Designing a power clock generator for adiabatic logic in low-power VLSI design requires careful consideration of energy efficiency and adiabatic principles. Adiabatic logic is a specialized approach that aims to minimize power consumption by using reversible logic operations. Here are the key steps to design a power-efficient clock generator for adiabatic logic in low-power VLSI design:

1. Choose Adiabatic Logic Family: Select the appropriate adiabatic logic family, such as Adiabatic Static CMOS Logic (ASCL) or Dual-Rail Adiabatic Logic (DRAL), based on the specific design requirements and trade-offs between complexity and energy efficiency.

2. Clock Generation Mechanism: The clock generator for adiabatic logic must provide efficient and robust clock signals. Adiabatic clock generation methods include:

a. Charge Recovery Clocking: In this technique, the energy from the discharging nodes is recovered and reused for charging other nodes. It involves capacitive coupling between clock signals and the internal nodes of the adiabatic logic gates.

b. LC Resonant Clocking: LC resonant clocking utilizes inductive and capacitive coupling to generate oscillating clock signals with low power dissipation. This approach is particularly useful for low-power clock generation.

3. Minimize Clock Power Dissipation: Design the clock generator circuitry with low power dissipation in mind. This can be achieved by using low-power components and optimizing the clocking scheme to reduce unnecessary switching and dynamic power consumption.

4. Implement Energy Recovery Circuits: Energy recovery circuits are crucial in adiabatic logic to recover and recycle energy from the discharging nodes. These circuits help reduce power consumption significantly by reusing the energy instead of dissipating it as heat.

5. Clock Distribution: Efficient clock distribution is vital to ensure accurate timing across the entire adiabatic logic circuitry. Implement clock distribution networks with minimal skew and jitter, considering the challenges specific to adiabatic logic.

6. Clock Synchronization: In a low-power VLSI design, it's essential to synchronize the clock signals carefully to minimize power consumption. Clock gating techniques and level-sensitive latches can be employed to selectively enable and disable clock signals based on the logic's activity.

7. Layout Considerations: Optimize the physical layout of the clock generator and adiabatic logic circuitry to minimize parasitic capacitance, reduce switching capacitance, and achieve better energy efficiency.

8. Simulation and Verification: Thoroughly simulate and verify the clock generator and adiabatic logic circuitry to ensure correct functionality and energy efficiency. Use advanced simulation tools to analyze the power consumption and timing characteristics.

Remember that designing power-efficient adiabatic logic circuits requires a deep understanding of adiabatic principles and low-power VLSI design techniques. Additionally, the choice of clock generation mechanism and clock distribution strategy can significantly impact the overall energy efficiency of the design. Careful attention to design details and trade-offs is crucial to achieve the desired low-power performance.