The dynamic rearrangement of a molecule at finite temperature is not captured by a single static input geometry to a quantum chemical calculation. Multilevel workflows have established themselves as standard procedures to capture the dependence of the molecule’s configuration on computed properties. Each step within this workflow uses an electronic structure theory method that features the optimal computational time to accuracy ratio. For exploratory steps the computational expense of a method needs to be minimal as several thousand energy and nuclear gradient evaluations are needed. Semiempirical tight binding methods, such as GFN2-xTB are often used for such purposes. However, these methods usually lack the accuracy to rank conformers relative to each other within chemical accuracy (2 kcal/mol). Therefore, so-called “low-cost” DFT methods are commonly used for geometry optimizations and conformer ranking. The combination of (semi)empirical correction models with small basis sets leads to good accuracy at moderate computational cost. However, even these highly efficient methods reach the limits of feasibility for very large systems (> 200 atoms). This work proposes solutions to partially alleviate those restrictions and allow routine calculations of these system sizes outside of large high-performance computing facilities. The key to unlock those calculations is to combine tailored algorithmic developments with consumer-grade GPUs. A GPU-enabled linear algebra library is developed to accelerate further development and make the entry to GPU-accelerated software development easier. To demonstrate the ease of implementation, the addition of Mulliken-approximated exchange to GFN2-xTB will be shown. In most semiempirical methods, the general eigenvalue solver algorithm becomes the computational bottleneck, dominating the walltime with increasing system size. A density matrix purification algorithm is tailored to give up to six-fold acceleration of GFN2-xTB calculations using a mixed-precision approach. Lastly, 3c-methods are added to the GPU-accelerated TeraChem software package. In combination with the “mixed-precision” scheme for computing the electron repulsion integrals, this addition decreases the runtime of DFT calculations by up to an order of magnitude on mid-level consumer hardware. The overall goal of these projects is to make GPU-accelerated calculations in quantum chemistry more available. This achieve by exposing algorithmic developments that are performant on reasonably priced hardware and making GPU computing more accessible to non-experts.
The search for new computational tasks of quantum chemistry that can be performed on current quantum computers is important for the development of quantum computing and quantum chemistry. Although calculations of chemical reactions have a wide range of applications in quantum chemical calculations, a quantum algorithm for obtaining activation energy
Ea, which determines the rate of chemical reactions, has not been performed. In this study, we propose a quantum algorithm for the chemical reaction path optimization to obtain
Ea. In our algorithm, quantum circuits can be used not only for the energy evaluation by the variational quantum eigensolver (VQE) but also for chemical reaction path generation. The chemical reaction path is obtained by encoding the initial reaction path to the circuit, operating parameterized gates, and extracting the path information by measurement. The nudged elastic band method was used for optimizing a reaction path, and the ground-state calculation for each state on the path was performed by the VQE or the exact diagonalization (ED). The proposed algorithm was applied to
H2+H→H2+H reaction, and we confirmed that
Ea was obtained accurately in the case of both the VQE and the ED. We also obtained numerical results that the entanglement between the images accelerates the path optimization. From these results, we show the feasibility of performing fast and accurate chemical reaction calculations by using quantum algorithms.
Quantum computers are expected to perform full-configuration interaction calculations with less computational resources compared to classical ones, thanks to the use of quantum phase estimation (QPE) algorithms. However, only a limited number of QPE-based quantum chemical calculations have been reported even for numerical simulations on a classical computer, and the practical workflow for the QPE computation has not yet been established. In this paper, we report the QPE simulations of the electronic ground and the π-π* excited singlet state of benzene and its chloro- and nitro-derivatives as the representative industrially important systems, with the aid of GPGPU acceleration of quantum circuit simulations. We adopted the pseudo-natural orbitals obtained from the MP2 calculation as the basis for the wave function expansion, the CISD calculation within the active space to find the main electronic configurations to be included in the input wave function of the excited state, and the technique to reduce the truncation error of the calculated total energies. The proposed computational workflow is easily applicable to other molecules and can be a standard approach for performing QPE-based quantum chemical calculations of practical molecules.