Spin-component Scaled Research Articles

Do any types of double-hybrid models render the correct order of excited state energies in inverted singlet-triplet emitters?

Organic emissive materials with the inverted singlet-triplet energy gaps, where in violation of Hund's multiplicity rule the lowest triplet excited-state is higher in energy than the lowest singlet excited-state, have recently come into the limelight. This unique feature is of important relevance, where the emitters meeting the singlet-triplet inversion have potential to usher in the next generation of organic light emitting diodes (OLEDs). Since experimental data in this context are currently sparse, necessity of the cost-effective theoretical tools able to provide reliable results seems to be evident. Following our recent endeavors on the spin-component-scaled (SCS), spin-opposite-scaled (SOS), and SOS-range separated exchange (SOS-RSX) double-hybrids (DHs) as well as other efforts revealing the superior performances of such models for time-dependent computations, in the present work, we develop and validate several models based on the SOS-configuration interaction singles with perturbative doubles correction [SOS-CIS(D)] devoid of any fitting procedure for describing the singlet-triplet inversion. Taking a series of emitters with the available reference values for the inverted singlet-triplet energy gaps as working models, it is unveiled that the extremes of the same-spin and opposite-spin parameters included in the direct and indirect terms of the SOS-CIS(D) correlation energy as well as the nonlocal exchange and correlation contributions do not necessarily work well for the inverted gaps, but particular proportions among them are needed to achieve a reliable accuracy. Perusing the results of our developed methods, the best one based on the Perdew-Burke-Ernzerhof (PBE) exchange and correlation terms and the quadratic integrand model, denominated as SOS0-CIS(D)-PBE-QIDH, is shown to be highly efficient and robust for computations of the inverted singlet-triplet energy gaps. Furthermore, through detailed comparisons, we have also evaluated the performances of a variety of the recently presented DHs, including parameterized, parameter-free, RSX, as well as spin-component and spin-opposite scaling models for the purpose. Dissecting all the findings, it is disclosed that the results of any type of the DHs cannot be reliable, leading to positive energy gaps in most cases. Nonetheless, there are still some approximations, including SCS-PBE-QIDH, dispersion corrected spin-component scaled double-hybrids (DSD) of DSD-PBEP86 and DSD-BLYP, SOS-PBE-QIDH, SOS-ωPBEPP86, and SOS-RSX-QIDH, that can predict the negative singlet-triplet energy gaps for all the considered emitters and provide comparable performances with respect to our proposed model. To wrap up, among the large panel of different families of DHs on the market, the newly proposed model herein alongside these latter functionals can be recommended as the currently best affordable methods for subsequent applications on the inverted singlet-triplet emitters in OLED materials.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States.

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput.17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

How Can We Predict Accurate Electrochromic Shifts for Biochromophores? A Case Study on the Photosynthetic Reaction Center.

Protein-embedded chromophores are responsible for light harvesting, excitation energy transfer, and charge separation in photosynthesis. A critical part of the photosynthetic apparatus are reaction centers (RCs), which comprise groups of (bacterio)chlorophyll and (bacterio)pheophytin molecules that transform the excitation energy derived from light absorption into charge separation. The lowest excitation energies of individual pigments (site energies) are key for understanding photosynthetic systems, and form a prime target for quantum chemistry. A major theoretical challenge is to accurately describe the electrochromic (Stark) shifts in site energies produced by the inhomogeneous electric field of the protein matrix. Here, we present large-scale quantum mechanics/molecular mechanics calculations of electrochromic shifts for the RC chromophores of photosystem II (PSII) using various quantum chemical methods evaluated against the domain-based local pair natural orbital (DLPNO) implementation of the similarity-transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD). We show that certain range-separated density functionals (ωΒ97, ωΒ97X-V, ωΒ2PLYP, and LC-BLYP) correctly reproduce RC site energy shifts with time-dependent density functional theory (TD-DFT). The popular CAM-B3LYP functional underestimates the shifts and is not recommended. Global hybrid functionals are too insensitive to the environment and should be avoided, while nonhybrid functionals are strictly nonapplicable. Among the applicable approximate coupled cluster methods, the canonical versions of CC2 and ADC(2) were found to deviate significantly from the reference results both for the description of the lowest excited state and for the electrochromic shifts. By contrast, their spin-component-scaled (SCS) and particularly the scale-opposite-spin (SOS) variants compare well with the reference DLPNO-STEOM-CCSD and the best range-separated DFT methods. The emergence of RC excitation asymmetry is discussed in terms of intrinsic and protein electrostatic potentials. In addition, we evaluate a minimal structural scaffold of PSII, the D1–D2–CytB559 RC complex often employed in experimental studies, and show that it would have the same site energy distribution of RC chromophores as the full PSII supercomplex, but only under the unlikely conditions that the core protein organization and cofactor arrangement remain identical to those of the intact enzyme.

Assessment of second-order Møller-Plesset perturbation theory for isomerization and dissociation energies of nitramide

Based on the optimized molecular geometries at the B3LYP/cc-pVDZ level, the electronic and nuclear repulsion energies of nitramide (NH2NO2), O-nitrosohydroxylamine (NH2ONO), 1-hydroxydiazene 1-oxide (NH=N(O)OH), the transition state between NH2NO2 and NH2ONO, the transition state between NH2NO2 and NH=N(O)OH, NH2 radical, NO2 radical, H2O, N2O, H2, N2, O2, H, N and O were calculated by various second-order Møller–Plesset perturbation theory (MP2) methods. The domain based local pair natural orbital (DLPNO), explicitly correlated F12, density fitting (RI), spin-component scaled (SCS) and orbital optimized (OO) calculations were employed in MP2 calculations. The isomerization and dissociation energies of NH2NO2 were estimated by CCSD(T)-F12-RI as benchmark method. The testing results indicate that the deviations can be reduced by SCS method efficiently.

Accuracy of Spin-Component Scaled ADC(2) Excitation Energies and Potential Energy Surfaces.

In a recent paper of this journal ( Tajti ; ; Szalay . J. Chem. Theory Comput. 2019 , 15 , 5523 ), we have shown that failures of the CC2 method to describe Rydberg excited states as well as potential energy surfaces of certain valence excited states can be cured by spin-component scaled (SCS) versions SCS-CC2 and SOS-CC2 to a large extent. In this paper, the related and popular second-order algebraic diagrammatic construction (ADC(2)) method and its SCS variants are inspected with the previously established methodology. The results reflect the similarity of the CC2 and ADC(2) models, showing identical problems in the case of the canonical form and the same improvement when spin-component scaling is applied.

Accurate interaction energies by spin component scaled Möller-Plesset second order perturbation theory calculations with optimized basis sets (SCS-MP2mod): Development and application to aromatic heterocycles.

The Spin Component Scaled (SCS) MP2 method using a reduced and optimized basis set (SCS-MP2mod) is employed to compute the interaction energies of nine homodimers, formed by aromatic heterocyclic molecules (pyrrole, furan, thiophene, oxazole, isoxazole, pyridine, pyridazine, pyrimidine, and pyrazine). The coefficients of the same-spin and opposite-spin correlation energies and the Gaussian type orbitals (GTO) polarization exponents of the 6-31G** basis set are simultaneously optimized in order to minimize the energy differences with respect to the coupled-cluster with single, double and perturbative triples excitations [CCSD(T)] reference interaction energies, extrapolated to a complete basis set. It is demonstrated that the optimization of the spin scale factors leads to a noticeable improvement of the accuracy with a root mean square deviation less than 0.1 kcal/mol and a largest unsigned deviation smaller than 0.25 kcal/mol. The pyrrole dimer provides an exception, with a slightly higher deviation from the reference data. Given the high benefit in terms of computational time with respect to the CCSD(T) technique and the small loss of accuracy, the SCS-MP2mod method appears to be particularly suitable for extensive sampling of intermolecular potential energy surfaces at a quantum mechanical level. Within this framework, a transferability test of the SCS-MP2mod parameters to a benchmark set of this class of molecules is very promising as the reference interaction energies of several heterocyclic aromatic heterodimers were reproduced with a standard deviation of 0.30 kcal/mol. The SCS-MP2mod remarkably outperforms the value of 1.95 kcal/mol obtained with standard MP2/6-31G**.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Heats of Formation of Medium-Sized Organic Compounds from Contemporary Electronic Structure Methods

Computational electronic structure calculations are routinely undertaken to predict thermodynamic properties of various species. However, the application of highly accurate wave function theory methods, such as the "gold standard" coupled cluster approach including single, double, and partly triple excitations in perturbative fashion, CCSD(T), to large molecules is limited due to high computational cost. In this work, the promising domain based local pair natural orbital coupled cluster approach, DLPNO-CCSD(T), has been tested to reproduce 113 accurate formation enthalpies of medium-sized molecules (few dozens heavy atoms) important for bio- and combustion chemistry via the reaction based Feller-Peterson-Dixon approach. For comparison, eight density functional theory (B3LYP, B3LYP-D3, PBE0, PBE0-D3, M06, M06-2X, ωB97X-D3, and ωB97M-V) and MP2-based (B2PLYP-D3, PWPB95-D3, B2T-PLYP, B2T-PLYP-D, B2GP-PLYP, DSD-PBEP86-D3, SCS-MP2, and OO-SCS-MP2) methods have been tested. The worst performance has been obtained for the standard hybrid DFT functionals, PBE0 (mean unsigned error (MUE)/mean signed error (MSE) = 9.1/6.0 kcal/mol) and B3LYP (MUE/MSE = 13.5/-13.3 kcal/mol). The influence of an empirical dispersion correction term on these functionals' performance is not homogeneous: B3LYP performance is improved (B3LYP-D3 (MUE/MSE = 6.0/0.8 kcal/mol)); meanwhile PBE0 performance is worse (PBE0-D3 (MUE/MSE = 14.1/13.6 kcal/mol)). The Minnesota functionals, M06 (MUE/MSE = 3.8/-2.0 kcal/mol) and M06-2X (MUE/MSE = 3.5/3.0 kcal/mol), and recently developed ωB97X-D3 (MUE/MSE = 3.2/0.2 kcal/mol) and ωB97M-V (MUE/MSE = 2.2/1.3 kcal/mol) methods provided significantly better formation enthalpies. Enthalpies of similar quality can also be obtained from some double hybrid methods (B2PLYP-D3 (MUE/MSE = 4.7/2.0 kcal/mol), PWPB95-D3 (MUE/MSE = 4.3/3.2 kcal/mol), B2T-PLYP (MUE/MSE = 4.1/-3.0 kcal/mol), and B2T-PLYP-D (MUE/MSE = 3.3/1.7 kcal/mol)). The two spin component scaled (SCS) MP2 methods resulted in even smaller errors (SCS-MP2 (MUE/MSE = 1.9/1.2 kcal/mol) and OO-SCS-MP2 (MUE/MSE = 1.6/0.1 kcal/mol)). The best performance was found for the frozen core (FC) DLPNO-CCSD(T) method with a MUE/MSE of 1.6/-1.2 kcal/mol. The performance of the DLPNO-CCSD(T) method can be further improved by running the post-SCF calculations on the B3LYP orbitals: the MUE/MSE for the DLPNO-CCSD(T,B3LYP) approximation is 1.2/-0.4 kcal/mol. We recommend the DLPNO-CCSD(T,B3LYP) method for black box applications in thermodynamics of medium-sized organic molecules when the canonical CCSD(T) calculations with basis sets of reasonable quality are prohibitively expensive.

Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation.

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time. The SCS-dRPA75 method with the aug-cc-pVTZ basis set results in an average error lower than 1.5 kcal mol-1 for the entire n-homodesmotic hierarchy of hydrocarbon reactions (RC0-RC5 test sets). The overall performance of this method is better than the related direct random phase approximation-based double-hybrid PWRB95 method on open-shell systems of main-group elements (from the GMTKN30 database) and comparable to the best O(N4)-scaling opposite-spin second-order perturbation theory-based double-hybrid methods like PWPB95-D3 and to the O(N5)-scaling RPAX2@PBEx method, which also includes exchange interactions. Furthermore, it gives well-balanced performance on many types of barrier heights similarly to the best O(N5)-scaling second-order perturbation theory-based or spin-component scaled second-order perturbation theory-based double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show that the SCS-dRPA75 method has reduced self-interaction and delocalization errors compared to the parent dRPA75 method and a slightly smaller static correlation error than the related PWRB95 method.

Highly accurate benchmark calculations of the interaction energies in the complexes C6H6···C6X6 (X = F, Cl, Br, and I)

AbstractDifferent from the case of the benzene dimer, the differences between the interaction energies are always less than 0.50 kcal/mol for face‐to‐face eclipsed, face‐to‐face staggered, and parallel‐displaced configurations of all investigated complexes C6H6···C6X6 (X = F, Cl, Br, and I). Hence, it is a great challenge for quantum chemists to accurately calculate the interaction energies for the three configurations of the complexes C6H6···C6X6. This work demonstrates that results obtained with the PBE0 density functional combined with the D3 dispersion correction (PBE0‐D3) and the basis set def2‐TZVPP are in excellent agreement with the estimates of the coupled‐cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set (CBS) limit. The other finding in this study is that, in comparison with the gold‐standard CCSD(T)/CBS benchmark, the spin‐component scaled (SCS) zeroth‐order symmetry‐adapted perturbation theory (SAPT0), when paired with the basis set aug‐cc‐pVDZ, performs also very well, and its performance is even better than that of the PBE0‐D3/def2‐TZVPP method or the conventional SAPT/aug‐cc‐pVQZ method. The findings of this study are very significant because both PBE0‐D3/def2‐TZVPP and SCS‐SAPT0/aug‐cc‐pVDZ can deal with the systems with more than 200 atoms.

Quadratic integrand double-hybrid made spin-component-scaled.

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model.

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Attenuated MP2 with a Long-Range Dispersion Correction for Treating Nonbonded Interactions.

Attenuated second order Møller-Plesset theory (MP2) captures intermolecular binding energies at equilibrium geometries with high fidelity with respect to reference methods, yet must fail to reproduce dispersion energies at stretched geometries due to the removal of fully long-range dispersion. For this problem to be ameliorated, long-range correction using the VV10 van der Waals density functional is added to attenuated MP2, capturing short-range correlation with attenuated MP2 and long-range dispersion with VV10. Attenuated MP2 with long-range VV10 dispersion in the aug-cc-pVTZ (aTZ) basis set, MP2-V(terfc, aTZ), is parametrized for noncovalent interactions using the S66 database and tested on a variety of noncovalent databases, describing potential energy surfaces and equilibrium binding energies equally well. Further, a spin-component scaled (SCS) version, SCS-MP2-V(2terfc, aTZ), is produced using the W4-11 database as a supplemental thermochemistry training set, and the resulting method reproduces the quality of MP2-V(terfc, aTZ) for noncovalent interactions and exceeds the performance of SCS-MP2/aTZ for thermochemistry.

The elusive S2 state, the S1/S2 splitting, and the excimer states of the benzene dimer

We observe the weak S0 → S2 transitions of the T-shaped benzene dimers (Bz)2 and (Bz-d6)2 about 250 cm(-1) and 220 cm(-1) above their respective S0 → S1 electronic origins using two-color resonant two-photon ionization spectroscopy. Spin-component scaled (SCS) second-order approximate coupled-cluster (CC2) calculations predict that for the tipped T-shaped geometry, the S0 → S2 electronic oscillator strength fel(S2) is ∼10 times smaller than fel(S1) and the S2 state lies ∼240 cm(-1) above S1, in excellent agreement with experiment. The S0 → S1 (ππ(∗)) transition is mainly localized on the "stem" benzene, with a minor stem → cap charge-transfer contribution; the S0 → S2 transition is mainly localized on the "cap" benzene. The orbitals, electronic oscillator strengths fel(S1) and fel(S2), and transition frequencies depend strongly on the tipping angle ω between the two Bz moieties. The SCS-CC2 calculated S1 and S2 excitation energies at different T-shaped, stacked-parallel and parallel-displaced stationary points of the (Bz)2 ground-state surface allow to construct approximate S1 and S2 potential energy surfaces and reveal their relation to the "excimer" states at the stacked-parallel geometry. The fel(S1) and fel(S2) transition dipole moments at the C2v-symmetric T-shape, parallel-displaced and stacked-parallel geometries are either zero or ∼10 times smaller than at the tipped T-shaped geometry. This unusual property of the S0 → S1 and S0 → S2 transition-dipole moment surfaces of (Bz)2 restricts its observation by electronic spectroscopy to the tipped and tilted T-shaped geometries; the other ground-state geometries are impossible or extremely difficult to observe. The S0 → S1/S2 spectra of (Bz)2 are compared to those of imidazole ⋅ (Bz)2, which has a rigid triangular structure with a tilted (Bz)2 subunit. The S0 → S1/ S2 transitions of imidazole-(benzene)2 lie at similar energies as those of (Bz)2, confirming our assignment of the (Bz)2 S0 → S2 transition.

Appointing silver and bronze standards for noncovalent interactions: a comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches.

A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, respectively. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014)] and density functional theory [L. A. Burns, Á. Vázquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys. 134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance.

Vibrational frequency scaling factors for correlation consistent basis sets and the methods CC2 and MP2 and their spin-scaled SCS and SOS variants.

We present scaling factors for vibrational frequencies calculated within the harmonic approximation and the correlated wave-function methods coupled cluster singles and doubles model (CC2) and Møller-Plesset perturbation theory (MP2) with and without a spin-component scaling (SCS or spin-opposite scaling (SOS)). Frequency scaling factors and the remaining deviations from the reference data are evaluated for several non-augmented basis sets of the cc-pVXZ family of generally contracted correlation-consistent basis sets as well as for the segmented contracted TZVPP basis. We find that the SCS and SOS variants of CC2 and MP2 lead to a slightly better accuracy for the scaled vibrational frequencies. The determined frequency scaling factors can also be used for vibrational frequencies calculated for excited states through response theory with CC2 and the algebraic diagrammatic construction through second order and their spin-component scaled variants.

A Parametrized Coupled-Pair Functional for Molecular Interactions: PCPF-MI.

We present a parametrized coupled-pair functional, optimized to describe molecular interactions (PCPF-MI). The method has the same computational cost as singles and doubles configuration interaction, is size extensive, and yields energies that are stationary with respect to variations in all of its excitation coefficients. This last property facilitates the construction of density matrices and the evaluation of one- and two-electron properties. For the S22, HSG, S66, and A24 databases of van der Waals dimers, PCPF-MI computations yield interaction energies with mean unsigned errors of 0.326, 0.149, 0.214, and 0.044 kcal mol(-1), respectively, relative to benchmark computations. PCPF-MI interaction energies consistently improve upon those obtained from several other coupled-pair methods, including the averaged coupled-pair functional (ACPF), the coupled electron-pair approximation [CEPA(n), n = 0,1,3], and averaged quadratic coupled cluster (AQCC). Optimal parameters for spin-component-scaled (SCS) variants of each of these methods are also presented. SCS-CEPA(0), SCS-CEPA(1), SCS-ACPF, and SCS-PCPF-MI all perform similarly, with average errors for the four databases of roughly 0.1 kcal mol(-1). The PCPF-MI method, without additional SCS parametrization, has an average error of 0.192 kcal mol(-1) over the four databases and, when compared to the SCS-parametrized coupled-pair methods, has the added benefit that the energy is stationary with respect to variations in all its excitation coefficients.

Benchmark theoretical study of the π-π binding energy in the benzene dimer.

We establish a new estimate for the binding energy between two benzene molecules in the parallel-displaced (PD) conformation by systematically converging (i) the intra- and intermolecular geometry at the minimum, (ii) the expansion of the orbital basis set, and (iii) the level of electron correlation. The calculations were performed at the second-order Møller-Plesset perturbation (MP2) and the coupled cluster including singles, doubles, and a perturbative estimate of triples replacement [CCSD(T)] levels of electronic structure theory. At both levels of theory, by including results corrected for basis set superposition error (BSSE), we have estimated the complete basis set (CBS) limit by employing the family of Dunning's correlation-consistent polarized valence basis sets. The largest MP2 calculation was performed with the cc-pV6Z basis set (2772 basis functions), whereas the largest CCSD(T) calculation was with the cc-pV5Z basis set (1752 basis functions). The cluster geometries were optimized with basis sets up to quadruple-ζ quality, observing that both its intra- and intermolecular parts have practically converged with the triple-ζ quality sets. The use of converged geometries was found to play an important role for obtaining accurate estimates for the CBS limits. Our results demonstrate that the binding energies with the families of the plain (cc-pVnZ) and augmented (aug-cc-pVnZ) sets converge [within <0.01 kcal/mol for MP2 and <0.15 kcal/mol for CCSD(T)] to the same CBS limit. In addition, the average of the uncorrected and BSSE-corrected binding energies was found to converge to the same CBS limit much faster than either of the two constituents (uncorrected or BSSE-corrected binding energies). Due to the fact that the family of augmented basis sets (especially for the larger sets) causes serious linear dependency problems, the plain basis sets (for which no linear dependencies were found) are deemed as a more efficient and straightforward path for obtaining an accurate CBS limit. We considered extrapolations of the uncorrected (ΔE) and BSSE-corrected (ΔEcp) binding energies, their average value (ΔEave), as well as the average of the latter over the plain and augmented sets (ΔẼave) with the cardinal number of the basis set n. Our best estimate of the CCSD(T)/CBS limit for the π-π binding energy in the PD benzene dimer is De = -2.65 ± 0.02 kcal/mol. The best CCSD(T)/cc-pV5Z calculated value is -2.62 kcal/mol, just 0.03 kcal/mol away from the CBS limit. For comparison, the MP2/CBS limit estimate is -5.00 ± 0.01 kcal/mol, demonstrating a 90% overbinding with respect to CCSD(T). The spin-component-scaled (SCS) MP2 variant was found to closely reproduce the CCSD(T) results for each basis set, while scaled opposite spin (SOS) MP2 yielded results that are too low when compared to CCSD(T).

Noncovalent π⋅⋅⋅π interaction between graphene and aromatic molecule: Structure, energy, and nature

Noncovalent π⋅⋅⋅π interactions between graphene and aromatic molecules have been studied by using density functional theory with empirical dispersion correction (ωB97X-D) combined with zeroth-order symmetry adapted perturbation theory (SAPT0). Excellent agreement of the interaction energies computed by means of ωB97X-D and spin component scaled (SCS) SAPT0 methods, respectively, shows great promise for the two methods in the study of the adsorption of aromatic molecules on graphene. The other important finding in this study is that, according to SCS-SAPT0 analyses, π⋅⋅⋅π interactions between graphene and aromatic molecules are largely dependent on both dispersion and electrostatic type interactions. It is also noticed that π⋅⋅⋅π interactions become stronger and more dispersive (less electrostatic) upon substitution of the very electronegative fluorine atoms onto the aromatic molecules.

Separate Electronic Attenuation Allowing a Spin-Component-Scaled Second-Order Møller–Plesset Theory to Be Effective for Both Thermochemistry and Noncovalent Interactions

Spin-component-scaled (SCS) second-order Møller-Plesset perturbation theory (MP2) improves the treatment of thermochemistry and noncovalent interactions relative to MP2, although the optimal scaling coefficients are quite different for thermochemistry versus noncovalent interactions. This work reconciles these two different scaling regimes for SCS-MP2 by using two different length scales for electronic attenuation of the two spin components. The attenuation parameters and scaling coefficients are optimized in the aug-cc-pVTZ (aTZ) basis using the S66 database of intermolecular interactions and the W4-11 database of thermochemistry. Transferability tests are performed for atomization energies and barrier heights, as well as on further test sets for inter- and intramolecular interactions. SCS dual-attenuated MP2 in the aTZ basis, SCS-MP2(2terfc, aTZ), performs similarly to SCS-MP2/aTZ for thermochemistry while frequently outperforming MP2 at the complete basis set limit (CBS) for nonbonded interactions.