron (3.291) we might call borderline cations. The greater the IC than that of hydrogen, the more covalent and the less ionic the caton is, and vice versa.

3.3. Diagonal Relationship (Top Periods)

Chart 2 and Chart 3 show that the IC and the XIC scales of the top period rationalize an interesting empirical observation of a similar situation that exists for the pairs of elements. The first element in a given family of the periodic chart tends to resemble the second element in the family to the right as indicated below:

Table Chart 1. Ionocovalency.

Click here to display table

Chart 1. Ionocovalency.
HHe
(1)2.297(2)5.173
LiBeBCNOFNe
(1)1.023(2)2.064(3)3.291(4)4.302(5)5.329(6)6.273(7)7.370(4)6.949
(2)2.998(3)4.030(2)3.648(2)5.203
NaMgAlSiPSClAr
1.130(2)1.933(3)2.730(4)3.371(5)4.355(6)5.165(7)6.048(4)4.845
(1)1.585(2)2.322(4)3.872(4)4.093(5)4.977(2)3.762
(3)3.286(2)2.121(1)2.851
KCaScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr
(1)0.999(2)1.617(3)2.494(4)3.374(5)4.359(6)5.287(7)6.012(6)5.520(4)4.261(4)4.537(3)3.918(2)2.772(3)3.281(4)3.895(5)4.502(6)5.209(7)5.941(6)5.422
(3)2.824(4)3.772(5)4.691(6)5.426(5)4.879(3)3.591(3)3.802(2)3.155(1)2.331(1)1.841(2)2.639(3)3.364(4)4.090(5)4.869(4)4.562
(2)2.258(3)3.143(4)4.058(5)4.810(4)4.203(2)2.874(2)3.029(1)2.343(1)2.422(2)3.146(1)2.815(2)3.538
(2)2.502(3)3.395(4)4.161(3)3.431(1)2.113(1)2.330
(1)2.077(2)2.719(1)2.253
(1)2.185
RbSrYZrNbMoTcRuRhPdAgCdInSnSbTeIXe
(1)0.988(2)1.576(3)2.332(4)3.716(5)4.043(6)4.964(7)5.593(8)6.394(6)5.450(5)4.842(3)3.592(2)2.658(3)2.923(4)3.601(5)4.057(6)4.641(7)5.339(8)5.553
(3)2.267(4)3.575(5)4.547(6)5.090(7)5.890(4)4.233(4)4.277(2)2.973(1)2.174(1)1.678(2)2.472(3)3.036(4)3.675(5)3.817(6)4.667
(2)1.884(3)3.052(4)3.980(5)4.563(6)5.355(3)3.638(3)3.672(1)2.147(2)2.832(1)2.530(4)3.900
(2)2.532(3)3.318(4)4.008(5)4.791(2)2.993(2)3.042(2)3.044
(1)2.040(2)2.760(3)3.425(4)4.189(1)2.287
(1)2.155(2)2.762(3)3.525
Δ(1)2.218(2)2.924
CsBaLaHfTaWReOsIrPtAuHgTlPbBiPoAtRn
(1)0.992(2)1.646(3)2.185(4)3.624(5)4.393(6)5.178(7)5.874(8)6.616(6)5.683(6)5.640(5)5.033(2)3.118(3)3.307(4)3.780(5)4.273(6)4.707(7)5.430(8)5.567
(3)3.170(4)3.924(5)4.697(6)5.383(7)6.122(5)5.107(5)5.056(3)3.965(1)2.653(1)1.887(2)2.574(3)3.162(4)3.700(5)4.419(6)5.046
(2)2.691(3)3.462(4)4.200(5)4.881(6)5.608(4)4.478(4)4.518(2)3.412(3)3.285(3)3.522(4)4.183
(2)3.056(3)3.707(4)4.344(5)5.066(3)3.910(3)3.963(1)2.689(2)2.811(1)2.473
(1)2.473(2)3.261(3)3.795(4)4.483(2)3.324(2)3.405
(2)3.237(3)3.869(1)2.831(1)2.749
(1)2.597(2)3.370
ΔΔ(1)2.779
FrRaAcΔCePrNdPmSmEuGdTbDyHoErTmYbLu
(1)0.959(2)1.400(3)2.093(4)3.074(4)3.037(3)2.572(3)2.606(3)2.604(3)2.385(3)2.637(4)3.301(3)2.730(3)2.754(3)2.780(3)2.829(3)2.649(3)2.592
(3)2.506(3)2.368(2)2.050(2)1.858(2)2.213(3)2.686(2)2.286(2)2.112
ΔΔThPaUNpPuAmCmBkCfEsFmMdNoLw
(4)2.789(3)2.279(3)2.316(4)2.341(4)2.354(4)2.349(3)2.165(3)2.215(3)2.229(3)2.262(3)2.278(3)2.309(3)2.323(3)3.900
(3)2.431

Note: Some ions which might not actually exist are included here just for research reference.

Table Chart 2. IC-diagonal relationship.

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Chart 2. IC-diagonal relationship.
Be2+ (2.252)B3+ (3.291)C4+ (4.320)N5+ (5.554)O6+ (6.939)
Mg2+ (1.933)Al3+ (2.730)Si4+ (3.371)P5+ (4.355)S6+ (5.165)
Table Chart 3. XIC-diagonal relationship.

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Chart 3. XIC-diagonal relationship.
Be2+ (1.315)B3+ (1.743)C4+ (2.167)N5+ (2.675)O6+ (3.246)
Mg2+ (1.184)Al3+ (1.418)Si4+ (1.776)P5+ (2.181)S6+ (2.515)
Table Chart 4. Iav-diagonal relationship.

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Chart 4. Iav-diagonal relationship.
Be2+ (13.76)B3+ (23.800)C4+ (37.015)N5+ (53.406)O6+ (72.020)
Mg2+ (11.325)Al3+ (17.763)Si4+ (25.763)P5+ (35.358)S6+ (46.077)
Table Chart 5. n*/rc-diagonal telationship.

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Chart 5. n*/rc-diagonal telationship.
Be2+ (2.238)B3+ (2.488)C4+ (2.618)N5+ (2.803)O6+ (3.015)
Mg2+ (2.119)Al3+ (2.189)Si4+ (2.449)P5+ (2.701)S6+ (2.806)

The reason for this relationship is that the pairs of element have approximately similar ionocovalency, IC = I(Iav)C(n*rc−1), due to the approximately similar ionic function I(Iav) (Chart 4) and covalent function C(n*rc−1) (Chart 5). Because of the electron configuration nature of the elements, the downwards vertical trend in decreasing covalency rc−1 is the opposite of the downwards vertical trend in increasing principal quantum number n*, and in this section of the Periodic Table the two opposing trends in C(n*rc−1) approximately cancel each other, resulting in similar values of ionicity, I(Iav).

3.4. Carbon, Sulfur, P-elements and Hydrogen

There are some arguments about the values of electronegativities of carbon, sulfur, selenium, tellurium, iodine and hydrogen [22]. Chart 1 shows IC values in the order:

S e 2 + ( 3.146 ) > S 2 + ( 3.121 ) > C 2 + ( 2.998 ) > T e 2 + ( 2.832 ) > I + ( 2.530 ) > H + ( 2.297 )

The results are consistent with the observations that hydrides H2Se, H2S, H2C, H2Te and HI form H3O+ ions in water [35].

As Thomas reviewed, the electronegativity of carbon and sulfur in most of the scale are almost identical. The key point, however, so far as their role as poisons is concerned, is that they differ markedly in the distance at which they sit on the nickel overlayers [36]. The calculations for these locations show that sulfur is very much stronger than carbon as a poison.

The results are also consistent with the experiment data of the dipole moment, which indicates that the electron clouds on the C-S and C-I bond in the molecules CS2 and CI4 are close to the sulfur end and the iodine end, respectively [37]. From IC model data (Chart 4), we can see that S6+ has a greater ionicity than that of C4+: Iav (S6+ = 46.077, C4+ = 37.015), although they have the close spatial covalency, n*rc−1 (C4+ = 2.618, S6+ = 2.805) (Chart 5).

3.5. 3d and 4f Electron Inefficient Screening (p-Block)

As Chart 1 and Table 1 show, the IC and XIC run the same uneven trend that is expected to decrease down a group with the features in terms of As3+(IC = 3.364, XIC = 1.773) and Bi3+(IC = 3.162, XIC = 1.690) both having higher than expected values, comparing those of P3+(IC = 3.286, XIC = 1.741) and Sb3+(IC = 3.036, XIC = 1.638). This apparent anomaly derives from the filling of the 3d row prior to gallium and the 4f row prior to thallium, both of which lead to higher effective nuclear charges (Table 1) than the previous periods as a result of inefficient screening of the nuclear charge by the 3d and 4f electrons, respectively.

3.6. Standard Potential Redox E0 (Transition Elements)

The IC values with a trend of decreasing at d5 and d10 agree well with the variation in values of E0 (M2+/M) [38] as a function of dn configuration for the first row of transition metals; the d0 corresponds to M = Ca (Table 5).

3.7. Inert Pair Effect (6s2 Elements)

The IC model, based on the VB approximation’s intuitive appeal and determined by covalent radius and ionization energy, is in accord with the relativistic effects with which contributions to the unusual chemistry of the heavier elements are two principal consequences. First, the s orbitals become more stable. Second, d and f orbitals expand and their energies are less.

For the inert pair effect in Tl(I), Pb(II), and Bi(III), the relativistic effects can give a qualitative verbalization: “The s orbitals of the heavier elements become more stable than otherwise expected” [39]. In the IC model, as Table 6 shows, the effect is attributable to the fact that the bond property in this case is controlled by the ionic function I(Iz, Iav). They are more stable in ionic compounds than in the entirely covalent form. Their IEs for forming higher covalent bonds are too much higher to form a stable hybridizing ionicity Iav:

3.8. Color of Copper, Silver and Gold

According to the relativistic effects: “The s orbitals of the heavier elements become more stable than otherwise expected” [39], we can only give a qualitative overview on the color of gold and silver, but this has nothing to do with the color of copper.

In the IC model, the phenomenon of “the Color of Copper, Silver and Gold” is attributable to the fact that their bond structure is controlled by their ionocovalency dual properties and we can get a satisfactory explanation by the Dual method.

As Table 7 shows, with the increase of the contraction of the s orbital, the outer d orbitals expand and their ionicities Iav are decreased from Cu3+ via Ag3+ to Au3+, however, with the increase of their effective principle quantum number n* the covalency rc−1 decreases from Cu3+ to Ag3+ but increases from Ag3+ to Au3+, which causes the spatial covalency n*rc−1 of Cu3+ higher than that of Ag3+ but close to Au3+, leading to same trend in ionocovalency.

This quantitative trend in their structure and energy nicely reflect their character of color. Copper and gold are the only two elemental metals with a natural color other than gray or silver, which depends on their ionic delocalizing property of “electron sea” that is capable of absorbing and re-emitting photons over a wide range of frequencies. Copper in its liquefied state, a pure copper surface without ambient light, appears somewhat greenish, a characteristic shared with gold.

4. Applications

4.1. Covalency Result Is Retrieved

Villesuzanne et al. proposed the study: “New considerations on the role of covalency in ferroelectric niobates and tantalites” [23]. Here, covalency means the amount of mixing of oxygen 2p and metal d orbitals to form valence bands; it is evaluated quantitatively through the computation of the crystal orbital overlap population (COOP). The energies of Ta 5d and Nb 4d atomic orbitals are the same in EHTB parameters. The bond lengths are equal too, as found experimentally. The difference in COOP’s occurs because of larger radial extension of Ta 5d compared to Nb 4d orbitals, leading to a greater overlap with oxygen 2p orbitals. The fact that Ta5+-O bonds are more covalent than Nb5+-O bonds is due to a larger radial expansion of Ta 5d orbitals. This effect is not accounted for in Pauling electronegativity scales [3], which give information on the energy difference between valence orbitals, not on their spatial overlap. The arguments led to the opposite assumption of reference [24] concerning the covalency of Ta5+-O and Nb5+-O bonds from Pauling electronegativity Xp: Ta(1.5) < Nb(1.6).

In their later paper, they proposed that the explicit calculation of the electronic structure—COOP’s in particular—gives a larger covalency for Ta5+-O bonds than for Nb5+-O bonds. This result is retrieved in the Allred and Rochow scale [7] and in Zhang electronegativity scales for ions [9]. The results can be fairly well accounted in IC model: the energies of Ta 5d and Nb 4d atomic orbitals are the same in EHTB parameters due to having similar atomic ionicity Iav of 24.89 and 27.02, respectively. The bond lengths are equal due to having similar linear covalency rc−1 of 0.745 and 0.745, respectively. The big difference is the spatial covalency, n*rc−1, in I(Iav)C(n*rc−1) = n*(Iav/R)½rc−1. The Ta 5d orbitals, compared to Nb 4d orbitals, involve greater spatial covalency, n*rc−1, (Ta5+ = 3.246, Nb5+ = 2.869), leading to a greater overlap with oxygen 2p orbitals and a greater IC: Ta5+ (4.393) > Nb5+ (4.043) and XIC: Ta5+(2.197) > Nb5+(2.053).

4.2. Mössbauer Parameters δ and Δ

As the IC model, n*(Iav/R)½rc−1, is defined as ionocovalent density of the effective nuclear charges at covalent boundary, it is strongly related with the Mössbauer parameters δ and Δ [40,41]. The value of the isomer shift, δ, depends particularly on the density of s electrons at the nucleus. Therefore, in iron-57 an increase in electron density causes a negative isomer shift; since d electrons tend to shield the nucleus slightly from the s electrons, the value of δ falls as the number of d electrons in the iron atom falls. Mean values of δ [42], Z* and IC for some oxidation states of iron are shown in Table 8 and Figure 2.

4.3. Effective Polarizing Power and Fajans Rules

Fajans suggested the rules to estimate the extent to which a cation could polarize an anion and thus induce covalent character. This Fajans phenomenon happens to be the IC-potential, the ionocovalency, the effective ionic potential (or the effective polarizing power), n*(Iav/R)½rc−1.

The simple form of the ionic potential considered the valence charge of the ion with respect to its size. The valence charge is numerically equal to the number of valence electrons of the ion. In some cases we may consider the effective nuclear charge Z*. For two ions of the same actual nuclear charge, Hg2+ and Ca2+, the Hg2+ has the higher effective nuclear charge Z* (4.490) and the IC (3.118), it is considerably more polarizing and its compounds are considerably more covalent than those of Ca2+ which has the smaller effective nuclear charge Z* (2.807) and the IC (1.617). So we have their related melting points HgCl2 = 276 and CaCl2 = 772. Comparisons of more compounds are listed in Table 9 (below).

4.4. Melting Points and Bond Properties

Table 9 shows that for the covalent bonding, the increased covalent bonding resulting from increasing the ionicity Iav, the σ covalency rc−1 or the spatial covalency n*rc−1 can lower the transition temperatures. The melting points decrease with increasing the covalency rc−1 and the spatial covalency n*rc−1.

However, for ionic bonding (see 4.5.), the ionic compounds are characterized by very strong IC potentials holding the ions together. Increasing the ionic function I(Z*, Iav) tends to increase the lattice energy of a crystal. For compounds which are predominantly ionic, increased ionic function I(Z*, Iav) or covalent function C(rc−1, n*rc−1) will result in increased melting points.

4.5. Lattice Energy

The IC model Equation 2.1.5 is correlated with the electrostatic energy of a cation in Born-Landé equation of the lattice energy

U = Z 2 e 2 A N / 4 π ɛ 0 r ( 1 n 1 )

The both equations reveal how ionic bond strengths vary with the cation ionic charges and inversely with the distance between ions in the lattice. The IC gives a reasonable correlation to the lattice energy as shown in Table 10 and Table 11.

4.6. Lowis Acid Strengths

As we have described [810], the stability of a metal complex (the strength of metal-ligand bond) should be a function of the electron-attraction power of the metal. The IC value agrees fairly well with the lattice energy and the crystal field stabilization energy (CFES):

Table Table 10. Parameters and lattice energies, −U.

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Table 10. Parameters and lattice energies, −U.
CompoundCationZ*Iavrc−1n*rc−1XICICU(kJmol 1) [44]
LiHLi+1.2535.390.8162.2380.8081.023905.4
NaHNa+1.7775.140.6361.8380.8531.13810.9
KHK+1.9494.340.5131.7690.7990.999714.2

AgFAg+2.8747.580.7472.8751.2712.147954
NaFNa+1.7775.140.6361.8380.8531.13903.9
KFK+1.9494.340.5131.7690.7990.999801.2

AgClAg+2.8747.580.7472.8751.2712.147904
TlClTl+2.9226.110.6462.8151.1641.887732
KClK+1.9494.340.5131.7690.7990.999697.9
RbClRb+2.1344.180.4551.750.7870.97677.8

Table 11 shows that the IC values correlate with the lattice energies derived from Born-Haber cycle data for MCl2 where M is a first row d-block metal; the point for d0 corresponds to CaCl2. (Data are not available for scandium where the stable oxidation state is +3) [38].

Crystal field stabilization energy (CFES) causes to d level an effect upon thermodynamic stability of complex ions. Owing to the overall contraction in size on traversing a period from left to right, there is an increase in CFES from Ca2+ to Zn2+ and same trend occurred in IC and XIC, For weak-field ligands (Table 12), the formation constants log β [38] follow the uneven trend and the IC and XIC run in same way: Mn2+ < Fe2+< Co2+ < Ni2+ < Cu2+ < Zn2+.

5. Dual Method

We couldn’t expect “verbum sat sapienti”, but we have a dual parameter group that can dialectically serve many purposes. When IC and XIC correlate with some properties, their dual component parameters and sub-models would give some reason to an observation or find some clue to a new idea. See above all parameters, sub-models and observations to which we have applied the Dual Method. Further examples are as follows:

5.1. An Interesting Comparison

In Table 13 an interpretation for an interesting comparison can be made between the predominantly ionic species CsF and BaF2 and the more covalent species KBr and CaBr2. For ionic species, the bond strengths are controlled by the ionic function I(Iav). Doubling the Iav from 3.890 to 7.605 in the highly ionic fluorides produces the expected increase in lattice energy and correspondingly doubles the transition temperatures (from 684 °C to 1,28 °C). For covalent bonding, the covalent function C(n*rc−1) is controlling factor. The little change in covalency rc−1: 0.513, 0.576 and spatial covalency n*rc−1: 1.769, 1.987 produces the expected little change in transition temperatures (from 730 °C to 765 °C), despite the doubling of Iav from 4.340 to 9.345.

5.2. “Inverted” Sodium-Lithium Electronegativity

Table 14 shows why electronegativity of sodium is higher than that of lithium. When we correlate IC or XIC with lattice energies, there is the “inverted” sodium-lithium electronegativity [8,9,45]; that Li+ has unexpectedly low values of IC and XIC. However, we can ask I(Iav, Z*) and C(n*, rc−1) to dialectically explain it: after 1st filling of p orbitals, Na+ reaches a much higher effective nuclear charge Z*(1.777) than that of Li+(1.253). The spatial covalency n*rc−1(Na+ = 1.838, Li+ = 1.624) does not cancel the higher effective nuclear charge Z* anymore. Dialectically, however, Li+ still has higher ionicity, Iav(5.390) and covalency rc−1(0.816) than that of Na+(Iav = 5.140, rc−1 = 0.636) although covalency is not so important in lattice energy.

5.3. Predicting Raw Material for InN Nanocrystals

Changzheng et al. [46] presented an effective synthetic protocol to produce high quality InN nanocrystals using indium iodide (InI3). There has been a question: “Is it possible for high-quality InN to be synthesized from indium halides?” The positive answer has been found in their work using InI3. Concerning the four kinds of indium halides, InF3, InCl3, InBr3, and InI3, InI3 has the strongest covalent ability. As is known, when two atoms form a chemical bond, the greater the difference between the electronegativity values for the two atoms, the more ionic the chemical bond between them [810].

According to the IC model, in the effective polarizing power, n*(Iav/R)½rc−1, both the effective principle quantum number, n*, and the covalent radius, rc, for halogens are increased in the order: F < Cl < Br < I (Table 1). The polarizability of the anion will be related to its “softness”; that is, to the deformability of its electron cloud. Both increasing n* and rc will cause this cloud to be less under the influence of the nuclear charge of the anion and more easily influenced by the charge on the cation. So concerning the four kinds of indium halides, InI3 is more covalent than the other three. And it is possible for high-quality InN to be synthesized from indium iodide (InI3).

Comparison of melting points for the anion pairs KF/KBr and CaCl2/CaBr2 from Table 9 can be treated in same way. KBr and CaBr2 are more covalent and have lower melting points than KF and CaCl2 respectively (see 4.4.).

6. Conclusions

Bond properties can be described quantitatively by an atomic dual nature, Ionocovalency (IC), which is defined and correlated with quantum-mechanical potential.

Ionocovalency, n*(Iav/R)½rc−1, which is a dual ionocovalent function of bond strength, charge distribution, charge density, effective ionic potential, or effective polarizing power, is composed of quantum parameters or sub-models, which in turn exhibit versatile specific bond properties and applications, forming a multiple functional Dual Method.

The Dual Method of multiple-functional prediction of that the dual properties of ionocovalency, which is a bridge of the chemical bond and the potential, should be able to explain fairly well the chemical observations of elements throughout the Periodic Table because they are based on the electron configuration and spectroscopy from 1s to nf.

Ionocovalency will be further tested against accurate experimental results and in our later papers we shall apply ionocovalency to discuss the types of chemical bonds, the Lewis acid strengths and the glass crosslink density with the Dual Method. And we believe more new applications will be followed by our colleagues.

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Ijms 11 04381f1 200
Figure 1. IC vs. XIC for hydrogen and the top elements indicated in Table 2.

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Figure 1. IC vs. XIC for hydrogen and the top elements indicated in Table 2.
Ijms 11 04381f1 1024
Ijms 11 04381f2 200
Figure 2. IC vs. δ for iron-57 as indicated in Table 9.

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Figure 2. IC vs. δ for iron-57 as indicated in Table 9.
Ijms 11 04381f2 1024
Table Table 1. Atomic parameters.

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Table 1. Atomic parameters.
Atm.NoCationsn*IzIavrc−1n*rc−1Z*rcXzXICIC
1H+0.8513.60013.6002.7032.2970.8500.3702.2711.3332.297
2He2+0.8554.40039.5003.5713.0361.4490.2806.0012.5185.173
3Li+1.995.39005.39000.8161.6241.2531.2250.9760.8081.023
4Be2+1.9918.20013.7601.0312.0522.0020.9701.3651.2372.064
5B3+1.9937.90023.8001.2502.4882.6330.8002.0261.7433.291
6C4+1.9964.50037.0151.3162.6183.2830.7602.5832.1674.320
6C3+1.9947.90027.8531.3162.6182.8480.7602.3331.9313.747
6C2+1.9924.40017.8301.3162.6182.2790.7601.8871.6222.998
7N5+1.9997.90053.4061.3512.6893.9430.7403.1252.5835.329
7N4+1.9977.50042.2831.3512.6893.5090.7402.8662.3414.742
7N3+1.9947.50030.5431.3512.6892.9820.7402.4122.0474.030
7N2+1.9929.60022.0651.3512.6892.5350.7402.0671.7983.425
7N+1.9914.53014.5301.3512.6892.0570.7401.6801.5322.780
8O6+1.99138.0072.0201.3702.7264.5790.7303.6422.9726.273
8O2+1.9935.10024.3601.3702.7262.6630.7302.2211.8903.648
9F7+1.99185.0094.0301.4082.8035.2330.7104.2843.4237.370
10Ne4+1.9997.10055.7851.7243.4314.0300.5804.5843.2506.949
10Ne2+1.9941.00031.2701.7243.4313.0180.5803.2502.5305.203
11Na+2.895.14005.14000.6361.8381.7771.5720.9480.8531.130
12Mg2+2.8915.00011.3250.7332.1192.6371.3641.1681.1841.933
13Al3+2.8928.50017.7630.8262.3883.3031.2101.4641.5122.730
13Al+2.895.99005.99000.8262.3881.9181.2101.0911.0401.585
14Si4+2.8945.10025.7630.8472.4493.9781.1801.6861.7763.371
14Si2+2.8916.30012.2250.8472.4492.7401.1801.3231.3442.322
15P5+2.8965.00035.3580.9352.7014.6601.0702.1052.1814.355
15P4+2.8951.40027.9480.9352.7014.1431.0701.9581.9823.872
15P3+2.8930.20020.1300.9352.7013.5161.0701.6821.7413.286
15P+2.8910.49010.4900.9352.7012.5381.0701.3091.3642.372
16S6+2.8988.00046.0770.9712.8065.3191.0302.4452.5155.165
16S4+2.8947.30028.9400.9712.8064.2161.0301.9992.0734.093
16S2+2.8923.30016.8300.9712.8063.2151.0301.6341.6733.121
17Cl7+2.89114.0058.3811.0102.9195.9880.9902.8322.8796.048
17Cl5+2.8967.80039.5341.0102.9194.9270.9902.3622.4384.977
17Cl3+2.8939.60025.4571.0102.9193.9540.9901.9882.0323.994
17Cl+2.8912.97012.9701.0102.9192.8220.9901.4691.5622.851
18Ar4+2.8959.80035.9651.0312.9794.7000.9702.3272.3834.845
18Ar2+2.8927.60021.6801.0312.9793.6490.9701.8301.9373.762
19K+3.454.34004.34000.5131.7691.9491.9500.8990.7990.999
20Ca2+3.4511.9009.00500.5761.9872.8071.7361.0331.0531.617
21Sc3+3.4524.80014.7130.6952.3973.5881.4391.3171.4142.494
22Ti4+3.4543.30022.8050.7552.6064.4681.3241.6211.7773.374
22Ti3+3.4527.50015.9730.7552.6063.7391.3241.4491.5502.824
22Ti2+3.4513.60010.2100.7552.6062.9891.3241.2491.3172.258
23V5+3.4565.20032.5280.8172.8195.3361.2241.9902.1834.359
23V4+3.4546.70024.3600.8172.8194.6171.2241.8031.9413.772
23V3+3.4529.30016.9130.8172.8193.8471.2241.5901.6823.143
23V2+3.4514.70010.7200.8172.8193.0631.2241.3521.4182.502
23V+3.456.74006.74000.8172.8192.4291.2241.1661.2051.984
24Cr6+3.4590.60043.8780.8532.9446.1971.1722.3372.5655.287
24Cr5+3.4569.30034.5340.8532.9445.4981.1722.1412.3204.691
24Cr4+3.4549.10025.8430.8532.9444.7561.1721.9252.0594.058
24Cr3+3.4531.00018.0900.8532.9443.9791.1721.6891.7863.395
24Cr2+3.4516.50011.6350.8532.9443.1911.1721.4421.5092.723
24Cr+3.456.77006.77000.8532.9442.4341.1721.2021.2432.077
25Mn7+3.45119.0056.3340.8562.9547.0221.1682.5782.8646.012
25Mn6+3.4595.00045.8900.8562.9546.3371.1682.3862.6225.426
25Mn5+3.4572.40036.0680.8562.9545.6181.1682.1812.3694.810
25Mn4+3.4551.20026.9850.8562.9544.8601.1681.9582.1014.161
25Mn3+3.4533.70018.9130.8562.9544.0681.1681.7341.8223.483
25Mn2+3.4515.60011.5200.8562.9543.1751.1681.4281.5072.719
25Mn+3.457.44007.44000.8562.9542.5521.1681.2261.2872.185
26Fe6+3.4599.00047.2620.8582.9616.4311.1652.4282.6615.520
26Fe5+3.4575.00036.9140.8582.9615.6841.1652.2142.3974.879
26Fe4+3.4554.80027.3930.8582.9614.8961.1652.0052.1194.203
26Fe3+3.4530.70018.2570.8582.9613.9971.1651.6951.8013.431
26Fe2+3.4516.20012.0350.8582.9613.2451.1651.4441.5352.786
26Fe+3.457.87007.87000.8582.9612.6241.1651.2411.3152.253
27Co4+3.4551.30027.4400.8703.0004.9011.1501.9962.1434.261
27Co3+3.4533.50019.4870.8703.0004.1301.1501.7621.8673.591
27Co2+3.4517.10012.4800.8703.0003.3051.1501.4801.5712.874
27Co+3.457.86007.86000.8703.0002.6231.1501.2531.3272.281
28Ni4+3.4554.90028.9850.9013.1085.0371.1102.1312.2564.537
28Ni3+3.4535.20020.3470.9013.1084.2201.1101.8611.9533.802
28Ni2+3.4518.20012.9200.9013.1083.3631.1101.5561.6353.029
28Ni+3.457.64007.64000.9013.1082.5861.1101.2811.3472.330
29Cu3+3.4536.80021.6100.9013.1084.3491.1101.8852.0013.918
29Cu2+3.4520.30014.0150.9013.1083.5021.1101.5991.6873.155
29Cu+3.457.73007.73000.9013.1082.6011.1101.2841.3522.343
30Zn2+3.4518.00013.6950.8012.7623.4621.2491.3881.5292.772
30Zn+3.459.39009.39000.8012.7622.8671.2491.2181.3332.295
31Ga3+3.4530.70019.0670.8032.7714.0851.2451.5811.7393.281
31Ga+3.456.00006.00000.8032.7712.2921.2451.1311.1451.841
32Ge4+3.4545.70025.9250.8182.8214.7631.2231.7941.9923.895
32Ge2+3.4515.90011.9000.8182.8213.2271.2231.3761.4742.639
33As5+3.4562.60033.9020.8262.8515.4471.2101.9932.2424.502
33As3+3.4528.40018.9370.8262.8514.0711.2101.5961.7733.364
33As+3.459.8109.81000.8262.8512.9301.2101.2571.3852.422
34Se6+3.4581.70042.4420.8552.9496.0951.1702.2642.5335.209
34Se4+3.4542.90026.1630.8552.9494.7851.1701.8542.0724.090
34Se2+3.4521.20015.4800.8552.9493.6811.1701.5331.6833.146
35Br7+3.45103.0052.6010.8763.0216.7851.1422.5292.8355.941
35Br5+3.4559.70035.3220.8763.0215.5601.1422.1112.3934.869
35Br+3.4511.81011.8100.8763.0213.2151.1421.3691.5472.815
36Kr6+3.4578.50045.2000.8622.9746.2901.1602.2602.6215.422
36Kr4+3.4552.50032.0000.8622.9745.2921.1601.9892.2674.562
36Kr2+3.4524.50019.2500.8622.9744.1051.1601.6041.8453.538
37Rb+3.854.18004.18000.4631.7822.1342.1600.8850.7940.988
38Sr2+3.8511.0008.35000.5222.0113.0171.9141.0031.0361.576
39Y3+3.8520.50013.0270.6192.3823.7681.6161.2111.3482.332
40Zr4+3.8534.30019.3100.6882.6484.5881.4541.4721.6873.155
40Zr3+3.8523.00014.3130.6882.6483.9501.4541.3461.5062.716
40Zr2+3.8513.1009.97000.6882.6483.2961.4541.2061.3212.267
41Nb5+3.8550.60027.0160.7452.8695.4261.3421.7692.0534.043
41Nb4+3.8538.30021.1200.7452.8694.7981.3421.6401.8603.575
41Nb3+3.8525.00015.3930.7452.8694.0961.3421.4741.6443.052
41Nb2+3.8514.30010.5900.7452.8693.3971.3421.3031.4302.532
41Nb+3.856.88006.88000.7452.8692.7381.3421.1411.2282.040
42Mo6+3.8568.00037.6830.7752.9826.4091.2912.0202.4324.964
42Mo5+3.8561.20031.6200.7752.9825.8701.2911.9562.2604.547
42Mo+43.8546.40024.2250.7752.9825.1381.2911.8032.0273.980
42Mo+33.8527.20016.8330.7752.9824.2831.2911.5621.7543.318
42Mo+23.8516.20011.6500.7752.9823.5631.2911.3831.5242.760
42Mo+3.857.10007.10000.7752.9822.7821.2911.1771.2752.155
43Tc7+3.8594.00046.2970.7873.0317.1031.2702.2872.6915.593
43Tc6+3.8576.00038.3470.7873.0316.4651.2702.1352.4845.090
43Tc5+3.8559.00030.8160.7873.0315.7951.2701.9732.2674.563
43Tc4+3.8543.00023.7700.7873.0315.0901.2701.7982.0384.008
43Tc3+3.8529.50017.3600.7873.0314.3501.2701.6221.7983.425
43Tc2+3.8515.30011.2900.7873.0313.5081.2701.3851.5252.762
43Tc+3.857.28007.28000.7873.0312.8171.2701.1961.3012.218
44Ru8+3.85119.0057.7710.8063.1027.9351.2412.5573.0216.394
44Ru7+3.85100.0049.0240.8063.1027.3101.2412.4092.8145.890
44Ru6+3.8581.00040.5280.8063.1026.6461.2412.2452.5935.355
44Ru5+3.8563.00032.4340.8063.1025.9461.2412.0722.3614.791
44Ru4+3.8546.50024.7930.8063.1025.1981.2411.8892.1134.189
44Ru3+3.8528.50017.5570.8063.1024.3741.2411.6471.8393.525
44Ru2+3.8516.80012.0850.8063.1023.6291.2411.4451.5922.924
45Rh6+3.8585.00042.3770.8023.0876.7961.2472.2672.6325.450
45Rh4+3.8545.60025.5650.8023.0875.2791.2471.8682.1314.233
45Rh3+3.8531.10018.8870.8023.0874.5371.2471.6771.8863.638
45Rh2+3.8518.10012.7800.8023.0873.7321.2471.4631.6202.993
45Rh+3.857.46007.46000.8023.0872.8511.2471.2171.3292.287
46Pd6+3.8590.00044.2730.7823.0136.9461.2782.2362.6265.435
46Pd5+3.8566.00035.1280.7823.0136.1881.2782.0262.3824.842
46Pd4+3.8549.00027.4100.7823.0135.4661.2781.8532.1494.277
46Pd3+3.8532.90020.2100.7823.0134.6931.2781.6591.9003.672
46Pd2+3.8519.40013.8700.7823.0133.8881.2781.4531.6403.042
47Ag3+3.8534.60021.2270.7472.8754.8101.3391.6001.8673.592
47Ag2+3.8521.50014.5400.7472.8753.9811.3391.4261.6122.973
47Ag+3.857.58007.58000.7472.8752.8741.3391.1611.2712.147
48Cd2+3.8516.90012.9450.7082.7253.7561.4131.2931.4822.658
48Cd+3.858.99008.99000.6942.6743.1301.4401.1391.2832.174
49In3+3.8528.00017.5630.6682.5724.3751.4971.3691.5912.923
49In+3.855.79005.79000.6682.5722.5121.4971.0451.0781.678
50Sn4+3.8540.70023.2850.7152.7525.0381.3991.5951.8713.601
50Sn2+3.8514.60010.9700.7152.7523.4581.3991.2661.4052.472
51Sb5+3.8555.50030.0280.7092.7305.7211.4101.7182.0594.057
51Sb3+3.8525.30016.8130.7092.7304.2811.4101.4121.6383.036
52Te6+3.8570.70037.0850.7302.8106.3581.3701.9022.2994.641
52Te4+3.8537.40023.2530.7302.8105.0341.3701.5951.9013.675
52Te2+3.8518.60013.8100.7302.8103.8801.3701.3531.5542.832
53I7+3.8592.34446.5350.7502.8867.1221.3342.1342.5875.339
53I5+3.8552.39523.7940.7502.8865.0921.3341.7981.9603.817
53I+3.8510.45010.4500.7502.8863.3751.3341.2321.4292.530
54Xe8+3.85112.9155.460.7142.7507.7751.4002.1392.6755.553
54Xe6+3.8568.71839.180.7142.7506.5341.4001.8392.3104.667
54Xe4+3.8543.95627.350.7142.7505.4591.4001.6261.9943.900
54Xe2+3.8521.20016.6700.7142.7504.2621.4001.3661.6413.044
55Cs+4.363.89003.89000.4261.8552.3322.3500.8770.7960.992
56Ba2+4.3610.0007.60500.5052.2013.2601.9811.0051.0651.646
57La3+4.3619.20011.9600.5342.3304.0891.8711.1321.2872.185
58Ce4+4.3636.72018.3110.6082.6495.0591.6461.4121.6533.074
58Ce3+4.3620.19912.1740.6082.6494.1251.6461.2481.4202.506
59Pr4+4.3638.97917.9180.6072.6465.0051.6481.4301.6383.037
59Pr3+4.3621.61910.8980.6072.6463.9031.6481.2631.3632.368
60Nd4+4.3640.42019.6760.6092.6555.2441.6421.4471.7033.194
60Nd3+4.3622.07512.7620.6092.6554.2231.6421.2721.4472.572
60Nd2+4.3610.7168.1050.6092.6553.3661.6421.1211.2322.050
61Pm3+4.3622.28312.9140.6132.6754.2491.6301.2811.4612.606
62Sm3+4.3623.42313.3730.6022.6274.3231.6601.2751.4602.604
63Eu3+4.3624.87413.9290.5412.3574.4121.8501.1901.3702.385
63Eu2+4.3611.2458.45700.5412.3573.4381.8501.0541.1531.858
64Gd3+4.3620.62412.9620.6202.7014.2561.6141.2721.4742.637
64Gd2+4.3612.1269.13100.6202.7013.5721.6141.1561.2992.213
65Tb4+4.3639.79819.7590.6282.7395.2551.5921.4841.7473.301
65Tb3+4.3621.86813.0790.6282.7394.2761.5921.3011.4942.686
66Dy3+4.3622.80113.4660.6292.7444.3391.5891.3141.5122.730
67Ho3+4.3622.80113.5420.6332.7594.3511.5801.3201.5212.754
68Er3+4.3622.69713.5770.6382.7824.3561.5671.3281.5322.780
69Tm3+4.3623.67113.9700.6402.7914.4191.5621.3431.5532.829
69Tm2+4.3612.0539.11900.6402.7913.5701.5621.1801.3292.286
70Yb3+4.3625.02914.4870.5892.5664.5001.6991.2691.4782.649
70Yb2+4.3612.1789.21600.5892.5663.5891.6991.1191.2572.112
71Lu3+4.3620.95613.4230.5982.6094.3321.6711.2421.4552.592
72Hf4+4.3633.30019.5380.6933.0245.2261.4421.5661.8803.624
72Hf3+4.3623.30014.9500.6932.0244.5711.4421.4361.6933.170
72Hf2+4.3614.90010.7750.6932.0243.8811.4421.3041.4962.691
73Ta5+4.3645.00024.8980.7453.2465.8991.3431.8352.1974.393
73Ta4+4.3633.10019.8730.7453.2465.2701.3431.6842.0043.924
73Ta3+4.3622.30015.4630.7453.2464.6491.3431.5211.8133.462
73Ta2+4.3616.20012.0500.7453.2464.1041.3431.4111.6463.056
73Ta+4.367.89007.89000.7453.2463.3211.3431.2191.4062.473
74W6+4.3661.00032.3630.7703.3566.7261.2992.0942.5205.178
74W5+4.3648.00026.6360.7703.3566.1021.2991.9452.3224.697
74W4+4.3635.40021.2950.7703.3565.4561.2991.7802.1174.200
74W3+4.3624.10016.5930.7703.3564.8161.2991.6041.9143.707
74W2+4.3617.70012.8400.7703.3564.2361.2991.4851.7313.261
75Re7+4.3679.00040.3110.7823.4127.5061.2782.3262.8075.874
75Re6+4.3664.00033.8630.7823.4126.8801.2782.1712.6055.383
75Re5+4.3651.00027.8360.7823.4126.2381.2782.0212.3984.881
75Re4+4.3637.70022.0450.7823.4125.5511.2781.8462.1774.344
75Re3+4.3626.00016.8270.7823.4124.8501.2781.6651.9503.795
75Re2+4.3616.60012.2400.7823.4124.1361.2781.4861.7203.237
75Re+4.367.88007.88000.7823.4123.3191.2781.2651.4572.597
76Os8+4.3699.00049.3250.7973.4748.3031.2552.5753.1136.616
76Os7+4.3683.00042.2300.7973.4747.6831.2552.4232.9096.122
76Os6+4.3668.00035.4330.7973.4747.0381.2552.2672.6975.608
76Os5+4.3654.00028.9200.7973.4746.3581.2552.1042.4745.066
76Os4+4.3640.00022.6500.7973.4745.6271.2551.9192.2344.483
76Os3+4.3625.00016.8670.7973.4744.8551.2551.6801.9813.869
76Os2+4.3616.90012.8000.7973.4744.2301.2551.5191.7763.370
76Os+4.368.70008.70000.7973.4743.4871.2551.3091.5322.779
77Ir6+4.3672.00036.6830.7943.4607.1611.2602.2982.7285.683
77Ir5+4.3657.00029.6200.7943.4606.4341.2602.1302.4915.107
77Ir4+4.3639.00022.7750.7943.4605.6421.2601.8962.2324.478
77Ir3+4.3627.00017.3670.7943.4604.9271.2601.7081.9983.910
77Ir2+4.3616.00012.5500.7943.4604.1881.2601.4931.7573.324
77Ir+4.369.10009.10000.7943.4603.5661.2601.3161.5532.831
78Pt6+4.3675.00037.8670.7753.3807.2751.2902.2582.7115.640
78Pt5+4.3655.00030.4400.7753.3806.5231.2902.0452.4705.056
78Pt4+4.3641.10024.3000.7753.3805.8281.2901.8732.2484.518
78Pt3+4.3628.50018.7000.7753.3805.1131.2901.6892.0203.963
78Pt2+4.3618.60013.8000.7753.3804.3921.2901.5131.7903.405
78Pt+4.369.00009.00000.7753.3803.5471.2901.2891.5202.749
79Au5+4.3658.00032.3460.7493.2636.7241.3361.9912.4615.033
79Au3+4.3630.50020.0770.7493.2635.2971.3361.6572.0213.965
79Au2+4.3620.50014.8650.7493.2634.5581.3361.4981.7933.412
79Au+4.369.23009.23000.7493.2633.5921.3361.2601.4952.689
80Hg2+4.3318.80014.6200.6943.0084.4901.4401.3671.6723.118
80Hg+4.3610.44010.4400.6943.0283.8201.4401.2191.4802.653
81Tl+34.3629.80018.7700.6462.8155.1221.5491.4231.7493.307
81Tl+4.366.11006.11000.6462.8152.9221.5491.0691.1641.887
82Pb4+4.3642.30024.1800.6502.8355.8141.5381.5581.9443.780
82Pb2+4.3615.00011.2100.6502.8353.9581.5381.2421.4472.574
83Bi5+4.3656.00030.1780.6582.8686.4951.5201.6982.1474.273
83Bi+34.3625.60016.5300.6582.8684.8071.5201.3991.6903.162
84Po6+4.3671.48837.1110.6542.8507.2021.5301.8042.3264.707
84Po4+4.3637.44822.9220.6542.8505.6601.5300.7751.9113.700
84Po3+4.3627.74518.0720.6542.8505.0261.5301.4161.7403.285
84Po2+4.3618.05113.2350.6542.8504.3011.5301.2921.5452.811
85At7+4.3688.29144.3450.6903.0077.8731.4502.0482.6245.430
85At5+4.3688.29129.3700.6903.0076.4071.4502.0482.2084.419
85At3+4.3629.26218.6600.6903.0075.1071.4501.5081.8383.522
85At+4.369.20009.20000.6903.0073.5861.4501.1861.4062.473
86Rn8+4.36106.5444.7000.7043.0707.9041.4202.2342.6805.567
86Rn6+4.3665.49036.7300.7043.0707.1651.4201.9192.4665.046
86Rn4+4.3641.90025.2500.7043.0705.9411.4201.6902.1114.183
87Fr+4.363.98003.98000.4071.7722.3592.4600.8690.7820.959
88Ra2+4.3610.2007.7400.4261.8553.2892.3500.9400.9641.400
89Ac3+4.3619.69212.3210.5042.1994.1501.9831.0971.2492.093
90Th4+4.3628.80016.5950.5812.5334.8161.7211.2911.5402.798
90Th3+4.3620.00012.5270.5812.5334.1841.7211.2051.3892.431
91Pa4+4.360.5842.5483.9001.7111.0961.3262.279
92U4+4.360.5942.5893.9001.6841.1061.3412.316
93Np4+4.360.6002.6173.9001.6661.1141.3512.341
94Pu4+4.360.6042.6313.9001.6571.1171.3572.354
95Am4+4.360.6022.6273.9001.6601.1161.3552.349
96Cm3+4.360.5552.4213.9001.8011.0651.2792.165
97Bk3+4.360.5682.4763.9001.7611.0781.2992.215
98Cf3+4.360.5712.4913.9001.7501.0821.3052.229
99Es3+4.360.5802.5293.9001.7241.0911.3192.262
100Fm3+4.360.5842.5473.9001.7121.0961.3262.278
101Md3+4.360.5922.5813.9001.6891.1041.3382.309
102No3+4.360.5962.5973.9001.6791.1081.3442.323
103Lw3+4.361.0004.3603.9001.0001.7151.9943.900
Table Table 2. IC and XIC for hydrogen and the top elements.

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Table 2. IC and XIC for hydrogen and the top elements.
ElementsLiBeHBCNOF
IC1.0232.0642.2973.2914.3025.3296.2737.37
XIC0.8081.2371.3331.7432.1672.5832.9723.423
Table Table 3. Point-charge distribution qA and dipole moment.

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Table 3. Point-charge distribution qA and dipole moment.
HydridesLiHBeHBHCHNHOHFH
Bond Length (expr)1.5951.3431.2331.121.0380.9710.917
Dipole Moment (expr)5.88--1.46-1.661.82
Dipole Moment (calc)5.9990.281−1.689−1.647−1.743−1.864−2.02
qA0.7830.044−0.285−0.306−0.350−0.400−0.459
Table Table 4. Bond length and dipole moment

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Table 4. Bond length and dipole moment
BondH-NaH-MgH-AlH-SiH-SeH-PH-SH-Cl
Bond Length (expr)1.8871.731.6481.521.4751.4221.3411.275
Dipole Moment (cal)5.9661.231−0.169−0.332−0.634−0.651−1.06−1.468
Table Table 5. Correlation of IC with the standard redox potential E0 (M2+/M).

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Table 5. Correlation of IC with the standard redox potential E0 (M2+/M).
dn02345678910
E0/V−2.87−1.63−1.18−0.971−1.19−0.44−0.28−0.250.34−0.76
IC1.6172.2582.5022.7232.7192.7862.8743.0293.1552.772
Table Table 6. Atomic parameters of Tl, Pb and Bi.

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Table 6. Atomic parameters of Tl, Pb and Bi.
CationsTl+Tl2+Tl3+Pb2+Pb3+Pb4+Bi3+Bi4+Bi5+
Iz6.1120.429.8153242.325.645.356
Iav6.1113.2618.7711.2118.1424.1816.6323.7230.18
XIC1.161.591.751.451.741.941.691.952.15
IC1.892.923.312.583.443.783.163.814.27
Table Table 7. Atomic parameters of Cu, Ag and Au.

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Table 7. Atomic parameters of Cu, Ag and Au.
CationsCu3+Ag3+Au3+
n*3.453.854.36
Z*4.3494.815.297
rc1.111.3391.336
rc−10.9010.7470.749
n*rc−13.1082.8753.263
Iav21.61021.22718.77
XIC1.8851.8672.021
IC3.9183.5923.965
Table Table 8. IC, Z* and δ for Iron-57.

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Table 8. IC, Z* and δ for Iron-57.
Iron-57FeIFeIIFeIIIFeIVFeV
δ/mm s−12.31.50.70.2−0.6
Z* = n*(Iav/R)½2.6243.2453.9974.8965.684
IC = n*(Iav/R)½rc−12.2532.7863.4314.2034.879
Table Table 9. Parameters and melting points.

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Table 9. Parameters and melting points.
CompoundCationZ*Iavrc−1n*rc−1XICICMelt.pt (°C) [43]
KFK+1.9494.340.5131.7690.7990.999880⋄
AgFAg+2.8747.580.7472.8751.2712.147435⋄

CaCl2Ca+22.8079.0050.5761.9871.0531.617772⋄
HgCl2Hg+24.4914.820.6943.0081.6723.118276⋄

CaCl2Ca+22.8079.0050.5761.9871.0531.617772⋄
BeCl2Be+22.00213.761.1252.2381.3152.252405⋄

NaBrNa+1.7775.140.6361.8380.8531.13755⋄
MgBr2Mg+22.63711.330.7332.1191.1841.933700⋄
AlBr3Al+33.30317.760.8262.3881.5122.7397.5⋄

KBrK+1.9494.340.5131.7690.7990.999730⋄
CaBr2Ca+22.8079.0050.5761.9871.0531.617765⋄

CsFCs+2.3323.890.411.7870.7810.956684⋄
BaF2Ba+23.267.6050.5052.2011.0651.6461280⋄
Table Table 11. Lattice energies U (kJmol−1) for MCl2 correlate with IC.

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Table 11. Lattice energies U (kJmol−1) for MCl2 correlate with IC.
dn02345678910
U2260250025802580255026502700279028402760
IC1.6172.2582.5022.7232.7192.7862.8743.0293.1552.772
Table Table 12. Values of log β for complexes of 1st row metal ions.

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Table 12. Values of log β for complexes of 1st row metal ions.
Mn2+Fe2+Co2+Ni2+Cu2+Zn2+
IC2.7192.7862.8743.0293.1552.772
Xic1.5071.5351.5711.6351.6871.529
Log β for [M(en)3]2−5.79.513.818.618.712.1
Log β for [M(EDTA)]2−13.814.316.318.618.716.1

This order is some time called Irving-Williams series, and is often used in discussing metalloenzyme stabilities (e.g., bioinorganic chemistry).

Table Table 13. Parameters and melting points.

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Table 13. Parameters and melting points.
CompoundCationZ*Iavrc−1n*rc−1XICICMelt.pt (°C) [43]
KBrK+1.9494.340.5131.7690.7990.999730
CaBr2Ca+22.8079.0050.5761.9871.0531.617765

CsFCs+2.3323.890.411.7870.7810.956684
BaF2Ba+23.267.6050.5052.2011.0651.6461280
Table Table 14. Parameters and lattice energies, −U.

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Table 14. Parameters and lattice energies, −U.
CompoundCationZ*Iavrc−1n*rc−1XICICU (kJmol−1) [44]
LiHLi+1.2535.390.8162.2380.8081.023905.4
NaHNa+1.7775.140.6361.8380.8531.13810.9
KHK+1.9494.340.5131.7690.7990.999714.2
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