Targeted excited state algorithms

To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen [SIAM J. Matrix Anal. Appl. 17, 401 (1996)], we have implemented harmonic Davidson and state-averaged harmonic Davidson algorithms within the context of the density matrix renormalization group (DMRG). We have assessed their accuracy and stability of convergence in complete-active-space DMRG calculations on the low-lying excited states in the acenes ranging from naphthalene to pentacene. We find that both algorithms offer increased accuracy over the traditional state-averaged Davidson approach, and, in particular, the state-averaged harmonic Davidson algorithm offers an optimal combination of accuracy and stability in convergence.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Electronic excitations of hypervalent configurations in amorphous selenium: Quantum-chemical modeling

The first excited states of the clusters modeling fragments of a continuous random network and the most stable local defects in solid selenium have been calculated by different ab initio methods (TD-DFT, EOM CCSD, CASSCF). A split-valence double-zeta basis set augmented with polarization and diffuse functions has been used. The effect of the cluster size and structure on the energies of transitions is considered, and the tendencies of geometric relaxation of excited states for the most typical structures are assessed.     

New algorithm for tensor contractions on multi‐core CPUs,GPUs, and accelerators enables CCSD and EOM‐CCSD calculations with over 1000 basis functions on a single compute node

A new hardware‐agnostic contraction algorithm for tensors of arbitrary symmetry and sparsity is presented. The algorithm is implemented as a stand‐alone open‐source code libxm . This code is also integrated with general tensor library libtensor and with the Q‐Chem quantum‐chemistry package. An overview of the algorithm, its implementation, and benchmarks are presented. Similarly to other tensor software, the algorithm exploits efficient matrix multiplication libraries and assumes that tensors are stored in a block‐tensor form. The distinguishing features of the algorithm are: (i) efficient repackaging of the individual blocks into large matrices and back, which affords efficient graphics processing unit (GPU)‐enabled calculations without modifications of higher‐level codes; (ii) fully asynchronous data transfer between disk storage and fast memory. The algorithm enables canonical all‐electron coupled‐cluster and equation‐of‐motion coupled‐cluster calculations with single and double substitutions (CCSD and EOM‐CCSD) with over 1000 basis functions on a single quad‐GPU machine. We show that the algorithm exhibits predicted theoretical scaling for canonical CCSD calculations, O (N ⁶), irrespective of the data size on disk. © 2017 Wiley Periodicals, Inc.     

Geometries,vibrational frequencies,and excitation energies of a series of fluorine‐substituted carbenes,FCX (X = H,F, Cl,Br, and I): A high‐level multireference configuration interaction study

High‐level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine‐substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S‐T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin‐orbit coupling, and core‐valence correlation, have been studied in calculating the transition energies and the S‐T gaps, especially for heavy‐atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high‐resolution laser‐based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine‐substituted carbenes which are void in the literature have been provided with consistent high‐level calculations. © 2013 Wiley Periodicals, Inc.     

Excitation Energies of Canonical Nucleobases Computed by Multiconfigurational Perturbation Theories

In this computational work, we assessed the performance of ab initio multireference (MR) methods for the calculation of vertical excitation energies of five nucleobases: adenine, guanine, cytosine, thymine and uracil. In total, we have studied 38 singlet and 30 triplet excited states. Where possible we used the multireference configuration interaction (MRCI) method as a reference for various flavors of multireference perturbation theory to second order. In particular, we have benchmarked CASPT2, NEVPT2 and XMCQDPT2. For CASPT2, we have analyzed the single‐state, multistate (MS) and extended MS variants. In addition, we have assessed the effect of the ionization potential electron affinity (IPEA) shift. For NEVPT2, we have used the partially and the strongly contracted variants. Further, we have tested the commonly used RI‐CC2, RI‐ADC2 and EOM‐CCSD methods. Generally, we observe the following trends for singlet excited states: NEVPT2 is the closest MR method to MRCISD+Q, closely followed by CASPT2 with the default IPEA shift. The same trend is observed for triplet states, although NEVPT2 and CASPT2‐IPEA are getting closer. Interestingly, the n, π* singlet excited states were described more accurately than π, π* excited states, while for triplet states the trend is inverted except for NEVPT2. This work is an important benchmark for future photochemical investigations.     

A theoretical description of charge reorganization energies in molecular organic P‐type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge‐transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP‐tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP‐EOM‐CCSD single‐point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X‐D and SOGGA11X yield accurate charge reorganization energies in comparison with IP‐EOM‐CCSD values. © 2016 Wiley Periodicals, Inc.     

Molecular parameters of tetraatomic carbonyls X2CO and XYCO (X,Y = H,F, Cl) in the ground and lowest excited electronic states,part 1: A test of ab initio methods

Geometrical parameters of tetraatomic carbonyl molecules X₂CO and XYCO (X, Y = H, F, Cl) in the ground (S₀) and lowest excited singlet (S₁) and triplet (T₁) electronic states as well as values of barriers to inversion in S₁ and T₁ states and S₁ ← S₀ and T₁ ← S₀ adiabatic transition energies were systematically investigated by means of various quantum‐chemical techniques. The following methods were tested: HF, MP2, CIS, CISD, CCSD, EOM‐CCSD, CCSD(T), CR‐EOM‐CCSD(T), CASSCF, MR‐MP2, CASPT2, CASPT3, NEVPT2, MR‐CISD, and MR‐AQCC within cc‐pVTZ and cc‐pVQZ basis sets. The accuracy of quantum‐chemical methods was estimated in comparison with experimental data and rather accurate structures of excited electronic states were obtained. MP2 and CASPT2 methods appeared to be the most efficient and CCSD(T), CR‐EOM‐CCSD(T), and MR‐AQCC the most accurate. It was found that at equilibrium all the molecules under study are nonplanar in S₁ and T₁ electronic states with CO out‐of‐plane angle ranging from 34° (H₂CO, S₁) to 52° (F₂CO, T₁), and height of barrier to inversion varying from 300 (H₂CO, S₁) to 11,000 (F₂CO, T₁) cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Difluorobenzenes revisited: an experimental and theoretical study of spin–spin coupling constants for 1,2‐, 1,3‐, and 1,4‐difluorobenzene

The experimental spin–spin coupling constants (SSCCs) for 1,3‐ and 1,4‐difluorobenzene have been determined anew, and found to be consistent with previously determined values. SSCCs for 1,2‐, 1,3‐, and 1,4‐difluorobenzene have been analyzed by comparing them with the coupling constants computed using the second‐order polarization propagator approximation (SOPPA) and the equation‐of‐motion coupled cluster singles and doubles method (EOM‐CCSD). Eighty experimental values have been analyzed using SOPPA calculations, and a subset of 40 values using both SOPPA and EOM‐CCSD approaches. One‐bond coupling constants ¹J(C? C) and ¹J(C? F) are better described by EOM‐CCSD, whereas one‐bond ¹J(C? H) values are better described by SOPPA. An empirical equation is presented which allows for the prediction of unknown coupling constants from computed SOPPA values. A similar approach may prove useful for predicting coupling constants in larger systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Lower scaling approximation to EOM‐CCSD: A critical assessment of the ionization problem

In this article, we investigate the performance of different approximate variants of the EOM‐CCSD method for calculation of ionization potential (IP), as compared to EOM‐CCSDT reference values. None of the lower scaling approximations to the EOM‐CCSD method give a consistent performance for valence, inner valence, and core ionization, favoring one, or the other depending on the nature of the approximation used. The parent EOMIP‐CCSD method gives superior performance for valence IP but can show large errors for inner valence and core ionization. The problem is particularly severe for core‐ionization, where even the EOMIP‐CCSDT method cannot provide quantitative accuracy.     

Analysis of approximations and errors in equations of motion method calculations

We analyze a number of fundamental questions associated with the use of a finite one-particle orbital basis in equations of motion (EOM) method calculations of excitation energies etc., of atomic and molecular systems. This approximation yields an approximate n_e-electron ground state and say, N excited states, while there are (N + 1)² different possible basis operators for EOM calculations. We show that sets of at most 2N basis operators can contribute to the EOM calculations. Any set of 2N basis operators, satisfying certain conditions, provides the exact EOM energies which are equivalent to complete configuration interaction results within the same orbital basis. We investigate the use of particle-particle shifting operators which are not employed in EOM calculations in model calculations on He with operator bases smaller than the complete 2V to consider the convergence of the expansion. The dependence of EOM calculations on the quality of the approximate ground state wavefunction is studied through calculations for Be where additional support is provided for the frequent need for multiconfigurational zeroth order reference functions (as corrected perturbatively). Excited state EOM wavefunctions from EOM calculations are shown to not necessarily be orthogonal to either the exact or approximate ground state wavefunction, suggesting implications in the use of EOM methods to evaluate excited state properties. The He and Be examples and a simple two-level problem are also utilized to illustrate questions concerning the use of the EOM equations to obtain an iteratively improved ground state wavefunction.     

Theoretical study of excited states of DNA base dimers and tetramers using optimally tuned range‐separated density functional theory

Excited states of various DNA base dimers and tetramers including Watson‐Crick H‐bonding and stacking interactions have been investigated by time‐dependent density functional theory using nonempirically tuned range‐separated exchange (RSE) functionals. Significant improvements are found in the prediction of excitation energies and oscillator strengths, with results comparable to those of high‐level coupled‐cluster (CC) models (RI‐CC2 and EOM‐CCSD(T)). The optimally‐tuned RSE functional significantly outperforms its non‐tuned (default) version and widely‐used B3LYP functional. Compared to those high‐level CC benchmarks, the large mean absolute deviations of conventional functionals can be attributed to their inappropriate amount of exact exchange and large delocalization errors which can be greatly eliminated by tuning approach. Furthermore, the impacts of H‐bonding and π‐stacking interactions in various DNA dimers and tetramers are analyzed through peak shift of simulated absorption spectra as well as corresponding change of absorption intensity. The result indicates the stacking interaction in DNA tetramers mainly contributes to the hypochromicity effect. The present work provides an efficient theoretical tool for accurate prediction of optical properties and excited states of nucleobase and other biological systems. © 2015 Wiley Periodicals, Inc.     

The photoisomerization of 11‐cis‐retinal protonated schiff base in gas phase: Insight from spin‐flip density functional theory

This extensive theoretical study employed the spin‐flip density functional theory (SFDFT) method to investigate the photoisomerization of 11‐cis‐retinal protonated Schiff base (PSB11) and its minimal model tZt‐penta‐3,5‐dieniminium cation (PSB3). Our calculated results indicate that SFDFT can perform very well in describing the ground‐ and excited‐state geometries of PSB3 and PSB11. We located the conical intersection (CI) point and constructed the photoisomerization reaction path of PSB3 and PSB11 by using the SFDFT method. To further verify the SFDFT results, we computed the energy profiles along the constructed linearly interpolated internal coordinate (LIIC) pathways by using high‐level theoretical methods, such as the EOM‐CCSD, CR‐EOM‐CCSD(T), CASPT2, NEVPT2, and XMCQDPT2 methods. The SFDFT method predicts that the photoisomerization of PSB3 is barrierless, in accordance with previous complete‐active‐space self‐consistent‐field (CASSCF) results. However, an energy barrier is predicted along the LIIC pathways of PSB11. This finding is different from previous CASSCF results and may indicate that the photoisomerization of PSB11 in gas phase is similar to that in solution. However, the higher spin contamination of the SFDFT method in the vicinity of the CI point caused the located CI geometry to deviate from that of the real CI. In addition, the LIIC pathways are only approximations to the minimum energy path (MEP). Thus, further experimental and theoretical studies are needed to verify the existence of an energy barrier along the photoisomerization reaction path of PSB11 in gas phase. © 2013 Wiley Periodicals, Inc.     

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

A recently developed Thouless‐expansion‐based diagonalization‐free approach for improving the efficiency of self‐consistent field (SCF) methods (Noga and ?imunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four‐component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four‐component diagonalization‐free SCF calculations on several heavy‐metal complexes, the largest of which contains more than 80 atoms (about 6000 4‐spinor basis functions). The diagonalization‐free procedure is about twice as fast as the corresponding diagonalization. © 2014 Wiley Periodicals, Inc.     

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-CC and configuration-interaction approaches for excited states is compared. The effect of higher excitations on excited-state properties is demonstrated in benchmark calculations for NH(2) and NH(3). As a first application, the stationary points of the S(1) surface of acetylene are characterized by high-accuracy calculations.     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

Coupled cluster methods including triple excitations for excited states of radicals

We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N(7)) computational steps and avoids storage of the triple-excitation amplitudes for both the ground- and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence (2)B(1) state of the allyl radical, low-lying states of the CH and CO(+) diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the (2)Sigma(+) state of CH, significant errors of more than 0.4 eV remain.     

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3

A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.