Project: s41467-025-58871-7 | Function: cpihmc::elec_num::mc_evolve (cpp)

system: You are an expert C++ programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow C++ best practices and maintain consistent code style.
Return **only** the complete C++ function code.

user: Complete this C++ function:

**DESCRIPTION:** Proton-coupled electron transfer (PCET) is the key step for energy conversion in electrocatalysis. Atomic-scale simulation acts as an indispensable tool to provide a microscopic understanding of PCET. However, consideration of the quantum nature of transferring protons under an exact grand canonical constant potential condition is a great challenge for theoretical electrocatalysis. Here, we develop a unified computational framework to explicitly treat nuclear quantum effects (NQEs) by a sufficient grand canonical sampling, further assisted by a machine learning force field adapted for electrochemical conditions. Our work demonstrates a non-negligible impact of NQEs on PCET simulations for hydrogen evolution reaction at room temperature, and provides a physical picture that wave-like quantum characteristic of the transferring protons facilitates the particles to tunnel through classical barriers in PCET paths, leading to a remarkable activation energy reduction compared to classical simulations. Moreover, the physical insight of NQEs may reshape our fundamental understanding of other types of PCET reactions in broader scenarios of energy conversion processes.

**KEY TERMS:** {
  "PCET": "However, atomic simulations offer a powerful alternative, allowing us to examine the kinetics and thermodynamics of elementary PCET steps",
  "HER": "Electrocatalytic HER is a notable green-energy technology producing clean fuels ^31 , it consists of multiple possible PCET steps, which is an ideal modeling system in electrochemistry",
  "Schiffer": "Hammes-Schiffer group pioneered the investigation on the quantum effect of homogeneous and heterogeneous PCET ^24"
}

**CONTEXT CODE:** #include "elec_num.h"
using namespace cpihmc;
using namespace std;

const bool_t cpihmc::elec_num::mc_evolve()
{
    // Grand canonical electron-number Monte Carlo moves are not enabled in this build.
    // Safely return false (no move attempted).
    return false;
}

Complete the function implementation replacing "throw std::runtime_error("Not implemented");".