Effect of semi-empirical parameters on the simple random-phase approximation calculations of conjugated hydrocarbons

Singlet-singlet transition energies, oscillator strengths, triplet energy levels, and the ground state correlation energy of a number of conjugated hydrocarbons have been calculated by the simple random-phase approximation (RPA ) within the framework of the Pariser-Parr-Pople (PPP ) model. The effect of semi-empirical parameters in such calculations has been examined in detail. A set of parameters has been deduced from these parametric studies which is found to yield results for the singlet spectra of the molecules in excellent agreement with experiment. It is, however, not possible to treat the triplet states using these same parameters, since they produce triplet instabilities in all the molecules. The triplet instability problem associated with semi-empirical RPA calculations has been discussed in detail.     

A simple but fully nonlocal correction to the random phase approximation

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction.     

Wavelength-decomposition-based embedded cluster density approximation for systems with nonlocal electron correlation

Local correlation methods rely on the assumption that electron correlation is nearsighted. In this work, we develop a method to alleviate this assumption. This new method is demonstrated by calculating the random phase approximation (RPA) correlation energies in several one-dimensional model systems. In this new method, the first step is to approximately decompose the RPA correlation energy to the nearsighted and farsighted components based on the wavelength decomposition of electron correlation developed by Langreth and Perdew. The short-wavelength (SW) component of the RPA correlation energy is then considered to be nearsighted, and the long-wavelength (LW) component of the RPA correlation energy is considered to be farsighted. The SW RPA correlation energy is calculated using a recently developed local correlation method: the embedded cluster density approximation (ECDA). The LW RPA correlation energy is calculated globally based on the system's Kohn-Sham orbitals. This new method is termed λ-ECDA, where λ indicates the wavelength decomposition. The performance of λ-ECDA is examined on a one-dimensional model system: a H₂₄ chain, in which the RPA correlation energy is highly nonlocal. In this model system, a softened Coulomb interaction is used to describe the electron-electron and electron-ion interactions, and slightly stronger nuclear charges (1.2e ) are assigned to the pseudo-H atoms. Bond stretching energies, RPA correlation potentials, and Kohn-Sham eigenvalues predicted by λ-ECDA are in good agreement with the benchmarks when the clusters are made reasonably large. We find that the LW RPA correlation energy is critical for obtaining accurate prediction of the RPA correlation potential, even though the LW RPA correlation energy contributes to only a few percent of the total RPA correlation energy.     

Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies

The second-order noniterative doubles-corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles-corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second-order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second-order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Electron correlation methods based on the random phase approximation

In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn–Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree–Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.     

Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Self-consistent correlation potentials for H(2) and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the improved total energy in the dissociation limit.     

Random-phase-approximation calculations on triplet spectra of conjugated molecules

Random-phase approximations (RPA) have been applied to the calculation of the triplet π-π* transition spectra of 18 conjugated molecules in the framework of Pariser-Parr-Pople approximations. It is found that the normal RPA (n-RPA) shows the triplet instability for most molecules in the Nishimoto-Mataga approximation of electron-repulsion integrals. However, it is shown that this instability can be circumvented by the use of the renormalized RPA (r-RPA) in which the correlated ground states are calculated by the second-order perturbation theory. It is also shown that even in the n-RPA the suitable parametrization of electron-repulsion integrals removes this instability. It is ascertained that such an increasing order of energies as ω(n-RPA)<ω(Tamm-Dancoff approximation)<ω(r-RPA) holds for most of energy levels.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

Increasing the applicability of density functional theory. II. Correlation potentials from the random phase approximation and beyond

Density functional theory (DFT) results are mistrusted at times due to the presence of an unknown exchange correlation functional, with no practical way to guarantee convergence to the right answer. The use of a known exchange correlation functional based on wave-function theory helps to alleviate such mistrust. The exchange correlation functionals can be written exactly in terms of the density-density response function using the adiabatic-connection and fluctuation-dissipation framework. The random phase approximation (RPA) is the simplest approximation for the density-density response function. Since the correlation functional obtained from RPA is equivalent to the direct ring coupled cluster doubles (ring-CCD) correlation functional, meaning only Coulomb interactions are included, one can bracket RPA between many body perturbation theory (MBPT)-2 and CCD with the latter having all ring, ladder, and exchange contributions. Using an optimized effective potential strategy, we obtain correlation potentials corresponding to MBPT-2, RPA (ring-CCD), linear-CCD, and CCD. Using the suitable choice of the unperturbed Hamiltonian, Kohn-Sham self-consistent calculations are performed. The spatial behavior of the resulting potentials, total energies, and the HOMO eigenvalues are compared with the exact values for spherical atoms. Further, we demonstrate that the self-consistent eigenvalues obtained from these consistent potentials used in ab initio dft approximate all principal ionization potentials as demanded by ionization potential theorem.     

Modifications of circular dichroism by electrostatic influence of the solvent. A theoretical approach in the random phase approximation

The random phase approximation (RPA) formalism has been extended to the calculation of electronic transitions of solvated molecules. The solvent is modelled by a continuum surrounding an ellipsoidal cavity containing the molecule. The effect of the environment is introduced in the hamiltonian of the molecule in the ground state. The variations in the interaction of the molecule in an electronically excited state with the solvent, which arise from the change in electronic distribution of the solute, are treated as a perturbation. The method is applied to (1S, 4R)-norcamphor and to (R)-2-methylcyclobutanone in a solvent of dielectric permittivity ? = 2. This method predicts an electrostatic solvent effect quite comparable with the observed ones. A detailed analysis of the phenomenon shows that under the influence of the solvent the electric transition moment is rotated around the magnetic transition moment which is almost coincident with the carbonyl group dipole moment.     

Structure of consistent ground state: Re—derivation of RPA vacuum and inclusion of higher RPA effects

Here is presented a method to determine the consistent ground state (CGS ) which satisfies the so-called killer condition for the excitation operator. This method may be called an extended application of the procedure employed by Weiner and Goscinski in deriving the random phase approximation (RPA ) vacuum. The RPA vacuum is derived by solving the recurrence formula of the configuration coefficients of a multiconfigurational state vector. The role of boson approximation to the primitive p-h excitation operator is also investigated and by using the present formalism the cluster-expansion-type CGS is derived as the RPA vacuum under the boson approximation. Inclusion of the effects of a higher RPA in the CGS leads to the simultaneous equations of the configuration coefficients of the CGS . In including the effect of the second RPA , only the symmetry-broken CGS can exist. When the third RPA effect is involved instead of the second RPA , there can be a symmetry-adapted CGS , in which the picture of electron pairs acquired in the standard RPA vacuum is modified. Thus the exact CGS vectors are analytically obtained in the case of simple model systems of two or four electrons.     

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.     

THE PHOTODYNAMIC IMMOBILIZATION OF ARTEMIA SALINA NAUPLII BY POLYCYCLIC AROMATIC HYDROCARBONS AND ITS RELATIONSHIP TO CARCINOGENIC ACTIVITY

Abstract— The rates of the photosensitized immobilization of the nauplii of the crustacean Artemia salina were measured as a function of irradiation time and the amount of light absorbed by the sensitizers. The nauplii were incubated in the dark in dilute solutions of the sensitizers for periods of 2 and 22 h prior to irradiation. Nineteen carcinogenic and 22 noncarcinogenic polycyclic aromatic hydrocarbons were used as sensitizers. Relative photodynamic activities (RPA) were determined from the rates of immobilization using benz[ c ]acridine as a standard (RPA = 1). High RPA was restricted to carcinogenic compounds with 4 and 5 fused rings, compounds with 6 or more fused rings had low RPA regardless of their carcinogenic activities. The correlation of RPA with carcinogenic activity was excellent ( P = 0.006 and 0.009 for the 2 and 22 h dark incubations, respectively). It is suggested that carcinogenesis by polycyclic aromatics may result from sublethal photodynamic effects.     

A new approach to intermolecular forces in non-bonding regions

A new method to compute intermolecular energies in non-bonding regions is presented. It is based on the assumption that in such regions molecules can be reviewed as the sum of distorted, possibly overlapping, and electron exchanging atoms. The intermolecular energy change at a given distance is due to the sum of the atomic energy changes caused by these distortions. The energy change of any particular atom is computed in a Hartree—Fock model in which the effect of the other atom is represented by an effective potential. This potential in turn is computed from a calculation at a slightly larger intermolecular distance of the potential seen by an external electron in the field of the “other” atom. This potential computed in the RPA approximation and involves the distorted Hartree—Fock orbitals of the other atom (computed in a similar manner to the above) and the RPA response function of the other distorted atom.     

Description of noncovalent interactions involving π-system with high precision: An assessment of RPA,MP2, and DFT-D methods

Efficient approaches with high precision are essential for understanding the formation and stability of noncovalent interaction complexes. Here, 21 noncovalent interaction complexes involving π-system are selected and grouped in three subsets according to ETS–NOCV method: dispersion-dominated, electrostatic-dominated, and mixed. We mainly focus on examining the performance of random-phase approximation (RPA) on these π systems. The tested RPA-based method includes standard RPA and its variants including the related single excitations (SEs), renormalized single excitations (rSEs), second-order screened exchange (SOSEX), and the renormalized second-order perturbation theory (rPT2). The routine second-order Møller–Plesset perturbation theory (MP2) and three popular DFT-D functionals (M06-2X-D3, ωB97XD, and PBE-D3(BJ)) are also assessed for comparison. In this work, besides the calculation of interaction energies at Dunning-type aug-cc-pVDZ and aug-cc-pVTZ basis set, we also present a larger database of interaction energies calculated using MP2 and RPA methods with Dunning-type aug-cc-pVQZ basis set. An accurate CCSD(T)/CBS scheme is used to provide benchmark database. In addition to the high-level results, we also provide potential energy surfaces (PES) of different interaction type. Among all the tested methods, MP2 has a satisfactory performance on electrostatic-dominated and mixed-type systems, except for dispersion-dominated systems. DFT-D functionals, especially ωB97XD functional, has a balanced performance across all the tested systems. Importantly, for RPA-based methods, the calculation accuracy can be dramatically improved by taking into account SE or exchange effects, especially in the mixed complexes. We conclude that rPT2 among all the test RPA-based methods gives an overall satisfactory performance across different interaction types. © 2019 Wiley Periodicals, Inc.     

考虑相关能效应的过渡态计算方法

提出了一种在X_a方法基础上,同时包含电子相关效应和考虑电子自相互作用的过渡态计算方法.由此计算的一系列原子电离势的结果表明,相关能对电离势的计算结果有很大影响,其数值为—0.41eV～0.94eV.引入相关能效应使计算结果明显趋于合理.此计算模型兼有简便和合理的特点,且能适用于分子体系的计算.     

On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions

The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.     

Calculation of molecular polarizabilities for large systems within the random phase approximation

We examine the static-field molecular polarizability from a sum over uncoupled Hartree—Fock states (SOS), the Tamm—Dancoff approximation (TDA), and the random phase approximation (RPA). An efficient algorithm for the inversion of the TDA or RPA matrix is outlined, which avoids matrix diagonalization and explicit construction of matrix elements over states, allowing for rapid calculation of molecular polarizabilities. The extension of the method is straightforward; third-order hyperpolarizability is developed as an example. Test cases are reported for molecules represented by an intermediate neglect of differential overlap (INDO) wavefunction.     

Equation for the screened potential

The equation for the screened potential in the RPA has been derived by using the method of functional differentiation of Martin and Schwinger. The contribution of the “oyster” diagram has been contained in this equation.