A new concept of
the molecular structure optimization method based
on quantum dynamics computations is presented. Nuclei are treated
as quantum mechanical particles, as are electrons, and the many-body
wave function of the system is optimized by the imaginary time evolution
method. The numerical demonstrations with a two-dimensional H
2
+
system and a H–C–N system exemplify
two possible advantages of our proposed method: (1) the optimized
nuclear positions can be specified with a small number of observations
(quantum measurements) and (2) the global minimum structure of nuclei
can be obtained without starting from any sophisticated initial structure
and getting stuck in the local minima. This method is considered to
be suitable for quantum computers, the development of which will realize
its application as a powerful method.
The possibility of
performing quantum-chemical calculations using
quantum computers has attracted much interest. Variational quantum
deflation (VQD) is a quantum-classical hybrid algorithm for the calculation
of excited states with noisy intermediate-scale quantum devices. Although
the validity of this method has been demonstrated, there have been
few practical applications, primarily because of the uncertain effect
of calculation conditions on the results. In the present study, calculations
of the core-excited and core-ionized states for common molecules based
on the VQD method were examined using a classical computer, focusing
on the effects of the weighting coefficients applied in the penalty
terms of the cost function. Adopting a simplified procedure for estimating
the weighting coefficients based on molecular orbital levels allowed
these core-level states to be successfully calculated. The O 1s core-ionized
state for a water molecule was calculated with various weighting coefficients,
and the resulting ansatz states were systematically examined. The
application of this technique to functional materials was demonstrated
by calculating the core-level states for titanium dioxide (TiO
2
) and nitrogen-doped TiO
2
models. The results demonstrate
that VQD calculations employing an appropriate cost function can be
applied to the analysis of functional materials in conjunction with
an experimental approach.
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