How to Calculate the Excited State

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Due to the bondage of the electric field of the nucleus, electrons in atoms, ions, or molecules generally have many different energy levels. When at the lowest possible energy level, the electrons in these molecules are in the ground state, and when at a higher energy level, these electrons are transferred to the excited state. As the electron grows from the ground state to the excited state, the distribution of the electron cloud will undergo some changes, the equilibrium distance between the nuclei of the molecule will increase slightly, and the chemical reaction activity will grow as well. This feature explains why scientists attach great importance to the calculation of excited states. Then, how to calculate the excited state? Three common calculation methods are introduced below, namely ZINDO, CIS and TDDFT.



What does ZINDO represent? In fact, ZINDO is an abbreviation for “Zerner's intermediate neglect of differential overlap.” In the 1970s, Michael Zerner and his colleagues further proposed ZINDO based on the original INDO method, making it a semi-empirical quantum chemistry method of computational chemistry commonly used by scientists. ZINDO is divided into two versions, which serve to calculate the ground state and the excited state respectively. The version used for excited state calculation is called ZINDO/S or INDO/S, which calculates the excited state through the INDO/1 molecular orbitals, thereby computing the electronic spectra. With ZINDO, researchers can complete basic tasks such as single-point energy, single-point forces, electronic excitations, geometry optimization, and transition-state optimization.



CIS, also known as a single excitation configuration interaction, is almost the most commonly used method for obtaining excited state energies, and it is also one of the easiest calculation methods to implement. At first, scientists usually adopted Hartree-Fock theory to calculate excited states. However, due to average potential used for the electron-electron interactions, the best energies obtained at the Hartree-Fock level are still inaccurate, resulting in failure of the excited state calculation. By adding a description of the correlated motions of electrons, CIS corrects the first and higher order of the Hartree-Fock wavefunction, which well overcomes the defects of Hartree-Fock method, allowing researchers to easily compute the energies of many excited states.



Time-dependent density-functional theory, also abbreviated as TDDFT, is a quantum mechanical theory developed from density-functional theory (DFT) and is widely used in different fields, such as physics, (bio)chemistry, and materials science. TDDFT studies the characteristics and dynamics of many-body systems in the presence of time-dependent potentials, such as electric and magnetic fields, in a formally exact and computationally efficient way. Since the linear response function, which refers to the changes of the electron density when the external potential varies, has a pole at the precise excitation energy of a system, TDDFT has now become a popular choice for scientists to calculate the energy of the excited state of an isolated system.


As a frontier in quantum chemistry, the calculation of excited states plays an important role in accelerating the discovery and research of new things, such as drugs, experimental materials and industrial catalysts, and has been widely loved and pursued by scientists and researchers in various fields. How to calculate the excited state energies more efficiently and accurately is obviously the first issue that they have to consider, and these three main methods meet their needs exactly. With these methods, combined with advanced technologies and rich knowledge of these researchers, the calculation of excited states will become easier and easier in the future.

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