Valence Bond Theory (VBT) is an important concept of chemistry that explains the bonding between two or more atoms with the help of atomic orbitals. It explains the shape, hybridization, and magnetic behavior of molecules and coordination compounds with the help of paired electrons in the valence shell. It is very important to understand the Valence Bond Theory to solve high weightage GATE chemistry syllabus problems accurately.
Fundamentals of Valence Bond Theory for GATE
Valence Bond Theory gives us the quantum mechanical explanation of the formation of covalent bonds in a compound. This theory is based on the fact that electrons are present in the atomic orbitals of separate atoms of a compound, and the bond between two atoms is formed by the overlap of these orbitals. For aspirants who want to read GATE notes, the first step towards solving complicated problems is to understand the basic mechanics of the overlap of orbitals.
Valence Bond Theory was originally proposed by Heitler and London, which was later modified by Pauling and Slater. Unlike earlier Lewis structures, Valence Bond Theory also takes into account the wave mechanical model of an atom. This theory states that the formation of a compound is due to the approach of two or more atoms, which retain their original character to a large extent. This is an important aspect of GATE questions based on VBT.
Key Postulates Determining Bond Formation
Valence Bond Theory operates on a specific set of rules that dictate which atoms can bond and how strong that bond will be. These postulates form the backbone of structural chemistry and are frequently tested in VBT MCQ practice sets.
- Atomic Orbital Overlap: A covalent bond forms when two half-filled valence atomic orbitals from different atoms overlap. The electron density concentrates between the nuclei, lowering the system’s potential energy.
- Spin Pairing: The overlapping orbitals must contain electrons with opposite spins. This pairing neutralizes the magnetic moment in the bond region, contributing to stability.
- Directional Nature: The direction of the bond is determined by the orientation of the overlapping orbitals. This postulate is vital for understanding molecular geometry and bond angles.
- Overlap Extent: The strength of the covalent bond is directly proportional to the extent of overlap. Greater overlap results in a stronger bond and higher bond dissociation energy.
Types of Covalent Bond Overlap
The nature of the overlap defines the type of covalent bond formed. Valence Bond Theory categorizes these overlaps into two primary types: Sigma ($\sigma$) and Pi ($\pi$) bonds. Distinguishing between these is a common requirement in VBT solved questions.
Sigma ($\sigma$) Bond Formation
The strongest covalent bond is known as a Sigma bond. This bond occurs by the end-to-end overlapping of two orbitals along the axis of the bond. The bond is said to be strong due to the fact that, as a result of this overlapping, the repulsion between two nuclei is minimized.
Sigma bonds can form through various overlap combinations:
- s-s overlap: Two s-orbitals overlap (e.g., $H_2$ molecule).
- s-p overlap: An s-orbital overlaps with a p-orbital (e.g., $HCl$ molecule).
- p-p overlap: Two p-orbitals overlap axially (e.g., $Cl_2$ molecule).
According to Valence Bond Theory, free rotation is possible around a sigma bond because the electron cloud distribution is cylindrically symmetrical around the internuclear axis.
Pi ($\pi$) Bond Formation
The formation of a Pi bond is through the lateral overlap of parallel P orbitals. The lateral overlap of P orbitals occurs above and below the internuclear axis, creating two nodes of electron density. The Valence Bond Theory states that a Pi bond results in a region of zero electron density along the bond axis.
Pi bonds are weaker than sigma bonds because of the lower bond overlap in the lateral orientation. Pi bonds also cannot exist in isolation; they can only form in pairs with sigma bonds in double or triple bond systems. The existence of Pi bonds limits rotation around the bond axis, resulting in geometric isomerism.
Hybridisation Rules and Geometry Prediction
While simple overlap explains diatomic molecules, Valence Bond Theory utilizes the concept of hybridization to explain the shapes of polyatomic molecules like methane ($CH_4$). Hybridization involves the intermixing of atomic orbitals of slightly different energies to form new, equivalent hybrid orbitals.
Understanding hybridisation rules is non-negotiable for GATE aspirants.
- sp Hybridization: Involves one s and one p orbital. It results in a linear geometry with a bond angle of $180^\circ$ (e.g., $BeCl_2$).
- $sp^2$ Hybridization: Involves one s and two p orbitals. This creates a trigonal planar geometry with $120^\circ$ angles (e.g., $BF_3$).
- $sp^3$ Hybridization: Involves one s and three p orbitals. This leads to a tetrahedral geometry with $109.5^\circ$ angles (e.g., $CH_4$).
- $sp^3d$ and $sp^3d^2$: These involve d-orbitals and are crucial for hypervalent compounds like $PCl_5$ (trigonal bipyramidal) and $SF_6$ (octahedral).
Applying Valence Bond Theory to hybridization allows students to predict bond angles and molecular shapes accurately, which is often the first step in solving structural VBT GATE problems.
Valence Bond Theory in Coordination Compounds
The application of Valence Bond Theory in the context of coordination compounds is perhaps the most fruitful topic for competitive examinations. Pauling has extended the Valence Bond Theory to account for the bonding in transition metal complexes, where the ligands’ ability to donate electron pairs to the empty hybrid orbitals of the central metal ion is emphasized.
In the context of coordination compounds, the central metal ion has a number of empty orbitals available for bonding, equal to the coordination number of the complex. These orbitals then hybridize to give a group of equivalent orbitals of definite geometry (tetrahedral, square planar, or octahedral). Ligands, being Lewis bases, then donate their lone pairs of electrons to the empty hybrid orbitals of the central metal ion to give coordinate covalent bonds. The type of hybridization occurs depending on the type of ligand (strong field or weak field), although the Valence Bond Theory does not specifically define the spectrochemical series.
Inner vs Outer Orbital Complexes
A critical distinction in Valence Bond Theory for complexes is the involvement of inner $(n-1)d$ or outer $nd$ orbitals.
- Inner Orbital Complexes: formed when the metal ion uses inner $(n-1)d$ orbitals for hybridization (e.g., $d^2sp^3$). These are often associated with strong field ligands that force electron pairing, resulting in low spin complexes.
- Outer Orbital Complexes: Formed when the metal ion uses outer $nd$ orbitals (e.g., $sp^3d^2$). These typically involve weak field ligands where electrons do not pair up against Hund’s rule, resulting in high spin complexes.
Distinguishing between these types is a standard VBT MCQ practice task. For example, $[Fe(CN)_6]^{3-}$ is an inner orbital complex, while $[Fe(H_2O)_6]^{3+}$ is an outer orbital complex.
Magnetic Properties Analysis using VBT
Valence Bond Theory provides a direct method to calculate the magnetic moment of a compound based on the number of unpaired electrons. This property is frequently tested in conjunction with hybridization questions in GATE notes.
If a complex has unpaired electrons after the ligands have approached and bonding orbitals have formed, it is paramagnetic. If all electrons are paired, it is diamagnetic. The “spin-only” magnetic moment ($\mu$) is calculated using the formula:
$$\mu = \sqrt{n(n+2)} \text{ BM}$$
Where $n$ is the number of unpaired electrons and BM is Bohr Magneton.
For instance, in the complex $[Ni(Cl)_4]^{2-}$, Valence Bond Theory shows that chloride is a weak ligand and does not pair the electrons in the $3d$ orbital. This leaves two unpaired electrons, making the complex paramagnetic with a tetrahedral geometry ($sp^3$). Conversely, in $[Ni(CN)_4]^{2-}$, cyanide causes pairing, resulting in zero unpaired electrons (diamagnetic) and square planar geometry ($dsp^2$).
Short Tricks to Solve VBT GATE Questions
Time management is crucial in GATE. Using standard derivations for every Valence Bond Theory question can be slow. These short tricks help determine geometry and magnetic nature rapidly for coordination compounds.
- Identify the Oxidation State: Quickly calculate the charge on the metal ion.
- Check the Ligand Strength:
- Strong Field Ligands (SFL): $CO, CN^-, NO_2^-, en, NH_3$. These generally force pairing of electrons in the d-orbitals.
- Weak Field Ligands (WFL): $H_2O, F^-, Cl^-, Br^-, I^-$. These generally do not cause pairing.
- The Coordination Number 4 Rule:
- If $d^8$ configuration + SFL $\rightarrow$ Square Planar ($dsp^2$), Diamagnetic.
- If $d^8$ configuration + WFL $\rightarrow$ Tetrahedral ($sp^3$), Paramagnetic.
- The Coordination Number 6 Rule:
- If $d^1, d^2, d^3$ $\rightarrow$ Always $d^2sp^3$ (Inner), Paramagnetic.
- If $d^8, d^9, d^{10}$ $\rightarrow$ Always $sp^3d^2$ (Outer), Paramagnetic.
- If $d^4$ to $d^7$ + SFL $\rightarrow$ Pair electrons $\rightarrow$ $d^2sp^3$ (Inner), Low Spin.
- If $d^4$ to $d^7$ + WFL $\rightarrow$ No pairing $\rightarrow$ $sp^3d^2$ (Outer), High Spin.
Applying these heuristics allows you to solve VBT solved questions in seconds without drawing full orbital diagrams.
Solved VBT MCQ Practice for High Scores
Practicing specific archetypes of questions is essential for mastering Valence Bond Theory. Below are detailed solutions to typical high-level questions found in VBT MCQ practice modules.
Question 1: According to Valence Bond Theory, what is the hybridization and geometry of $[Co(NH_3)_6]^{3+}$?
- Analysis: Cobalt is in the $+3$ oxidation state ($3d^6$ configuration). $NH_3$ acts as a strong field ligand in the presence of $Co^{3+}$.
- VBT Logic: The strong ligand forces the six 3d electrons to pair up in three orbitals, leaving two $3d$ orbitals empty. The hybridization uses these two $3d$, one $4s$, and three $4p$ orbitals ($d^2sp^3$).
- Result: Inner orbital octahedral complex, diamagnetic.
Question 2: Which orbital overlap leads to the strongest bond according to bond overlap principles?
- Options: $2s-2s$, $2s-2p$, $2p-2p$ (axial), $2p-2p$ (lateral).
- Analysis: Axial overlap is always stronger than lateral. Among axial overlaps, directional orbitals ($p$) overlap more effectively than non-directional ($s$).
- Result: The $2p-2p$ axial overlap forms the strongest sigma bond due to maximum extent of overlap.
Question 3: Why does $[Ni(CO)_4]$ have a tetrahedral geometry?
- Analysis: Nickel is in $0$ oxidation state ($3d^8 4s^2$). $CO$ is a very strong ligand.
- VBT Logic: $CO$ pushes the two $4s$ electrons into the $3d$ orbitals, filling them completely ($3d^{10}$). The empty $4s$ and three $4p$ orbitals hybridize.
- Result: $sp^3$ hybridization, tetrahedral, diamagnetic.
Critical Limitations of Valence Bond Theory
Despite its utility, Valence Bond Theory has significant shortcomings that necessitate the study of advanced theories like molecular orbital theory. Understanding these VBT limitations is crucial for theoretical questions in GATE.
- Magnetic Properties of Oxygen: Valence Bond Theory predicts that the oxygen molecule ($O_2$) is diamagnetic because all electrons are paired in the Lewis structure. However, experimental data shows $O_2$ is paramagnetic. VBT fails to explain this.
- Color of Complexes: VBT cannot explain the electronic spectra (color) of coordination compounds. It does not provide a mechanism for electron transitions that absorb visible light.
- Relative Stabilities: While it distinguishes between inner and outer orbital complexes, VBT does not quantitatively interpret the thermodynamic or kinetic stability of complexes.
- Distortion in Geometry: It assumes regular geometries and fails to explain distortions like the Jahn-Teller effect seen in certain copper(II) complexes.
VBT vs Molecular Orbital Theory
To address the flaws in Valence Bond Theory, chemists use Molecular Orbital (MO) Theory.
- Localization: VBT treats electrons as localized between atoms. MO theory treats electrons as delocalized over the entire molecule.
- Energy Levels: VBT focuses on individual atomic orbitals. MO theory considers the splitting of orbitals into bonding and antibonding molecular orbitals.
- Accuracy: MO theory successfully predicts the paramagnetism of $O_2$ and is superior for analyzing electron-deficient compounds and metallic bonding.
While Molecular Orbital theory offers higher accuracy, Valence Bond Theory remains the most intuitive tool for visualizing molecular shape and basic bonding in organic and inorganic chemistry for GATE.
