Density functional theory for large molecular systems

Nøyaktige simuleringer av kjemiske og biologiske prosesser på molekylært nivå har lenge vært uoppnålig for en rekke molekylære systemer, og har nå blitt mulig for mange av disse systemene gjennom ny metodeutvikling av Simen Reine, Trygve Helgaker og medarbeidere ved Universitetet i Oslo. Datasimuleringer er utbredt innen kjemi og relaterte felt som biologi, farmasi og medisin. Kvantekjemiske metoder er fundamentale for de mest nøyaktig simuleringsteknikkene, og er til stor hjelp ved bestemmelse og prediksjon av molekylære egenskaper, som for eksempel molekylers struktur, og gir i tillegg viktig og detaljert innsikt i kjemiske reaksjoner - både kvalitativt og kvantitativt. Anvendelsesområdet er nært knyttet til metodenes nøyaktighet, effektivitet og brukervennelighet. Utviklingen av nye og forbedrede metoder gjør oss i stand til å studere molekylære systemer som foreløpig har vært utenfor rekkevidde, og gir oss mer nøyaktig beskrivelse av de systemene vi allerede behandler idag. Som en konsekvens vil man kunne redusere bruken av kostbare og tidkrevende eksperimenter og samtidig hjelpe forskere verden over til bedre å forstå kjemiske mekanismer. De fleste kvantekjemiske beregninger som utføres idag benytter tetthetsfunksjonalteori (DFT), da denne metoden utgjør et godt kompromiss mellom nøyaktighet og beregningstid. Selv om DFT er meget nyttig, er dagens metoder begrenset til systemer bestående av noen få hundre atomer, og utelukker derfor en rekke systemer, for eksempel proteiner. I doktorgraden "Tetthetsfunksjonalteori for store molekylære systemer" har nye metoder innen DFT blitt utviklet med tanke på rutinemessige beregninger for store systemer. Beregninger for systemer med 1400 atomer er rapportert og metodene er i etterkant blitt benyttet for systemer med opp til 4000 atomer

Harmonic Infrared and Raman Spectra in Molecular Environments Using the Polarizable Embedding Model

We present a fully analytic approach to calculate infrared (IR) and Raman spectra of molecules embedded in complex molecular environments modeled using the fragment-based polarizable embedding (PE) model. We provide the theory for the calculation of analytic second-order geometric derivatives of molecular energies and first-order geometric derivatives of electric dipole moments and dipole–dipole polarizabilities within the PE model. The derivatives are implemented using a general open-ended response theory framework, thus allowing for an extension to higher-order derivatives. The embedding-potential parameters used to describe the environment in the PE model are derived through first-principles calculations, thus allowing a wide variety of systems to be modeled, including solvents, proteins, and other large and complex molecular environments. Here, we present proof-of-principle calculations of IR and Raman spectra of acetone in different solvents. This work is an important step toward calculating accurate vibrational spectra of molecules embedded in realistic environments

On Resolution-of-the-Identity Electron Repulsion Integral Approximations and Variational Stability

The definiteness of the Mulliken and Dirac electron repulsion integral (ERI) matrices is examined for different classes of resolution-of-the-identity (RI) ERI approximations with particular focus on local fitting techniques. For global RI, robust local RI, and nonrobust local RI we discuss the definiteness of the approximated ERI matrices as well as the resulting bounds of Hartree, exchange, and total energies. Lower bounds of Hartree and exchange energy contributions are crucial as their absence may lead to variational instabilities, causing severe convergence problems or even convergence to a spurious state in self-consistent-field optimizations. While the global RI approximation guarantees lower bounds of Hartree and exchange energies, local RI approximations are generally unbounded. The robust local RI approximation guarantees a lower bound of the exchange energy but not of the Hartree energy. The nonrobust local RI approximation guarantees a lower bound of the Hartree energy but not of the exchange energy. These issues are demonstrated by sample calculations on carbon dioxide and benzene using the pair atomic RI approximation. © 2017 American Chemical Societ

The Ring Planarity Problem of 2-Oxazoline Revisited Using Microwave Spectroscopy and Quantum Chemical Calculations

International audienceIn a previous infrared, Raman, and microwave spectroscopic work,1 it was claimed that 2-oxazoline has a planar ring equilibrium conformation, and the ring-puckering potential function V(z) = 22.2(z(4) + 1.31z(2)) cm(-1), where z is a dimensionless reduced coordinate, was derived. This function poorly reproduces the rotational constants of the lowest and most important puckering states. The microwave spectrum has been reinvestigated and largely extended to include more than 4600 transitions of the ground state and six excited states of the ring-puckering vibration allowing accurate centrifugal distortion constants to be obtained for the first time. A new potential function V(z) = 38.8(z(4) - 0.65z(2)) cm(-1) has been determined. This function yields much better agreement between calculated and observed rotational constants, especially for the lowest puckering states, than the previous function and predicts a nonplanar ring equilibrium conformation. The barrier to ring planarity is determined to be 49(8) J/mol. The ground-state energy level is 35 cm(-1) above the barrier maximum. Theory predicts that three of the five Watson centrifugal distortion constants, ΔJK, ΔK, and δK, should vary with the puckering state, whereas ΔJ and δJ should be unaffected. It was found that ΔJK and ΔK indeed behave in the expected manner, while deviations were seen for the three other centrifugal distortion constants. The ab initio methods HF, MP2, CCSD, CCSD(T), and CCSD(T)-F12 with large basis sets as well as several DFT methods were used in an attempt to reproduce the low experimental barrier to the planar ring. Only the MP2 method yielded a satisfactory prediction of the barrier. The CCSD and the CCSD(T) calculations predict a planar ring, whereas the energy differences between a planar and a nonplanar ring obtained in the CCSD(T)-F12 computations are so small that a definite conclusion cannot be drawn

Comparison of Three Efficient Approximate Exact-Exchange Algorithms: The Chain-of-Spheres Algorithm, Pair-Atomic Resolution-of-the-Identity Method, and Auxiliary Density Matrix Method

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree–Fock and hybrid Kohn–Sham calculations: the chain-of-spheres algorithm (COSX; Neese, F. Chem. Phys. 2008, 356, 98–109), the pair-atomic resolution-of-identity method (PARI-K; Merlot, P. J. Comput. Chem. 2013, 34, 1486–1496), and the auxiliary density matrix method (ADMM; Guidon, M. J. Chem. Theory Comput. 2010, 6, 2348–2364). Both the efficiency relative to that of a conventional linear-scaling algorithm and the accuracy of total, atomization, and orbital energies are compared for a subset containing 25 of the 200 molecules in the Rx200 set using double-, triple-, and quadruple-ζ basis sets. The accuracy of relative energies is further compared for small alkane conformers (ACONF test set) and Diels–Alder reactions (DARC test set). Overall, we find that the COSX method provides good accuracy for orbital energies as well as total and relative energies, and the method delivers a satisfactory speedup. The PARI-K and in particular ADMM algorithms require further development and optimization to fully exploit their indisputable potential

Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the integral equation formulation (IEF) of the polarizable continuum model (PCM), generally lead to working equations which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms