Implementation of the CCSD-PCM linear response function for frequency dependent properties in solution: Application to polarizability and specific rotation

This work reports the first implementation of the frequency dependent linear response (LR) function for the coupled cluster singles and doubles method (CCSD) combined with the polarizable continuum model of solvation for the calculation of frequency dependent properties in solution. In particular, values of static and dynamic polarizability as well as specific rotation are presented for various test molecules. Model calculations of polarizability show that a common approximation used in the definition of the LR function with solvation models recovers over 70% of the full response while maintaining a computational cost comparable to gas phase LR-CCSD. Calculations of specific rotation for three compounds for which gas phase methods predict the wrong sign of the rotation show that accounting for the electronic response of the solvent may be essential to assign the correct absolute configuration of chiral molecules

CCSD-PCM: Improving upon the reference reaction field approximation at no cost

The combination of the coupled cluster (CC) method with the polarizable continuum model (PCM) of solvation requires a much larger computational effort than gas phase CC calculations, since the PCM contribution depends nonlinearly on the CC reduced density: perturbation theoryenergy and density (PTED) scheme. An approximation can be introduced that neglects the “correlation” PCM contribution and only considers the “reference” PCM contribution to the free energy: PTE scheme. The PTE scheme is a computationally efficient strategy, since the cost is comparable to gas phase CC, but the difference in the free energy with respect to the PTED scheme can be significant. In this work, two intermediate approximations are presented, PTE(S) and PTES (where S stands for singles), which retain the computational efficiency of the PTE scheme while reducing the energy gap with the PTED scheme. PTE(S) only introduces an energy correction to the PTE free energy, while PTES introduces explicit PCM terms in the iterative solution of the CC equations. PTE(S) improves the PTE free energy, although such correction is small. PTES recovers 50%–80% of the PTE-PTED difference and represents a promising approach to perform calculations in solution of CC quality at a cost comparable to gas phase CC. The expressions for the CC-PTE(S) and -PTES wave functions,free energy, and free energy analytical gradients are presented, and the methods are tested with numerical examples

Link atom bond length effect in ONIOM excited state calculations

We investigate how the choice of the link atom bond length affects an electronic transition energy calculation with the so-called our own N-layer integrated molecular orbital molecular mechanics (ONIOM) hybrid method. This follows our previous paper [M. Caricato et al., J. Chem. Phys.131, 134105 (2009)], where we showed that ONIOM is able to accurately approximate electronic transition energies computed at a high level of theory such as the equation of motion coupled cluster singles and doubles (EOM-CCSD) method. In this study we show that the same guidelines used in ONIOM ground state calculations can also be followed in excited state calculations, and that the link atom bond length has little effect on the ONIOM energy when a sensible model system is chosen. We also suggest further guidelines for excited state calculations which can help in checking the effectiveness of the definition of the model system and controlling the noise in the calculation

Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods

In this work, we present a simple approach to simulate absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated efficiently at a high level of theory. The present approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g., band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems

Point charge embedding for ONIOM excited states calculations

Hybrid quantum mechanical methods can assist in the interpretation and prediction of the electronic spectra of large molecular structures. In this work, we study the performance of the ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics) hybrid method for the calculation of transition energies and oscillator strengths by embedding the core region in a field of fixed point charges. These charges introduce polarization effects from the substituent groups to the core region. We test various charge definitions, with particular attention to the issue of overpolarization near the boundary between layers. To minimize this issue, we fit the charges on the electrostatic potential of the entire structure in the presence of the link atoms used to cap dangling bonds. We propose two constrained fitting strategies: one that produces an average set of charges common to both model system calculations, EE(L1), and one that produces two separate sets of embedding charges, EE(L2). The results from our tests show that indeed electronic embedding with constrained-fitted charges tends to improve the performance of ONIOM compared to non-embedded calculations. However, the EE(L2) charges work best for transition energies, and the EE(L1) charges work best for oscillator strengths. This may be an indication that fixed point charges do not have enough flexibility to adapt to each system, and other effects (e.g., polarization of the embedding field) may be necessary

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution

A time-dependent polarizable continuum model: Theory and application

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N , N -dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well

On the difference between the transition properties calculated with linear response- and equation of motion-CCSD approaches

In this work, we quantitatively investigate the difference between the linear response (LR) and the equation of motion (EOM) coupled cluster (CC) approaches in the calculation of transition properties, namely, dipole and oscillator strengths, for the most widely used truncated CC wave function, which includes single and double excitation operators. We compare systems of increasing size, where the size-extensivity may be important. Our results suggest that, for small molecules, the difference is small even with large basis sets. The difference increases with the size of the system, but it is numerically small until hundreds of electron pairs are correlated. Although these calculations may be possible in a few years, at present the EOM approach is more advantageous, albeit more approximate, because it is computationally less demanding

Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves to be a superior O(N5) method for the description of Rydberg states