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Frozen density embedding (FDE) is an embedding method for complex environments that is simple for users to set up. It reduces the computation time by dividing the total system into small subsystems and approximating the interaction by a functional of their densities. Its combination with wavefunction methods is, however, limited to small- or medium-sized molecules because of the steep scaling in computation time of these methods. To mitigate this limitation, we present a combination of the FDE approach with pair natural orbitals (PNOs) in the TURBOMOLE software package. It combines the uncoupled FDE (FDEu) approach for excitation energy calculations with efficient implementations of second-order correlation methods in the ricc2 and pnoccsd programs. The performance of this combination is tested for tetraazaperopyrene (TAPP) molecular crystals. It is shown that the PNO truncation error on environment-induced shifts is significantly smaller than the shifts themselves and, thus, that the local approximations of PNO-based wavefunction methods can without the loss of relevant digits be combined with the FDE method. Computational wall times are presented for two TAPP systems. The scaling of the wall times is compared to conventional supermolecular calculations and demonstrates large computational savings for the combination of FDE- and PNO-based methods. Additionally, the behavior of excitation energies with the system size is investigated. It is found that the excitation energies converge quickly with the size of the embedding environment for the TAPPs investigated in the current study. [ABSTRACT FROM AUTHOR]

We present a pair natural orbital (PNO)-based implementation of CC3 excitation energies, which extends our previously published state-specific PNO ansatz for the solution of the excited state eigenvalue problem to methods including connected triple excitations. A thorough analysis of the equations for the excited state triples amplitudes is presented from which we derive a suitable state-specific triple natural orbital basis for the excited state triples amplitudes, which performs equally well for local and non-local excitations. The accuracy of the implementation is evaluated using a large and diverse test set. We find that for states with small contributions from double excitations, a T0 approximation to PNO-CC3 yields accurate results with a mean absolute error (MAE) for TPNO = 10−7 in the range of 0.02 eV. However, for states with larger double excitation contributions, the T0 approximation is found to yield significantly less accurate results, while the Laplace-transformed variant of PNO-CC3 shows a uniform accuracy for singly and doubly excited states (MAE and maximum error of 0.01 eV and 0.07 eV for TPNO = 10−7, respectively). Finally, we apply PNO-CC3 to the calculation of the first excited state of berenil at a S1 minimum geometry, which is shown to be close to a conical intersection. This calculation in the aug-cc-pVTZ basis set (more than 1300 basis functions) is the largest calculation ever performed with CC3 on excitation energies. [ABSTRACT FROM AUTHOR]

We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D8). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data. [ABSTRACT FROM AUTHOR]

We present a pair natural orbital (PNO)-based implementation of coupled cluster singles and doubles (CCSD) excitation energies that builds upon the previously proposed state-specific PNO approach to the excited state eigenvalue problem. We construct the excited state PNOs for each state separately in a truncated orbital specific virtual basis and use a local density-fitting approximation to achieve an at most quadratic scaling of the computational costs for the PNO construction. The earlier reported excited state PNO construction is generalized such that a smooth convergence of the results for charge transfer states is ensured for general coupled cluster methods. We investigate the accuracy of our implementation by applying it to a large and diverse test set comprising 153 singlet excitations in organic molecules. Already moderate PNO thresholds yield mean absolute errors below 0.01 eV. The performance of the implementation is investigated through the calculations on alkene chains and reveals an at most cubic cost-scaling for the CCSD iterations with the system size. [ABSTRACT FROM AUTHOR]

In this study, we predict vibronic two-photon absorption (TPA) spectra for 4-nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second-order coupled-cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium-sized systems. A special focus is put on the geometric derivatives of the second-order transition moment and the dipole moment difference between the charge-transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4-nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck-Condon contribution. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

At the example of the extended algebraic-diagrammatic construction through second order, ADC(2)-x, we study the performance of a pair natural orbital (PNO) expansion for the description of partially or dominantly doubly excited states within a response theory framework. We find that with the presence of dominantly doubly excited states in the ADC(2)-x spectra the PNO truncation errors are between a factor of two and five larger than for strict second-order methods, where such excitations are only described in a zeroth-order approximation, but that otherwise the rate of convergence with the PNO selection threshold is similar. Furthermore, we analyze the reason for the red shift of excitation energies in ADC(2)-x and trace it back to an unbalanced account of electron correlation effects in the ground and the excited state by the term added in the extended method to describe double excitations correct through first order. The balance can be restored by including the contributions from one additional commutator which accounts in lowest order for the coupling between double excitations in the ground and the excited state. A perturbative correction to ADC(2) which includes both correction terms for doubly excited configurations gives excitation energies close to results from CCSD with, however, much lower computational expenses. The truncated pair natural orbital expansion for the ground and excited state doubles amplitudes opens a route to reduce the steep cost-scaling of the extended ADC(2) and other higher-order response methods without significant degradation of their accuracy or a priori restriction of the double excitation manifold. Already our proof-of-principles implementation exhibits a cost-scaling between which can be further reduced with a stringent use of integral screening and local density fitting to a quadratic cost-scaling. [ABSTRACT FROM AUTHOR]

The excited state dipole moments of two positional isomers of dicyanobenzene have been determined from thermochromic shifts of the absorption and fluorescence emission spectra in ethyl acetate solution and compared to the results of ab initio calculations. We found that the dipole moments of excited states from thermochromic shifts closely resemble the ab initio values of the isolated molecule, while the results of conductor-like screening model (COSMO) using the same wave function model as for the isolated molecule, shows considerable deviations from the experimental values. It is shown that the dipole moments of the two cyano groups add up vectorially for both the ground and excited states. • Dipole moment of two isomeric dicyanobenzenes determined in ground and excited state from thermochromic shifts. • Comparison of the experimental results to SCS-CC2 calculations shows a very good agreement for excited state dipole moments of the isolated molecules. • Bad agreement with the results of COSMO calculations. • Additivity rule for dipole increments works in the ground state and the excited state. [Display omitted] [ABSTRACT FROM AUTHOR]