Coupled cluster theory in the standard formulation is unable to correctly describe conical intersections among states of the same symmetry. This limitation has restricted the practical application of an otherwise highly accurate electronic structure model, particularly in nonadiabatic dynamics. Recently, the intersection problem among the excited states was fully characterized and resolved. However, intersections with the ground state remain an open challenge, and addressing this problem is our objective here. We present a generalized coupled cluster framework that correctly accounts for the geometric phase effect and avoids bifurcations of the solutions to the ground state equations. Several applications are presented that demonstrate the correct description of ground state conical intersections. We also propose how the framework can be used for other electronic-structure methods.
Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray…
We present a discussion of recent progress in excited-state-specific quantum chemistry and quantum Monte Carlo alongside a demonstration of how a combination of methods from these two fields can offer reliably accurate excited state predictions across singly excited, doubly excited, and charge transfer states. Both of these fields have seen important advances supporting excited state simulation in recent years, including the introduction of more effective excited-state-specific optimization methods, improved handling of complicated wave function forms, and ways of explicitly balancing the qual…
Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model …
Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study
Ongoing developments in ultrafast X-ray sources offer powerful new means of probing the com- plex non-adiabatically coupled structural and electronic dynamics of photoexcited molecules. These non-Born-Oppenheimer effects are governed by general electronic degeneracies termed conical in- tersections which play a key role, analogous to that of a transition state, in the electronic-nuclear dynamics of excited molecules. Using high level ab initio quantum dynamics simulations, we studied time-resolved X-ray absorption and photoelectron spectroscopy (TRXAS and TRXPS, respectively) of the prototypic…
We theoretically investigate internal conversion processes of a photoexcited molecule in a condensed phase. The molecular system is described by two-dimensional adiabatic ground and excited potential energy surfaces (PESs) that are coupled to heat baths. We study the role of conical intersection (CI) by computing the time evolution of wavepackets for the PESs both with and without the CI. For this purpose, we employ the multi-state quantum Fokker-Planck equation (MSQFPE) for a two-dimensional Wigner space. Numerically integrating the MSQFPE, we investigated the time evolution of wavepackets fo…
We present a study of the two dimensional circular quantum dot model Hamiltonian using a range of quantum chemical ab initio methods. Ground and excited state energies are computed on different levels of perturbation theories including the coupled cluster method. We outline a scheme to compute the required Coulomb integrals in real space and utilize a semi-analytic solution to the integral over the Coulomb kernel in the vicinity of the singularity. Furthermore, we show that the remaining basis set incompleteness error for two dimensional quantum dots scales with the inverse number of virtual o…
A balanced description of ground and excited states is essential for the description of many chemical processes. However, few methods can handle cases where static correlation is present, and often these scale very unfavourably with system size. Recently, multiple Hartree--Fock (HF) solutions have been proposed as a basis for non-orthogonal configuration interaction (NOCI) to provide multireference ground and excited state energies, although applications across multiple geometries have been limited by the coalescence of HF solutions. Holomorphic HF (h-HF) theory allows solutions to be analytic…
Processes related to electronically excited states are central in many areas of science, however accurately determining excited-state energies remains a major challenge in theoretical chemistry. Recently, higher energy stationary states of non-linear methods have themselves been proposed as approximations to excited states, although the general understanding of the nature of these solutions remains surprisingly limited. In this Letter, we present an entirely novel approach for exploring and obtaining excited stationary states by exploiting the properties of non-Hermitian Hamiltonians. Our key …
We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system as the sum of the ($N-2$)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition …
We introduce a multimodel approach to solve coupled cluster equations, employing a quasi Newton algorithm for the ground state and an Olsen algorithm for the excited states. In these algorithms, both of which can be viewed as Newton algorithms, the Jacobian matrix of a lower level coupled cluster model is used in Newton equations associated with the target model. Improvements in convergence then implies savings for sufficiently large molecular systems, since the computational cost of macroiterations scales more steeply with system size than the cost of microiterations. The multimodel approach …
The direct observation of non-adiabatic dynamics at conical intersections is a long-standing goal of molecular physics. Novel time-resolved spectroscopies have been proposed which are sensitive to electronic coherences induced by the passage of an excited state wavepacket through a region of conical intersection. Here we demonstrate that inclusion of the geometric phase effect, and its manifestations, is essential for the correct description of the transient electronic coherences that may or may not develop. For electronic states of different symmetry, electronic coherences are suppressed by t…
Relativistic configuration interaction calculation on the ground and excited states of iridium monoxide
本文采用完全相对论多参考组态相互作用方法计算了IrO基态和低激发态的自旋轨道分量。对IrO的四个自旋轨道分量1/2，3/2，5/2和7/2的最低态进行了详细的计算，以明确IrO的基态.计算结果表明，基态具有1/2自旋轨道分量，在$Λ-S$表示下，基态与$^4Σ^-$和$^2Π$态高度混合. 5/2和7/2自旋轨道分量的两个低能级与基态几乎简并，分别位于$^{-1}$上方234和260 cm处。5/2自旋轨道分量的平衡键长为1.712 π/，谐振频率为903 cm $^{-1}$，与实验测量的1.724 π/和909 cm $^{-1}$接近，表明5/2态应该是实验研究中对光谱贡献最低的态.此外，电子状态，引起所观察到的过渡带被分配在5/2和7/2自旋轨道组件获得的激发能和振子强度。
The magnetic properties and electronic structure of the ground and excited states of two recently characterized endohedral metallo-fullerenes, [Gd$_2$@C$_{78}$]$^{-}$ (1) and [Gd$_2$@C$_{80}$]$^{-}$ (2), have been studied by theoretical methods. The systems can be considered as [Gd$_2$]$^{5+}$ dimers encapsulated in a fullerene cage with the fifteen unpaired electrons ferromagnetically coupled into an $S=15/2$ high-spin configuration in the ground state. The microscopic mechanisms governing the Gd--Gd interactions leading to the ferromagnetic ground state are examined by a combination of densi…
In this work, we revisited the idea of using the coupled-cluster ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-aufbau determinant optimized via the maximum overlap method the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of $Δ$CCSD and $Δ$CCSD(T) far surpasse…
A derivation of non-adiabatic coupling vectors for the density functional based tight binding method (DFTB) between ground and excited states is presented. The analytical result is valid both for semi-local and long-range corrected DFTB and includes all required Pulay terms. Electron-translation factors lead to a conceptual simplification of the Slater-Koster scheme for precomputed integrals. Compared to scalar couplings obtained from numerical derivatives, the present approach is computationally more efficient and can be applied to systems with hundreds of atoms. The accuracy of DFTB derivati…
The recently proposed many-body expanded full configuration interaction (MBE-FCI) method is extended to excited states and static first-order properties different from total, ground state correlation energies. Results are presented for excitation energies and (transition) dipole moments of two prototypical, heteronuclear diatomics---LiH and MgO---in augmented correlation consistent basis sets of up to quadruple-$ζ$ quality. Given that MBE-FCI properties are evaluated without recourse to a sampled wave function and the storage of corresponding reduced density matrices, the memory overhead assoc…
Partial atomic charges are a useful and intuitive concept for understanding molecular properties and chemical reaction mechanisms, showing how changes in molecular geometry can affect the flow of electronic charge within a molecule. However, the use of partial atomic charges remains relatively uncommon in the characterization of excited-state electronic structure. Here we show how well-established partial atomic charge methods perform for interatomic, intermolecular and inter-bond electron transfer in electronically excited states. Our results demonstrate the utility of real-space partial atom…
The rotational sublevels of the key (000) and (010) vibrational states of the H2S molecule were modeled with an accuracy close to experimental uncertainty using the generating function and Euler approaches. The predictive ability of the Hamiltonian parameters derived is tested against variational calculations. Comparison of transitions wavenumbers obtained from the presently calculated set of the H2S (000) and (010) energy levels with simulated (000)-(000), (010)-(010) transitions included in HITRAN 2016 database revealed a large discrepancy up to 44 cm-1. Large sets of accurate rotational sub…
We predict anti-alignment dynamics in the excited state of H2+ or related homonuclear dimers in the presence of a strong field. This effect is a general indirect outcome of the strong transition dipole and large polarizabilities typically used to control or to induce alignment in the ground state. In the excited state, however, the polarizabilities have the opposite sign than in the ground state, generating a torque that aligns the molecule perpendicular to the field, deeming any laser-control strategy impossible.
The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs…
We present an ab initio correlated approach to study molecules that interact strongly with quantum fields in an optical cavity. Quantum electrodynamics coupled cluster theory provides a non-perturbative description of cavity-induced effects in ground and excited states. Using this theory, we show how quantum fields can be used to manipulate charge transfer and photochemical properties of molecules. We propose a strategy to lift electronic degeneracies and induce modifications in the ground state potential energy surface close to a conical intersection.
Open-shell systems such as magnetic molecules or defects with a triplet ground state are challenging to describe in electronic structure methods, but are of great interest for quantum information applications. We demonstrate a spin-flip approach within the Bethe-Salpeter equation to calculate ground and excited states of open-shell molecules and defected solids. The approach works in periodic boundary conditions without any need for embedding or selection of a subspace. Our benchmark results for the torsion potential-energy surface of ethylene and the optical excitations of the diamond NV$^{-}…
We present a comprehensive theoretical study of the electronic structures of the Yb atom and the Yb$_2$ molecule, respectively, focusing on their ground and lowest-lying electronically excited states. Our study includes various state-of-the-art quantum chemistry methods such as CCSD, CCSD(T), CASPT2 (including spin--orbit coupling), and EOM-CCSD as well as some recently developed pCCD-based approaches and their extensions to target excited states. Specifically, we scan the lowest-lying potential energy surfaces of the \ce{Yb2} dimer and provide a reliable benchmark set of spectroscopic paramet…
We develop two novel models of the H$_2^+$ molecule and its isotopes from which we assess quantum-mechanically and semi-classically whether the molecule anti-aligns with the field in the first excited electronic state. The results from both models allow us to predict anti-alignment dynamics even for the HD$^+$ isotope, which possesses a permanent dipole moment. The molecule dissociates at angles perpendicular to the field polarization in both the excited and the ground electronic state, as the population is exchanged through a conical intersection. The quantum mechanical dispersion of the init…
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction Ansatz for strongly-correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed un-physical behaviour but in this contribution it is shown that with only the variational solution for the ground state, all the seniority-zero states are quite well approximated. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice and we expect it shoul…
We present a comprehensive relativistic coupled cluster study of the electronic structures of the ThO and ThS molecules in the spinor basis. Specifically, we use the single-reference coupled cluster and the multi-reference Fock Space Coupled Cluster (FSCC) methods to model their ground and electronically-excited states. Two variants of the FSCC method have been investigated: (a) one where the electronic spectrum is obtained from sector (1,1) of the Fock space, and (b) another where the excited states come from the doubly attached electronic states to the doubly charged systems (ThO$^{2+}$ and …
We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann-Wigner theorem. These conical intersections can occur when the Rydberg atom's quantum defect is similar in size to the electron--ground-state atom scattering phase shift divided by $π$, a condition satisfied in several commonly studied atomic species. The conical intersections have an observable c…
In the Noisy Intermediate-Scale Quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the "killer application" for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While…
