d-block contraction
The d-block contraction, also known as the scandide contraction, is a periodic trend in chemistry where the atomic radii of the transition metals in the d-block decrease only slightly across each period, in contrast to the more pronounced decreases observed in the s- and p-blocks.[1] This phenomenon arises primarily in the first row of transition metals (scandium through zinc) and subsequent rows, resulting in relatively constant or minimally varying atomic sizes despite the addition of electrons and protons.[1] The underlying cause of the d-block contraction is the inefficient shielding provided by electrons in the d-orbitals. As protons are added to the nucleus moving across a period, electrons fill the (n-1)d subshell, but these d-electrons are less effective at screening the outer s and p electrons from the increasing nuclear charge compared to s or p electrons.[1] This leads to a higher effective nuclear charge (Zeff) experienced by the valence electrons, which draws them closer to the nucleus and contracts the overall atomic radius more than anticipated from simple electron addition alone.[2] The effect is most notable in the 3d series, where the atomic radius drops from approximately 160 pm for scandium to 125 pm for copper, a change smaller than the ~50 pm decrease seen in the preceding s-block.[1] This contraction has significant implications for the chemical properties of transition metals and the elements immediately following them in the periodic table. For instance, the poor shielding extends its influence to the p-block elements in the same period (such as gallium through bromine in period 4), causing their atomic radii to be smaller than expected based on group trends, which alters their reactivity and bonding behavior.[2] The d-block contraction is analogous to the more pronounced lanthanide contraction in the f-block, where f-electrons provide even poorer shielding, but it is less severe overall due to the relatively better penetration of d-orbitals.[1] These shielding effects collectively contribute to irregularities in periodic properties like ionization energies and electronegativities across the transition series.[2]Periodic Trends in Atomic Properties
Atomic and Ionic Radii Across Periods
In the periodic table, atomic radii generally decrease from left to right across a period due to the increasing nuclear charge, which draws the electrons closer to the nucleus while electrons are added to the same principal quantum shell. This trend is evident in the s- and p-blocks, such as in period 2, where the atomic radius of lithium is approximately 152 pm, progressively decreasing to about 72 pm for fluorine; the van der Waals radius for neon is approximately 154 pm, which is not directly comparable to the covalent radii used for the other elements. Covalent radii, defined as half the distance between the nuclei of two identical atoms joined by a covalent bond, provide a consistent measure for this contraction in non-metallic elements. Ionic radii for cations follow a similar pattern of contraction across a period, as the increasing nuclear charge pulls the remaining electrons closer after ionization. These radii are typically determined using the Shannon-Prewitt system, which assigns effective ionic radii based on observed interatomic distances in crystal structures, referenced to the oxide ion radius of 140 pm and accounting for coordination number and oxidation state. For example, in period 3, the ionic radius of Na⁺ (102 pm, coordination number 6) is larger than that of Mg²⁺ (72 pm), continuing to decrease toward the p-block end. Without the influence of transition metals, the atomic and ionic radii in period 4 would be expected to exhibit a smooth decrease from potassium to krypton, analogous to the consistent contraction observed in shorter periods like 2 and 3. Early formulations of the periodic table by Dmitri Mendeleev highlighted irregularities in the properties of fourth-period elements, including deviations from anticipated size progressions, prompting him to adjust element placements and predict undiscovered species to maintain periodicity.Shielding Effects in Multi-electron Atoms
In multi-electron atoms, electrons in inner shells shield outer electrons from the full attractive force of the nucleus, resulting in an effective nuclear charge (Z_\text{eff}) that is less than the actual nuclear charge (Z). This shielding effect arises from the electrostatic repulsion between electrons, which partially cancels the nuclear attraction felt by valence electrons. The effective nuclear charge is quantitatively expressed as Z_\text{eff} = Z - \sigma, where \sigma is the shielding constant representing the total screening contribution from all other electrons. Slater's rules provide a semi-empirical method to estimate the shielding constant \sigma by grouping electrons into shells and assigning shielding contributions based on their positions relative to the electron of interest. For an electron in an ns or np orbital, electrons in the same (ns,np) group to the right contribute 0 (no shielding), while those to the left contribute 0.35 each (except 0.30 for the paired electron in the 1s group); electrons in the (n-1) shell contribute 0.85 each; and all electrons in inner shells (lower than n-1) contribute 1.00 each. For an electron in an nd or nf orbital, electrons in the same (nd) or (nf) group contribute 0.35 each; electrons in the (n-1) and all inner shells contribute 1.00 each. These rules, developed by John C. Slater, allow for approximate calculations of Z_\text{eff} and highlight how shielding varies with orbital type and principal quantum number. The efficiency of shielding is closely tied to orbital penetration, which describes how closely an electron's probability density approaches the nucleus. Electrons in s orbitals penetrate closest to the nucleus due to their spherical symmetry and non-zero probability at r=0, followed by p orbitals with lobes allowing some near-nuclear density; in contrast, d and f orbitals have nodal structures that keep their electron density farther from the nucleus, resulting in poorer penetration and less effective shielding of outer electrons. This penetration difference means that inner s and p electrons provide stronger shielding for valence electrons compared to inner d or f electrons, influencing the stability and energy of outer orbitals. In main group elements, shielding by successively added inner shells maintains larger atomic radii as one descends a group, despite increasing nuclear charge. For instance, in group 1 (alkali metals), the atomic radius increases from lithium (152 pm) to cesium (265 pm) because the additional core electrons in heavier elements effectively shield the valence ns electron, reducing Z_\text{eff} and allowing the outer electron to occupy a larger orbital volume. Similarly, in group 17 (halogens), radii grow from fluorine (72 pm) to iodine (140 pm) due to this shielding, which counteracts the rising Z and preserves the trend of expanding electron clouds down the group.[3][4]Definition and Mechanism
Poor Shielding by d-Electrons
The d-block contraction, also known as the scandide contraction, describes the smaller-than-expected decrease in atomic and ionic radii across the d-block transition metals from scandium (Sc) to zinc (Zn).[5] This phenomenon arises because the electrons added to the 3d subshell across the transition series fail to adequately screen the increasing nuclear charge from the outer 4s valence electrons, resulting in a sharper rise in effective nuclear charge than anticipated based on trends in the s- and p-blocks. The poor shielding efficiency of d-electrons stems from the geometric properties of d-orbitals, which are more diffuse and radially extended compared to s- or p-orbitals in the same principal quantum shell. These orbitals exhibit a probability distribution that places much of the electron density farther from the nucleus, reducing their ability to counterbalance the attractive pull of the nucleus on valence electrons. Empirical models like Slater's rules approximate this inefficiency, assigning a shielding constant of about 0.85 to each (n-1)d electron for ns,np valence electrons, though quantum calculations reveal even lower effectiveness due to the orbitals' spatial characteristics.[6] Quantum mechanically, the higher angular momentum quantum number (l = 2) for d-orbitals introduces two angular nodes, which constrain electron density away from the nuclear region and limit overlap with the nucleus, thereby minimizing shielding compared to lower-l orbitals like s (l = 0) or p (l = 1). This nodal structure contributes to the d-electrons' reduced penetration toward the nucleus, exacerbating the contraction effect. The term "scandide contraction" was coined analogously to the lanthanide contraction to highlight this d-series-specific trend, with the underlying atomic radius anomalies first observed in spectroscopic studies during the 1920s and 1930s as electron configurations were elucidated.[7][8]Increase in Effective Nuclear Charge
The d-block contraction arises primarily from the poor shielding provided by electrons in the 3d subshell, which results in a significantly higher effective nuclear charge (Zeff) experienced by the valence 4s electrons compared to what would be expected if shielding were more effective. Across the 3d transition series from scandium (Sc) to zinc (Zn), 10 protons are added to the nucleus while 10 electrons fill the 3d subshell; however, these 3d electrons fail to screen the increasing nuclear charge adequately for the outer electrons, leading to a steeper rise in Zeff, approximately +1 unit per added proton with minimal offset from shielding.[9] This phenomenon can be quantified using the relation Zeff = Z - σ, where Z is the atomic number and σ is the total screening constant; the contribution from the 3d electrons (σd) to screening the 4s valence electrons is notably low, approximately 3.5–4 for the full 3d10 subshell, reflecting their diffuse radial distribution and limited overlap with the more penetrating 4s orbitals.[9] As a result, after zinc, the subsequent elements in period 4 (e.g., gallium onward) experience an enhanced Zeff increase of about 0.6–0.7 units per added proton in the initial p-block steps, beyond the core and valence contributions, due to the absence of further d-electron shielding.[9] In terms of trends, the observed Zeff for period 4 valence electrons shows a gradual rise across the 3d series, contrasting with the expected near-constant Zeff if 3d electrons shielded perfectly (as in s- or p-block filling); this discrepancy manifests as a "step-like" elevation in Zeff post-zinc, compressing atomic sizes more than anticipated from earlier periodic trends.[10] Self-consistent field calculations confirm this pattern, with Zeff for 4s/4p orbitals increasing more sharply after the d-block completion.[11] Experimental support comes from photoelectron spectroscopy, where the binding energies of 4p-derived lone pairs in gallium compounds are tighter by nearly 1 eV or more compared to analogous aluminum compounds, directly evidencing the elevated Zeff due to inadequate 3d shielding.[11] This spectroscopic observation aligns with the theoretical predictions of enhanced nuclear attraction in post-transition period 4 elements.[11]Affected Elements and Data
Elements in Period 4 Post-Transition
The p-block elements in period 4 that follow the d-block and are most directly impacted by d-block contraction are those from groups 13 through 18: gallium (Ga), germanium (Ge), arsenic (As), selenium (Se), bromine (Br), and krypton (Kr). These elements occupy positions immediately following the completion of the 3d transition metal series with zinc (Zn) at the end of group 12.[3] The valence electrons of these elements reside in the 4s and 4p orbitals and are subject to incomplete shielding by the preceding ten electrons in the filled 3d subshell. This shielding failure causes the valence electrons to experience the full extent of the increased nuclear charge across the d-block, without adequate compensation.[11] Consequently, these elements exhibit general properties that deviate from standard periodic expectations, often resembling those of their period 3 analogs in terms of metallic character, yet displaying distinct anomalies; for instance, gallium demonstrates an unusually low melting point of 29.8 °C due to its electronic configuration influenced by this contraction.[12][2] Within the periodic table, the d-block contraction effectively compresses the initiation of the p-block in period 4, which alters the anticipated smooth progression of atomic sizes and related trends from left to right across the period.[3]Comparative Data: Radii and Ionization Energies
The d-block contraction manifests in empirical measurements of atomic and ionic radii, where the sizes of period 4 p-block elements are anomalously small compared to extrapolations from period 3 trends, reflecting the increased effective nuclear charge due to poor d-electron shielding. For Ga and Ge, sums of the first three ionization energies (IEs) are higher or similar to their period 3 counterparts, contrary to the typical decrease down a group, indicating stronger binding of valence electrons due to the contraction. For later elements like As, Se, and Br, the sums are lower than their analogs but show a less pronounced decrease than anticipated without the contraction. These data, drawn from standard tabulations, highlight the contraction's magnitude without the expected size increase down the group. Atomic radii data underscore the contraction, particularly for gallium and germanium. The observed metallic radius of gallium is 135 pm, compared to an expected value of approximately 140 pm extrapolated from the period 3 trend in group 13 (aluminum at 143 pm, but accounting for typical group descent). For germanium, the observed value is 122 pm versus an expected ~130 pm from silicon's 117 pm. These discrepancies arise across the early p-block in period 4, as shown in the following table of representative metallic or covalent radii (in pm) for consistency in comparison:| Element | Group | Period 3 Analog Radius (pm) | Period 4 Observed Radius (pm) | Approximate Expected Period 4 (pm) |
|---|---|---|---|---|
| Al/Ga | 13 | 143 (Al) | 135 (Ga) | ~140 |
| Si/Ge | 14 | 117 (Si) | 122 (Ge) | ~130 |
| P/As | 15 | 110 (P) | 121 (As) | ~125 |
| S/Se | 16 | 104 (S) | 116 (Se) | ~120 |
| Cl/Br | 17 | 99 (Cl) | 114 (Br) | ~115 |
| Element | First IE | Second IE | Third IE | Sum (kJ/mol) |
|---|---|---|---|---|
| Al | 578 | 1817 | 2745 | 5140 |
| Si | 787 | 1577 | 3232 | 5596 |
| P | 1012 | 1903 | 2912 | 5827 |
| S | 1000 | 2251 | 3361 | 6612 |
| Cl | 1251 | 2297 | 3822 | 7370 |
| Ga | 579 | 1980 | 2963 | 5522 |
| Ge | 762 | 1537 | 3302 | 5601 |
| As | 947 | 1798 | 2736 | 5481 |
| Se | 941 | 2045 | 2974 | 5960 |
| Br | 1140 | 2100 | 3500 | 6740 |