TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted

Benchmarks for Electronically Excited States with CASSCF Methods

The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of Schreiber, M.; et al. J. Chem. Phys. 2008, 128, 134110. Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility

CASSCF linear response calculations for large open-shell molecules

The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra

Improvements on the minimax algorithm for the laplace transformation of orbital energy denominators

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems

Circularly polarised fluorescence and phosphorescence calculations on organic molecules using the approximate coupled-cluster model CC2

We report the first calculations of rotational strengths for circularly polarised phosphorescence at the coupled cluster level. The rotational strengths for circular dichroism (CD), circularly polarised fluorescence (CPF) and circularly polarised phosphorescence (CPP) were calculated for β,γ-enones and ketones with conjugated double bonds using the CC2 model. To compute spin-forbidden CPP, spin–orbit coupling with perturbation theory is employed within a response theory framework (SOC-PT-CC2). For closed-shell molecules containing only light elements, a spin-free formalism is used to treat the singlet–triplet transitions. It is verified that the simplification obtained in the spin-free formulation from the Wigner–Eckart theorem for spin-forbidden oscillator strengths is also valid for the rotational strengths. Our implementation utilises the resolution of identity (RI) approximation for two-electron integrals which facilitates applications to larger molecules. In the current study, the rotational strength for spin-forbidden circularly-polarised phosphorescence was calculated for a chiral aromatic system, S-DMBDA, containing 44 atoms

An improved chain of spheres for exchange algorithm

In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve “chemical accuracy.” Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis–Rys–King and Head-Gordon–Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange matrix computation in a partially contracted basis when generally contracted shells occur. With our new RIJCOSX implementation, we facilitate accurate self-consistent field (SCF) binding energy calculations on a large supra-molecular complex composed of 320 atoms. The binding-energy errors with respect to the fully analytic results are well below 0.1 kcal/mol for the cc-pV(T/Q)Z basis sets and even smaller than for RIJ with fully analytic exchange. At the same time, our RIJCOSX SCF calculation even with the cc-pVQZ basis and the finest grid is 21 times faster than the fully analytic calculation

A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function

A perturbation theory‐based algorithm for the iterative orbital update in complete active space self‐consistent‐field (CASSCF) calculations is presented. Following Angeli et al. (J. Chem. Phys. 2002, 117, 10525), the first‐order contribution of singly excited configurations to the CASSCF wave function is evaluated using the Dyall Hamiltonian for the determination of a zeroth‐order Hamiltonian. These authors employ an iterative diagonalization of the first‐order density matrix including the first‐order correction arising from single excitations, whereas the present approach uses the single‐excitation amplitudes directly for the construction of the exponential of an anti‐Hermitian matrix resulting in a unitary matrix which can be used for the orbital update. At convergence, the single‐excitation amplitudes vanish as a consequence of the generalized Brillouin's theorem. It is shown that this approach in combination with direct inversion of the iterative subspace (DIIS) leads to very rapid convergence of the CASSCF iteration procedure

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted